Medicines Optimisation Training and
Assessment Schemes
Medicines Calculations
Student Workbook
Website: https://www.hee.nhs.uk/hee-your-area/yorkshirehumber/education-training/school-medicines-optimisation
Contact: Administration Team
School of Medicines Optimisation, Health Education England,
working across Yorkshire and the Humber
Willow Terrace Road, University of Leeds, Leeds, LS2 9JL
T: 0113 887 1688
E: [email protected]
Document Reference Number: PDU/MM/010ST
Review Date: Oct 2018
Version: 1.5 Oct 2016
Supersedes: all other versions
School of Medicines Optimisation, Health Education England, working across Yorkshire and the Humber. 2016
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Table of Contents
Table of Contents.................................................................................................................. 1
Introduction to the Module ..................................................................................................... 2
Work-Based Learning Programme ........................................................................................ 4
Aims and Objectives ............................................................................................................. 5
Section 1 – Formulae ............................................................................................................ 6
1.1 Basic Calculations ............................................................................................ 6
1.1.1 Expression of Units .................................................................................... 6
1.1.2 Expressions of Concentration .................................................................... 8
1.1.3 Conversion of Units .................................................................................... 9
1.1.4 Percentages ............................................................................................... 9
1.1.5 Ratio Strengths ........................................................................................ 10
1.1.6 Displacement Volume .............................................................................. 10
1.1.7 Decimals .................................................................................................. 11
1.1.8 Rounding Decimal Numbers .................................................................... 13
1.1.9 Good Practice Guidelines......................................................................... 14
1.2 Calculating Doses for Children ....................................................................... 15
1.3 Formulae Calculations .................................................................................... 16
1.3.1 Formulae .................................................................................................. 16
1.3.2 ‘Long-hand’ proportion method ................................................................ 16
Section 2 –Practice Questions ............................................................................................ 18
2.1 Level 1 Conversion of Units ............................................................................ 18
2.2 Level 1 and 2 Body Surface Area Calculations ............................................... 20
2.3 Level 1 Calculating Doses and Quantities ...................................................... 21
2.4 Level 1 Drug Strengths and Ratio Strengths .................................................. 23
2.5 Level 2 Drug Strengths and Expressions of Concentrations ........................... 24
2.6 Moles and Millimoles ...................................................................................... 25
2.6.1 Level 1 What is a Mole? ........................................................................... 25
2.6.2 Level 2 Atomic Mass and Mass Number .................................................. 25
2.6.3 Level 2 Moles and Millimoles Calculations ............................................... 27
Section 3 –Paediatric Dose Calculations ............................................................................. 29
3.1 Level 1 and 2 Paediatric Calculations ............................................................. 29
3.2 Level 2 Paediatric Intensive Care Unit (PICU) ................................................ 33
Section 4 –Intravenous Clinical Calculations and Activities ................................................. 34
4.1 Level 2 Paediatric Calculations ....................................................................... 34
4.1.1 Displacement Volume .............................................................................. 35
4.2 Level 2 Adult Calculations .............................................................................. 35
4.3 Level 2 Child Neonatal Unit (NNU) ................................................................. 37
4.4 Level 2 Children’s Paediatric Intensive Care Unit (PICU) ............................... 41
Section 5 Miscellaneous Calculations ................................................................................. 46
5.1 Level 1 Reducing and Loading Doses ............................................................ 46
5.2 Level 1 Reading Preparation Labels and Strengths........................................ 47
5.3 Level 2 Infusions ............................................................................................. 49
5.4 Level 2 Renal Impairment/The Elderly ............................................................ 51
Appendix 1 Reference Sources and Further Reading ......................................................... 56
Appendix 2 Acknowledgements .......................................................................................... 57
Appendix 3 Summary Of Achievements .............................................................................. 58
Appendix 4 Confirmation of Completion of Module .............................................................. 59
Appendix 5 Continuing Professional Development Evaluation (Reflection on Learning) ...... 60
Appendix 6 NHS Knowledge and Skills Framework ............................................................ 61
School of Medicines Optimisation, Health Education England, working across Yorkshire and the Humber. 2016
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Introduction to the Module
This module has been produced by the School of Medicines Optimisation to assist in
the training and development of staff working in Medicines optimisation roles.
The information contained in this booklet provides a variety of training methods,
which may be adapted to address the content and depth of training required in
each organisation. This workbook should be read in conjunction with the candidates
own Trusts Medicine Code if/where available, policies and procedures.
This module incorporates formulae and examples of calculations that you may come
across and be expected to carry out in your role.
You must always be aware of local SOPs and checking procedures for all
calculations made in the workplace.
Timescales
This is your learning programme to develop your knowledge and skills; therefore,
there is no fixed timescale for completion. For guidance purposes this module may
take up to five hours or more to complete, either over several days or several weeks.
Portfolio
You may wish to include examples from your workplace, to highlight specialist areas
in your role. We recommend that this module forms part of your portfolio of work and
is kept in a safe place for future reference. Any patient information must be
anonymised.
Levels of Information and Assessment
This module covers two levels of information and calculations practice content (see
below). You should discuss with your tutor which level is appropriate for you and fill
in the summary of achievements form (appendix 3) on completion of the module.
Assessments are covered in sections 2-5 and a tutors manual is available (please
contact the school for more information).
Level 1 tests your basic application of skill and understanding in:
Preparation and administration of oral and injectable medicines
Conversion of units
Measurement of medicines, drug strengths and volumes
Decimal place errors
Moles and millimoles in solution explanation
Paediatric calculations
Using sources of information
Level 2 tests your skills in more complex calculations:
Preparation and administration of oral and injectable medicines.
Calculation of infusion rates
Calculations based on body weights
Moles and millimoles formula and calculations
Complex paediatric and neonatal calculations
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Renal function calculations and doses for the elderly
Using sources of information
E-Learning
An e-learning program ‘Medicines Management Calculating Drug Doses' has been
developed by Health Education England working across Yorkshire and the Humber.
The topics have been designed to be used by any healthcare professional requiring
support in handling medicines safely, understanding drug doses and quantities and
gaining confidence in performing a variety of medicines calculations.
The e-learning module focuses on:
Identifying errors that regularly occur
Explaining the hazards involved in calculations
Methods to help prevent and reduce errors
Allow up to one hour to complete the e-learning module and assessments-a
certificate of completion is available after the assessments.
To access Calculating Drug Doses please visit our website.
Medicines Management
A wide range of eLearning courses are available through Health Education England
in Yorkshire and the Humber. The latest version of the eLearning Catalogue for
Health Education England within Yorkshire and the Humber contains information on
all eLearning courses.
https://hee.nhs.uk/hee-your-area/yorkshire-humber/education-training/elearning
To compliment this learning, we have also produced several Medicines
Management E-learning modules.
These are a series of modules covering: medicines management essentials,
prescribing and supply, administration of medicines and safe handling of medicines.
Suitable for all staff, each module focuses on a different topic, looking at how we
keep patients safe and introduces the basic concepts of delivering an effective and
safe medicines service to all staff new to medicines management.
Documentation and Certification
Please ask your mentor/manager to complete appendix 3 Summary of Achievements
(which has been adapted to allow for the variety and levels of training undertaken)
and appendix 4 Confirmation of Completion of Module and email to
[email protected] to receive your certificate.
Record Keeping
It is the responsibility of each organisation and the candidate to keep appropriate
and up to date records, keep certificates safe, and manage re-accreditation
timescales.
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Work-Based Learning Programme
This module is one of the core modules within the Medicines Optimisation WorkBased Learning Programmes. NB: Other professions may find this a useful resource
to support learning. You can find out more about this programme at our website
All candidates completing this module as part of a HEE Yorkshire and the Humber
training and Assessment Scheme will be required to complete a learning agreement
and application form (skills assessment pre-and post training to be added to
portfolio).
Candidates must have a nominated learning mentor* to support them through this
module.
The information contained in this booklet provides a variety of training methods,
which may be adapted to address the content and depth of training required in each
organisation. Not all sections will be applicable to everyone, so please select the
most appropriate sections to complete with your mentor.
As part of the training and assessment scheme, certificates of completion will be
issued by the School upon receiving the appropriate documentation. A regional
database will be maintained and updated for quality assurance and record keeping
purposes only.
When completing this module you should:
 Build a portfolio of evidence of learning and training
 Be familiar with and have a working knowledge of procedures and policies relevant
to this module.
 Demonstrate knowledge and understanding through completion of examples and
extra calculations exercises where needed
 Have regular reviews with mentor
 Undertake the assessments according to the levels and areas chosen
Assessments
Sections 2 to 5 contain two levels of assessment in this workbook and your tutor will
assess you in the appropriate areas related to your work.
You will need to decide which sections are relevant to your area of expertise and
role, however you should have achieved 100% in the relevant areas/sections
chosen, to complete the workbook.
It is recognised that you may need some support from your mentor, however to pass
the unit, all questions should be answered by you.
* The mentor will be a person who has been approved to mentor candidates completing this training
scheme/module
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Aims and Objectives
Aims
To be able to:
 develop the skills necessary to perform medicines calculations accurately and
consistently
 to identify methods to help prevent and reduce errors
 to identify errors that regularly occur
Objectives
On completion of the expected learning outcomes you will be able to:
 Understand how medicines and units of measure are expressed
 Understand decimal place errors
 Develop skills in complex calculations
 Competently perform clinical calculations in the workplace
 Accurately convert units
 Perform basic dosage calculations
 Calculate drug strengths/concentrations/volumes
 Calculate paediatric doses
 Calculate body surface area
 Develop skills in researching information and using resources
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Section 1 – Formulae
1.1 Basic Calculations
1.1.1 Expression of Units
Units commonly used within pharmaceutical language are: microgram, milligram,
gram & kilogram
There are:
1000 micrograms in 1 mg
1000 mg in 1 gram
1000 grams in 1kilogram
However, there are others which may be used:
Name
Abbreviation
Equivalent
1 kilogram
kg
1000g
1 gram
g
1000mg
1 milligram
mg
1000 (microgram) μg
1 microgram
μg
1000ηg
1 nanogram
ηg
1000pg
1 picogram
pg
1/1000ng
Volume
Units commonly used are millilitre and litre
1 litre (L)
1 millilitre (mL)
= 1000 millilitre
= 1000 microlitre
Drops
There are approximately 20 drops per mL of water.
N.B. This will be different for more viscous liquids.
You may see doses expressed in drops or drip rates calculated in drops per minute.
Oral drops examples from BNF69
Citalopram 40 mg/mL Oral Drops, 15 mL bottle
Example of dose ranges: 8 mg (4 drops), 16 mg (8 drops), 32 mg (16 drops)
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Alfacalcidol 2 micrograms/mL Oral Drops, 10 mL bottle
(1 drop contains approx. 100 nanograms alfacalcidol)
Example of doses expressed as nanograms/kg and 250–500 nanograms once daily
depending on condition and age
Drip rates and delivery systems
Gravity infusion or administration sets deliver a quantity of fluid over a number of
minutes. This is called the drip rate, and these rates will vary depending on the
manufacturer, product and set used. An example may be an administration set which
provides 20 drops per mL.
The infusion rate or flow rate is the drops per minute required for the dose. So you
may see instructions for example to set drip rate at 40 drops per minute.
Flow rate (drops/min) =
volume fluid (mL)
total infusion time (in minutes)
x (drops/mL of administration set)
Example
Patient A requires: 1000 mL Sodium chloride 0.9% over 8 hours (manufacturer
advises calibration of administration set is 20 drops/mL). Don’t forget to convert
hours to minutes (8 hours = 480 minutes).
1000mL
480
x 20 = 41.66
Flow rate = 42 drops/min
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1.1.2 Expressions of Concentration
Unit
Expression
Example
% weight in weight
% w/w
1% w/w = 1g in 100g
% volume in volume
% v/v
1% v/v = 1mL in 100mL
% weight in volume
% w/v
1% w/v = 1g in 100mL
% volume in weight
% v/w
1% v/w = 1mL per 100g
Molar
M
1molar = 1mole in 1 litre
1 part per 100 (solid in liquid)
1 in 100
1 in 100 = 1g in 100mL
1 part per 100 (solid in solid)
1 in 100
1 in 100 = 1g in 100g
1 part per 100 (liquid in liquid)
1 in 100
1 in 100 = 1mL in 100mL
1 part to 4 parts
1:4
5 parts in total
1 part in 4 parts
1 in 4
4 parts in total
Weight in weight
When there is a mixture of two solids the percentage is expressed as weight in
weight (w/w)
E.g. Hydrocortisone 1% w/w cream
This means there is 1g of hydrocortisone in 100g of cream.
Weight in volume
When a solid is dissolved or suspended in a liquid the percentage is expressed as
weight in volume (w/v)
E.g. Dexamethasone 0.1% eye drops
This means there is 100mg of dexamethasone in 100 mL of liquid.
E.g. Ceftriaxone infusion is prepared as 1000mg (1g) in 20mL w/v.
A dose of 600mg would be calculated as:
1000mg in 20mL
100mg in 2mL
Therefore: 600mg in 12mL
Volume in volume
When a solution is diluted in another solution, the percentage is expressed as
volume in volume (v/v)
E.g. 50% v/v
This means 50 mL of an ingredient solution is present in 100 mL of solution.
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1.1.3 Conversion of Units
To convert from smaller units to larger ones, we need to divide by 1000, or to convert
from a larger unit to a smaller unit, we need to multiply by 1000
There are practice questions with conversion of units in section 2.1
1.1.4 Percentages
Percent means ‘per hundred’.
For example:
15% means 15 parts per 100.
20 % means 20 parts per 100.
To calculate a percentage, put the figure above 100. e.g. 15% becomes
e.g.
15
100
15% of 300 is:
15
100
x 300
15
1ØØ
x 3ØØ
15 x 3 = 45
To calculate a percentage proportion (e.g. what percentage is 50g out of 250g) use
the following formula:
e.g.
50
250
5Ø
25Ø
5
25
x 100
x 100
x 100
0.2 x 100 = 20%
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Test yourself
a) How much is 28% of 250g?
b) What percentage is 160g of 400g?
c) How much is 62% of 450g?
d) What percentage is 125mg of 25g?
1.1.5 Ratio Strengths
Ratio strengths are also known as 1 in… Some well-known examples are:
Adrenaline/Epinephrine Injection 1 in 1000 or 1 in 10 000.
Bupivacaine and Adrenaline Injection BP 0.25% w/v, 1 in 200 000
For example 1 in 10 000 = 1g in 10 000mL
1000mg in 10 000mL
100mg in 1000mL
10mg in 100mL
1mg in 10mL
0.1mg in 1mL = 100 micrograms in 1 mL
There are practice questions with ratio strengths in section 2.4
1.1.6 Displacement Volume
‘What is a displacement volume?’
A ‘Displacement volume’ is the volume occupied by the powder when a suitable
diluent is added during reconstitution. This is particularly important to take into
account, e.g.: for children when the dose needed is only a proportion of the vial
content. If we look at amoxicillin injection as an example:
a) The displacement volume for amoxicillin 250mg is 0.2mL. Therefore if 4.8mL of
diluent is added to a 250mg vial, the resulting solution is amoxicillin 250mg in
5mL
There are more practice questions with displacement volumes in section 4.1.1
NB: the displacement volume is different for each drug, for each strength of drug and
for different brands/manufacturers formulae. Practice finding information on drugs
commonly used in your workplace.
Examples of where to find this information are:
Manufacturers information leaflets or Summary of Product Characteristics (SPC)
at www.medicines.org.uk
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1.1.7 Decimals
When decimal place errors occur in medicines calculations it can cause serious
harm or death to patients, especially neonates who usually receive fractions of the
dose and volume of those given to adults.
The decimal system is based on counting values in units of ten before and after the
decimal point, for example:
one hundred units
ten units
one unit
 fractions of units
Numbers are written according to their values (these are called place values) and
this is why tenfold and one hundred fold errors are possible when decimal places are
inserted in the wrong place.
Understanding Decimal Place Errors
1000
100
2
10
1
Decimal
point
tenths
2
2

0
2
0

1
hundredths
thousandths
0

1
5
1

5
0
5

0
Example 1 How does 22 micrograms become 220 micrograms in a calculation?
This is a tenfold error (ten times the amount of intended medication was
administered) which was fatal.
In other words, ten units of measure became one hundred units of measure when
the decimal point went in the wrong place. The decimal point was one place out.
one hundred units
220.0
ten units
22.0
What we know:
 The strength of Digoxin paediatric injection is 100 micrograms/mL (ref BNF
March 2015)
 The prescriber was unfamiliar with prescribing this drug intravenously
 The dose required for this neonatal patient was 10 micrograms/kg
 The patient had a low birth weight (i.e. under 2500g) at 2200g
Ref: BBC News Friday, 20 May, 2005 http://news.bbc.co.uk/1/hi/england/leicestershire/4566427.stm
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So the calculation is based on:
Dose
10 micrograms/kg
Patient weight
2200 grams
Preparation available 100 micrograms/mL
Conversions and multiplications:
The weight is in gram and dose is in kg. We need to work in the same unitsconversion needed from lower units (grams) to higher units (kg), we do this by
dividing by 1000.
2200 ÷ 1000 = 2.2 = baby’s weight is 2.2 kg
To get the administration dose we multiply the baby’s weight by the prescribed dose
2.2 kg x 10 micrograms = 22 micrograms
Example 2. How does an intended dose of 150 micrograms become 15 mg?
Building a Safer NHS for Patients: Improving Medication Safety (Author Dr Jim Smith Published
2004 DH) http://webarchive.nationalarchives.gov.uk/
Ref:
This is a one hundred fold error (one hundred times the amount of intended
medication was administered)
In other words, a fraction of a decimal unit of measure became ten units of
measure making a one hundred fold error which was fatal. The decimal point was
two places out
ten units
one unit
15.0
1.50
fractions of units
0.150
Converting the units from mg to micrograms may have added to the confusionremember:
You need to work in the same units, so you have to multiply by 1000 to
convert higher units (mg) to lower units (micrograms).
In this case 0.15 mg x 1000 = 150 micrograms
The doses for morphine in paediatrics are in micrograms/kg, and a premature baby
would have been weighed in grams, so another conversion may have been
necessary - grams to kg
Common sense should also be used – Think! There is a big difference between
150 micrograms and 15 mg-one hundred times the strength.
What about the quantity?
Be familiar with the drug you are handling- for example in paediatrics, morphine
doses are in micrograms/kg and in adult doses they are in mg/kg
Stop, ask yourself:
Is it a normal dose for this drug and/or this patient?
Does the volume seem to be the right amount?
How many ampoules or vials are your using?
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1.1.8 Rounding Decimal Numbers
The examples and assessments in this training may sometimes require you to round
up or down, so here’s a brief reminder.
When you complete a calculation and you have a lot of numbers on the right of the
decimal point, think how will you write, measure and administer the correct dose to
the patient?
Rounding numbers means reducing the digits in a number, but maintaining the value
of that number.
Decide on what number you need to stop at or keep
If the numbers to the right of the decimal point are 0 1 2 3 4 the number next to it
stays the same
If the numbers to the right of the decimal point are 5 6 7 8 9 increase the number
next to it by 1
Measuring What Is Workable
In these examples we are interested in the numbers on the right of the decimal point
which are the fractions of a decimal number (highlighted in red)
12.343 mL
1.379 mg
9.333 mL
2.3246 mg
12.379 mL  12.4 mL or 12.38 mL = rounding up to 1 or 2 decimal places
1.349 mL  1.4 mL or 1.35 mL = rounding up
9.333 mL  9.3 mL or 9.33 mL = rounding down
2.3246 mg  2.325 mg = rounding up to 3 decimal places
Sometimes we might not be able to measure or give a dose that is not a whole
number.
e.g. 249.9 mg 250 mg = rounding up to a whole number
If you need more practice with decimal numbers visit BBC Skillswise at
www.bbc.co.uk/skillswise
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1.1.9 Good Practice Guidelines
Micrograms should always be written in full
(Warning: may see mcg or μg - this is not an approved format and is potentially
harmful!)
Nanograms should always be written in full
(Warning: may see ng or ηg) - this is not an approved format and is potentially
harmful!)
Units should always be written in full
(Warning: may see the abbreviation I.U.(for international units) or U – this could be
mistaken for a zero and is potentially harmful!)
Unnecessary decimal places should be avoided i.e. 0.5g should be written as 500mg
Trailing decimals should be avoided i.e. 25 mg not 25.0 mg
See British National Formulary (BNF) for more information on guidance on
prescribing and prescription writing.
BNF available online at http://www.evidence.nhs.uk/formulary/bnf/current
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1.2 Calculating Doses for Children
N.B. Your organisation may have an agreed primary reference source e.g. BNF
under chapter ‘Prescribing for Children’, BNF for Children or Medicines for
Children. Check with your mentor/senior member of staff.
Doses for children may be calculated using a formula based on:
Body Surface Area (BSA)
Or
Weight basis e.g. mg/kg
Or
Proportion of Adult dose
a) To work out the dose for BSA you multiply:
Number of mg (or g) x number per m²
Example: the dose of drug is 1.5g/m² and the patient’s BSA is 0.8m²
the dose for that child is:
1.5 x 0.8 = 1.2g
b) To work out the doses based on weight as mg/kg you multiply:
Number of mg x number of kg
Example: the dose of a drug is 5mg/kg and the child weighs 20kg
the dose for that child is
5 x 20 = 100mg
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1.3 Formulae Calculations
There are two methods commonly used:
1. Formulae
2. Long hand (the proportion method)
The best and safest method to use is the one you understand!
1.3.1 Formulae
dose required
strength available
x
volume
=
volume required
=
volume required
Or more often said as:
what you want
what you've got
x
volume
e.g. We want to give a child 350mg Flucloxacillin IV. We have to make a
concentration of 500mg in 10mL. How is this calculated?
35Ø
50Ø
35
50
35
5Ø
35
5
x 10mL = ?mL
x 10mL = ?mL
x 1ØmL = ?mL
x 1mL = ?mL
7 x 1mL = 7mL
Therefore, you would give the child 7mL of reconstituted solution.
1.3.2 ‘Long-hand’ proportion method
It is often easier to work out how many milligrams are contained in 1mL.
If we look at an example where there are 500mg drug in 10mL:
Therefore:
Therefore:
Therefore:
500mg in 10mL
100mg in 2mL
50mg in 1mL
350mg in 7mL
Or if you want 35mg of a drug, 1mg is contained in ‘x’ amount, therefore 35mg will be
contained in 35 times ‘x’ amount.
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Example 1
You have a 100mg/5mL oral solution, you need to give a dose of 25mg, how many
mLs do you need?
Proportion method
Formula method
What you do to one side of the Dose you want divided by
equation is done to the other
Strength of preparation you have
Multiplied by volume it’s in
= the volume to be administered
100 mg in 5ml
Dose wanted = 25mg
10 mg in 0.5ml
Strength you have = 100mg
5 mg in 0.25ml
Volume it’s in = 5ml
25 mg is in 1.25ml
𝟐𝟓
×𝟓 = 1.25 mL (volume to be administered)
5x5=25 mg 5 x 0.25=1.25 mL
𝟏𝟎𝟎
Example 2
A bottle of haloperidol oral solution is labelled 5mg/5mL and has been sent back to
pharmacy as the staff require a 1mg in 1mL solution. Dose required for the patient is
3mg twice daily.
How do you work this out? You need to give a dose of 3mg, the product is labelled
5mg/5mL, how many ml do you require?
Proportion method
Formula method
What you do to one side of the Dose you want divided by
equation is done to the other
Strength of preparation you have
Multiplied by volume it’s in
= volume to be administered
5 mg in 5ml
Dose wanted = 3 mg
0.5mg in 0.5mL
Strength you have = 5 mg
1mg in 1mL
Volume it’s in = 5 mL
3 mg in 3 mL
𝟑
𝟓
×𝟓 = 3 mL (volume to be administered)
Remember 1 mg/1 mL is the same as 5 mg/5 mL
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Section 2 –Practice Questions
2.1 Level 1 Conversion of Units
1. Express the following in grams or parts of a gram
a) 125 mg
=
b) 1200 mg
=
c) 3 mg
=
d) 14 mg
=
e) 250 mg
=
2. Express the following as milligrams
a) 3.5 grams
=
b) 0.9 grams
=
c) 0.01 grams
=
d) 10.5 grams
=
e) 0.002 grams
=
3. Express the following as parts of a milligram
a) 750 micrograms
=
b) 30 micrograms
=
c) 1.5 micrograms
=
d) 55 micrograms
=
e) 125 micrograms
=
4. Express the following in micrograms
a) 0.044 milligrams
=
b) 0.75 milligrams
=
c) 0.1 milligrams
=
d) 0.05 milligrams
=
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e) 0.001 milligram
=
5. How many mg in
a) 1 gram
=
b) 0.8 grams
=
c) 0.001 grams
=
d) 0.05 grams
=
6. How many micrograms in
a) 5 milligrams
=
b) 0.5 milligrams
=
c) 0.001 milligrams
=
d) 0.075 milligrams
=
7. Tablets of 125 mg. How many are needed if prescribed
a) 0.125 grams
=
b) 0.375 grams
=
8. Tablets of 5 mg. How many are needed if prescribed
a) 0.02 grams
=
b) 0.1 grams
=
9. Tablets of 250 micrograms. How many are needed if prescribed
a) 1 mg
=
b) 0.25 milligram
=
10. Oral solution 200 micrograms/5 mL. How many mLs are needed if prescribed
a) 0.2 milligrams
=
b) 1 milligram
=
c) 0.04 milligrams
=
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11. 0.05 milligrams in 1 mL. How many mLs are needed if prescribed
a) 25 micrograms
=
b) 0.5 milligrams
=
c) 100 micrograms
=
d) 0.2 milligrams
=
2.2 Level 1 and 2 Body Surface Area Calculations
Conversion Information
You need to work in metric units, so conversion of pounds to kg and inches to cm will
often be necessary.
The formula for/as a guide to conversion from pounds (lb) to kilograms (kg) is:
1 pound
1 inch
= 0.45 kilogram
= 2.54 cm (see BNF for guidance on conversion)
Methods for Calculating Body Surface Areas
To calculate the surface area of a patient you can use nomogram graphs (separate
ones for adults and children) or body surface area (BSA) calculations based on
formulas (e.g. the Mosteller formula is often used as below).
The Mosteller formula: BSA (m²) = (Height (cm) x Weight (kg) / 3600)½
e.g. BSA = square root of (height (cm) x weight (kg) / 3600)
Examples of these may be found in many reference sources e.g. Martindale, BNF
and eBNF or Patient UK
Calculate the surface area of the following patients and state your reference source
and/or the formula used:
1. Patient’s Weight: 10kg
Height:100cm
Surface Area =
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2. Patient’s Weight: 140lb
Height: 5’ 6”
Surface Area =
3. Patient’s Weight: 112lb
Height: 4’ 8”
Surface Area =
4. Patient’s Weight: 63kg
Height: 160cm
Surface Area =
5. Use an adult nomogram to calculate BSA of a patient:
Patient’s Weight: 72kg
Height: 172cm
Surface Area =
6. Sometimes the dose required is expressed on a body weight basis or in terms of
body surface area.
Dose = 1.5mg/m² Surface Area = 1.55m²
What is the dose required =
2.3 Level 1 Calculating Doses and Quantities
1.
Syrup 60mg in 5mL, prescribed 15mg
How many mL would you give?
2.
Syrup 200mg in 5mL, prescribed 550mg
How many mL would you give?
3.
You have an aminophylline injection 250mg in 10mL
Amount required = 350mg
Dose =
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4.
You have a digoxin injection 500 micrograms/2mL
Amount required = 0.75mg
5.
Dose =
You have morphine sulphate elixir 10mg/mL
Amount required = 15mg
Dose =
6. A patient weighing 70kg requires a one off dose of enoxaparin 1mg/kg.
What dose should be prescribed?
7.
You have disopyramide injection 10 mg/mL, 5mL ampoules
Amount required = 300mg
How many ampoules?
8. A patient weighing 63kg requires a one off dose of immunoglobulin G 400mg/kg.
What dose should be prescribed?
9.
Dose = 3 micrograms/kg
patient weight = 73kg
Dose required =
10. A patient is prescribed Alimemazine 20mg via PEG. Alimemazine is available as
a syrup as 30mg in 5mL.
What volume would you give?
11. A patient weighing 72kg requires a one off dose of gentamicin 5mg/kg.
What dose should be prescribed?
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2.4 Level 1 Drug Strengths and Ratio Strengths
1. You need to give a 50mg dose of oral morphine sulphate to a patient. You have
a bottle of morphine sulphate oral solution at a concentration of 2mg/mL. How
much do you need for your dose?
2. You have a 10mL ampoule of adrenaline/epinephrine 1 in 10, 000. How much
adrenaline/epinephrine (in milligrams) does the ampoule contain?
(Refer back to section 1.1.4 Ratio Strengths for Q 2 and 3 if required)
3. You have a 1mL ampoule of adrenaline/epinephrine 1 in 10, 000. How much
adrenaline/epinephrine (in milligrams) does the ampoule contain?
4. A patient was taking Phenytoin at a dose of 200mg in capsule form but has had a
gastrostomy and now requires syrup. A 100mg capsule is therapeutically
equivalent to 90mg of syrup. Phenytoin syrup is 30mg in 5mL.
How much Syrup should be given?
1. You have an oral solution which is available as 50 micrograms/mL
(for the purposes working out this calculation, assume there are no issues with
formulations and equivalent doses)
How many mLs of the syrup are required for the following doses?
62.5 micrograms
2. A patient is prescribed
4micrograms/mL.
125 micrograms
400nanograms
250 micrograms
of
desmopressin
injection
How many mL of injection need to be given to the patient?
3. A patient is prescribed 500micrograms of dexamethasone syrup 2mg/5mL.
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How many mL of the syrup does the patient need to take?
4. A patient is prescribed 1mg of phytomenadione injection 10mg/mL.
How many mL of injection need to be given to the patient?
5. A patient is prescribed 270mg of phenytoin syrup 30mg/5mL.
How many mL of the syrup does the patient need to take?
6. A patient is prescribed 12,000units of tinzaparin injection. Tinzaparin is available
as a 14,000units in 0.7mL pre-filled syringe.
How many mL of injection need to be given to the patient?
2.5 Level 2 Drug Strengths and Expressions of Concentrations
1. How much sodium chloride (in grams) is there in a 500mL infusion of sodium
chloride 1.8% w/v?
2. How many g of glucose are contained in 30mL of a 10% w/v glucose solution?
3. You need to add 2g of potassium chloride to a litre of sodium chloride 0.9% w/v.
You have 10mL ampoules of 30% w/v potassium chloride. What volume of
potassium chloride do you draw up?
4. What is the concentration (in mg/mL) of an 8.4% sodium bicarbonate infusion?
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2.6 Moles and Millimoles
2.6.1 Level 1 What is a Mole?
A mole is simply the name given to a certain number. Let’s look at sodium chloride
as an example.
Each atom has an atomic weight e.g. sodium 23, and chlorine 35.4
Atoms combine to from molecules e.g. sodium combines with chlorine to form
sodium chloride which has a molecular weight of 58.4 (23 + 35.4)
Atomic and molecular weights of a drug can be used to measure the amount of a
drug. A mole is that weight (in this example molecular weight) expressed in grams.
E.g. the molecular weight of sodium chloride is 58.4; therefore 1 mole of sodium
chloride weighs 58.4g
In solution as 1 mole per litre (called molar solution) = 58.4 grams per mole
1 mole (mol) = 1000 millimole (mmol)
How do we work out how many millimoles there are in this common solution?
Sodium chloride Intravenous Solution 0.9%
= 9 grams of sodium chloride in 1 litre
= molecular weight of sodium chloride is 58.4
number of grams
molecular weight in grams
9
58.4
x 1000 (to give the answer in millimoles)
= 0.154 moles x 1000 = 154 millimoles/litre
2.6.2 Level 2 Atomic Mass and Mass Number
Each element on the table has two numbers beside it, an atomic number and a mass
number.
Mass Number
Mass Number
23
35.5
Na
Cl
11
Atomic Number
17
Atomic Number
Relative Atomic Mass, Ar
 The relative atomic mass, Ar, is nothing more than the mass number of the
element.
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
On the periodic table, the elements all have two numbers as shown above in
the sodium example. The smaller one is the atomic number (how many
protons it has). The bigger one is the mass number (how many protons and
neutrons it has).
Relative Formula Mass, Mr
If you have a compound like NaCl then it has a relative formula mass, M r, which is
just all the relative atomic masses added together.
For NaCl the Relative Formula Mass, Mr, would be:
NaCl
Mr:
23
+
35.5
= 58.5
For MgCl2 the Relative Formula Mass, Mr, would be:
MgCl2
Mr:
24
+
35.5 x 2
= 95
A mole of atoms or molecules of any substance will have a mass in grams equal to
the Relative Formula Mass (Ar or Mr) for that substance.
Carbon has an Ar of 12
Iron has an Ar of 56
Sodium Chloride has an Mr of 58.5
Carbon dioxide, CO, has an Mr of 44
So one mole of carbon weighs exactly 12g
So one mole of iron weighs exactly 56g
So one mole of NaCl weighs 58.5g
So one mole of CO2 weighs exactly 44g
This means that 12g of carbon, or 56g of iron, or 28g of N2, or 44g of CO2 all contain
the same number of atoms, namely ONE MOLE or 6 x 1023 atoms or molecules.
As an example:
One mole of Potassium Sulphate K2 SO4 has a Mr of 174 [i.e. (2x39) + 32 + (4x16)]
The formula for finding the Number of Moles in a given mass:
Number of Moles =
Mass in g (of element or compound)
Mr (of element or compound)
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Example:
How many moles are there in 42g of carbon?
Answer:
No. of moles
=
Mass (g)
Mr
=
42
12
= 3.5moles
So, to find out how many millimoles of a substance are contained in a given
volume:


Work out how many grams of a substance are in the given volume
Use the above formula
Multiply the answer (in moles) by 1000 to give the number of millimoles
2.6.3 Level 2 Moles and Millimoles Calculations (optional section)
1. Approximately how many millimoles of sodium chloride are there in a 10mL
ampoule of sodium chloride 30% injection?
2. Approximately how many mmol per litre of sodium chloride are there in an
infusion containing 1,800 mg of sodium chloride per litre?
3. How many millimoles of sodium chloride & potassium chloride are there in a
500mL infusion containing 9 mg / sodium chloride and 3mg / mL potassium
chloride (Remember: molecular masses: sodium 23, potassium 39, chloride 35.5)
4. Approximately how many millimoles of sodium bicarbonate are there in a litre
infusion containing 25.2g / litre sodium bicarbonate? (molecular mass: sodium
bicarbonate 84)
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5. You need to draw up 35 mmol of potassium chloride and to add this to a litre
infusion. You have an ampoule containing 2g of potassium chloride in 10 mL.
How much do you need to draw up?
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Section 3 –Paediatric Dose Calculations
3.1 Level 1 and 2 Paediatric Calculations
Calculate the volumes for each dose of the examples given below.
1. A 16 month old child with a respiratory infection weighing 13kg is prescribed
azithromycin 130mg OD.
The suspension is 200mg in 5mL.
What volume would you give?
2. A 10 year old child is prescribed a therapeutic dose of iron 30mg TDS. On the
ward you have Sytron oral solution which contains 27.5mg/5mL Iron.
What volume should you give?
3. A 2 year old child, weighing 14.4kg is prescribed Cefalexin 180mg BD. The
suspension is 250mg in 5mL.
What volume would you give?
4. You need to give Trimethoprim to a 7 year old child weighing 25kg at a dose
of 4mg/kg twice a day. Trimethoprim suspension is available as 50mg/5mL.
How much do you need for each dose?
5. A 3 month old baby weighing 5.6kg requires Clarithromycin and is prescribed
a dose of 7.5mg/kg.
a. What dose of Clarithromycin should the child be given?
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b. Pharmacy sends a bottle of Clarithromycin suspension 125mg in 5mL. What
volume would you give?
6. A 13 year old child is prescribed Sodium Valproate 650mg BD. She has had a
tonsillectomy and requires syrup which comes as 200mg in 5mL.
What volume would you give?
7. A 5kg child aged 9 months old is prescribed Paracetamol 100mg 6 hourly
PRN. The suspension is 120mg in 5mL.
What volume would you give?
8. A 12 year old child is prescribed Furosemide 15mg OM. On the ward you
have Furosemide oral solution that contains 50mg in 5mL.
What volume would you give?
9. Special care baby unit requires a dose of 60mg of Sodium Valproate by oral
syringe. A stock solution of Sodium Valproate 200mg in 5mL is available.
What volume should be given?
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10. A one month old baby requires a Salbutamol Nebuliser. The dose prescribed
is 1.25mg. Pharmacy sends supplies - the strength is 2.5mg in 2.5mL.
What volume of the nebuliser solution would be required for a 1.25mg dose?
11. A 3 month old baby (weight 6kg) is prescribed ibuprofen 30mg 6hrly PRN.
The suspension is 100mg in 5mL.
What volume would you give?
12. A 12 year old child is prescribed Sodium Valproate 430mg BD. Syrup is
available as 200mg in 5mL.
What volume would you give?
13. You want to give a 3 day old baby 50mg of Amoxicillin suspension. You have
a solution of 125mg in 5mL.
What volume would you give?
14. A 10kg child requires Alfacalcidol at a dose of 30 nanograms per kg.
a. What dose of Alfacalcidol does the child require?
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b. The stock bottle of Alfacalcidol is 2mcg in 1mL, however the dose is
measured in ‘drops’.
One drop = 100nanograms
How many drops would you give?
15. A 2 year old child is commenced on lamotrigine 1mg on alternate days.
Pharmacy has supplied 5mg dispersible tablets.
How could this dose be achieved?
16. A 6 year old child is commenced on diclofenac 20mg TDS. Pharmacy has
supplied 50mg dispersible tablets.
How would you give this dose?
17. Chloe is to be prescribed tobramycin for suspected neutropenic sepsis. She is
also receiving ciclosporin post BMT - calculate the dose and frequency of the
tobramycin, she weighs 26kg.
a. Look up the dose (mg/kg) and frequency in BNF for Children (BNFC).
b. Using patient’s weight above, what is the correct dose?
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18. Tom needs to start IV antibiotics for suspected febrile neutropenia, calculate
the dose of piperacillin tazobactum required - he weighs 38 kg.
a. Look up the dose (mg/kg) in BNFC.
b. Using patient’s weight above, what is the correct dose?
3.2 Level 2 Paediatric Intensive Care Unit (PICU)
1. Describe how you would give a bolus of 15mL over a set time of 15 mins via a
syringe pump. The syringe pump is set in mL/hour
2. Gentamicin vial contains 20mg in 2mL. How much is 1.2mL in milligrams?
3. What dose of Cefuroxime is usually prescribed on PICU?
☐ 20mg / kg
☐ 50mg / kg
☐ 80mg / kg
☐ 125mg / kg
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Section 4 –Intravenous Clinical Calculations and Activities
a) This section contains some activities using sources of information and more
complex questions you may find in the workplace.
b) You may want to refer to manufacturer’s data sheets to help you understand the
problem.
c) You may also wish to include additional examples from your workplace.
d) Indicate the reference sources you have used.
4.1 Level 2 Paediatric Calculations
1. A child is prescribed 350mg of ceftazidime. When 5mL of diluent is added to a
500mg vial, a dilution of 90mg per mL is stated in the data sheet. Calculate the
total volume to be administered to the child.
2. You need to give benzylpenicillin at a dose of 35mg/kg four times a day to a six
month old baby weighing 8kg. How much do you need to draw up from each
dose assuming each 600mg vial is to be reconstituted to 6mL?
3. A baby weighing 700g is prescribed vancomycin 15mg/kg every 24 hours. How
many milligrams will each dose be?
4. A baby weighing 1.3kg is prescribed 6mg per kilogram per day of aminophylline
to be administered by continuous infusion. If a solution containing 250mg
aminophylline in 500mL glucose 5% is prepared, what volume of this solution
would you require to administer the daily dose and at what rate would you set the
syringe driver?
5. A baby is to receive 120mL per kg per day of fluid. If the patient weighs 800g,
what volume of fluid is required and at what rate (in mL/hr) should the infusion be
set?
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4.1.1 Displacement Volume
1. A child is prescribed 250mg of flucloxacillin. A 0.4mL displacement is stated in
the literature when 10mL WFI is added to a 500mg vial. Calculate the total
volume to be administered to the child.
2. A child is prescribed 675mg of cefotaxime. The data sheet advises the addition of
4mL of diluent to a 1g vial. No displacement values are given. Calculate the total
volume to be administered to the child.
3. The displacement volume of ceftazidime 500mg is 0.5mL. What volume of diluent
would you add to a 1g vial to give a concentration of 100mg/mL? What volume of
this solution would you administer, per dose, to a 1.4kg baby prescribed
60mg/kg/day, to be administered every 12 hours?
4.2 Level 2 Adult Calculations
1. Calculate the dose of etoposide for a patient, given the following details:
Dose/m² - 75mg
Patient’s weight - 10st 10lb
Patient’s height - 5ft 8”
Male
N.B. See conversion units and BSA in BNF or use a nomogram.
2. A patient weighing 64kg requires a dose of amiodarone 5mg/kg to be
administered in 250mL glucose 5% over thirty minutes.
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What dose and rate of infusion should be prescribed?
3. A patient weighing 53kg requires an infusion of doxapram 3mg/min. Doxapram is
available as a 2mg/mL infusion bag.
At what rate should it be infused?
4. A patient weighing 78kg requires an infusion of dobutamine 2.5microg/kg/min.
Dobutamine is available as a 250mg in 500mL infusion bag.
At what rate should it be infused?
5. Sarah needs to start IV antibiotics for suspected febrile neutropenia, she is
currently receiving high dose methotrexate chemotherapy - which broad
spectrum IV antibiotic would she be prescribed?
6. Which two antibiotics commonly used in oncology / haematology require blood
levels to be monitored?
7. A patient weighing 87kg requires a dose of acyclovir 5mg/kg to be administered
in 100mL glucose 5% over sixty minutes.
What dose and rate of infusion should be prescribed?
8. A patient weighing 78kg requires an infusion of salbutamol 7.5micrograms/min.
Salbutamol is available as a 5mg in 500mL infusion bag.
At what rate should it be infused?
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9. A patient weighing 49kg requires an infusion of aminophylline 500microg/kg/hour.
Aminophylline is available as a 500mg in 1000mL infusion bag.
At what rate should it be infused?
10. A patient weighing 92kg requires a dose of N-acetylcysteine 150mg/kg in 200mL
glucose 5% over fifteen minutes.
What dose and rate of infusion should be prescribed?
11. A patient weighing 86kg requires an infusion of GTN 100micrograms/min. GTN is
available as a 1mg/mL syringe (100mL).
At what rate should it be infused?
12. A patient weighing 66kg requires an infusion of esmolol 75microg/kg/min.
Esmolol is available as a 2.5g in 250mL infusion bag.
At what rate should it be infused?
4.3 Level 2 Child Neonatal Unit (NNU)
1. Baby A was born at 26 weeks gestation and is now 14 days of age weighing
850 grams. She has developed abdominal distension and the medical staff have
prescribed the following medication:
a. IV Vancomycin 15mg / Kg 12 hourly (5mg/mL)
b. IV Ceftazidime 25mg / Kg 12 hourly (100mg/mL)
c. IV Metronidazole 7.5mg / Kg 12 hourly (5mg/mL)
Calculate the doses of medicine required and the volume of drug. Give your
answer with two decimal places.
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Drug
Dose
Volume
Vancomycin
Ceftazidime
Metronidazole
2. Baby B was born at 25 weeks gestation weighing 650 grams and has a low mean
blood pressure and is prescribed the following infusions:
a. Dopamine 10 micrograms / kg / min | Syringe concentration 60mg / 50mL
b. Dobutamine 7.5 micrograms / kg / min | Syringe concentration 60mg / 50mL
Please calculate the rate of infusion in mL/hr.
Infusion
Rate
Dopamine
Dobutamine
3. Baby C is a term baby at 3 hours of age weighing 3.25KG she has risk factors for
suspected sepsis and is commenced on first line antibiotics.
a. Benzylpenicillin 50mg / Kg | 12 hourly | (600mg / 4mL)
b. Gentamicin 4mg / kg | 24 hourly | (4mg / mL)
Calculate the doses of medication required and the volume of drug.
Drug
Dose
Volume
Benzylpenicillin
Gentamicin
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4. Baby D weighs 2.25 Kg and is commencing a morphine infusion at 20
micrograms / kg / hour, the syringe concentration is 3mg / 50mL, please calculate
the hourly rate.
5. Baby E is a 29 week gestation baby weighing 980 grams which is 48 hours of
age and is being weaned on the ventilator and requires a loading dose of caffeine
citrate at 20mg / kg.
A caffeine citrate IV solution is available 20mg/mL or oral solution 10mg/mL.
a. Calculate the dose and volume of medication required.
Drug
Dose
Volume
Caffeine Citrate
b. A maintenance dose of caffeine citrate at 5mg / kg is prescribed. This dose
will be administered 24 hours after the loading dose, please state the dose
and volume of the maintenance dose.
Drug
Dose
Volume
Caffeine Citrate
6. Baby F is unsettled and fighting the ventilator and required an Atracurium
infusion. She weighs 750 grams and is prescribed 1mg / kg / hour. The syringe
concentration is 250mg / 50mL.
Infusion
Rate
Atracurium
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7. Baby G weighs 630 grams and has hyperglycaemia requiring an insulin infusion.
a. The infusion is prescribed as 10 units of Human Actrapid in 50mL 0.9%
Sodium Chloride commencing at 0.04 units / kg / hour. Please calculate the
rate of infusion.
Infusion
Rate
Insulin
b. After 2 hours the blood sugar has increased and according to policy the
infusion is increased by 0.02 units / kg / hour to 0.06 units kg / hour, please
calculate the rate of infusion.
Infusion
Rate
Insulin
8. Baby H is prescribed IV paracetamol at 7.5 mg / kg six hourly, weight 4kg.
a. Please calculate the dose and volume. Concentration 10mg / mL.
Drug
Dose
Volume
Paracetamol
b. Baby H is now taking oral feeds and the paracetamol is changed to oral at
15mg / kg six hourly, please calculate the dose and volume. Concentration
120mg / 5mL.
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Drug
Dose
Volume
Paracetamol
9. Baby I is a term baby weighing 2.9 kg who has been ante natally diagnosed with
a duct dependent lesion and has been prescribed Alprostadil at 10 nanograms /
kg / min, syringe concentration 300 micrograms / 50mL.
Please calculate the rate of infusion.
Infusion
Rate
Alprostadil
10. Baby J is prescribed oral diuretics of Frusemide at 1mg / kg BD and
Spironlactone 1mg / kg BD. Baby J weighs 1.56kg.
Spironlactone 50mg / 5mL
Frusemide 50mg / 5mL
Please calculate the dose and volume.
Drug
Dose
Volume
Spironlactone
Frusemide
4.4 Level 2 Children’s Paediatric Intensive Care Unit (PICU)
1. An asthmatic with peripheral access requires an aminophylline infusion.
a. What is the recommended dose of aminophylline and how should the infusion
be prepared?
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b. At what stage would you send blood to determine therapeutic levels?
c. What levels would you ask for?
d. What side effects should you observe for?
2. What is the loading dose of phenytoin and what is the maximum rate of delivery?
What special considerations are associated with the oral preparation?
3. How much water for injection would you add to a 1200mg vial of co-amoxiclav?
a. What is the displacement value?
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b. If you wanted to give 240mg what volume would this be?
c. If you wanted to convert this to the oral route how should the prescription be
written?
4. What is the loading dose of IV amiodarone for a 2 year old child?
5. What dose of oral ranitidine would you give a 3 month old infant?
6. What dose of oral ranitidine would you give a 4 year old child?
7. What starting dose of vancomycin should be prescribed for a 12kg child with
normal renal function?
8. What starting dose of vancomycin should be prescribed for a 72kg teenager with
normal renal function?
9. A child weighs 14.7kg. A morphine infusion is prescribed as 15mg in 50mL. The
preparation of morphine available is 10mg / mL.
a. What volume of morphine is required to make this infusion?
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b. If the infusion is running at 1.5mL / hour what does is being delivered, in
microgram / kg / hour?
c. If the required dose is 10 microgram / kg / hour what rate should be set?
10. Hannah is a 4year old 14kgs patient who is NBM following abdominal surgery.
The following has been prescribed:
IV Paracetamol 15mg/kg/per 6 hourly dose.
Paracetamol IV solution = 10mg/mL
a. Calculate the dose.
b. Calculate the volume to be administrated.
11. Tom is a 8 month old 8kgs patient who is NBM following abdominal surgery. The
following has been prescribed:
IV Paracetamol 15mg/kg/per 6 hourly dose.
Paracetamol IV solution = 10mg/mL
a. Calculate the dose.
b. Calculate the volume to be administrated.
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12. What is the test dose of captopril?
a. What do you record after this and for how long?
b. How long after the test dose can you give the next dose?
c. What is the maximum dose of captopril?
13. Describe the procedure for giving adenosine.
14. Name a drug you can give as a slow bolus over 3 – 5 minutes.
15. Name one drug to be given over a specific amount of time.
16. Describe why monitoring of blood levels is important for some drugs and name of
2 these drugs.
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Section 5 Miscellaneous Calculations
5.1 Level 1 Reducing and Loading Doses
1. Prednisolone reducing dosing.
The patient is prescribed 40mg/day, to be reduced by 5mg per week until stop.
Calculate the number of tablets needed to complete the course and attach a
steroid reducing chart
2. A patient on temazepam oral solution (10mg/5mL) is reducing the dose weekly as
follows:
Week 1 – 9mg nocte
Week 2 – 8mg nocte
Week 3 – 7.5mg nocte
For each week, calculate the quantity in mL required:
a) For each dose
b) For a week’s supply
3. The patient is prescribed amiodarone tablets.
follows:
A loading dose is required as
200mg tds
F 7/7 then
200mg bd
F 7/7 then
200mg od
thereafter
Dispense 28 days supply.
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5.2 Level 1 Reading Preparation Labels and Strengths
1. What volume of phenytoin suspension needs to be given for the prescription
below? NB the preparation referred to (90mg/5mL) below is an unlicensed
preparation, available from a ‘specials manufacturer’.
Phenytoin syrup cannot be interchanged dose for dose with the capsules.
90mg syrup = 100mg caps
Phenytoin
5. Drug
Dose
Route
225mg po
0600
Start
Finish
1000

4/8
1200
Special Directions
1400
Signature
Print Name
Pharm
A. Jones
A. Jones
X
Bleep
911
1800
2200
Dispense using the following preparation:
PHENYTOIN SUSPENSION
90mg/5mL (Sugar Free)
Each 5mL contains 90mg Phenytoin BP.
Dosage as directed by the prescriber.
BN:9035576 Expires: Jan 2018
500mL Generic Manufacture
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2. What volume needs to be given for the prescription below?
5. Drug
Digoxin
0600
Dose
Route
Start
200 microgram
IV
4/8
Finish
1000

1200
Special Directions
1400
Signature
Print Name
Pharm
A. Jones
A. Jones
X
Bleep
1800
2200
911
The following preparation is available:
Lanoxin 0.5mg Injection
Each 2mL contains: digoxin 500 micrograms (0.5mg)
Also contains: Ethanol, propylene glycol, citric acid monohydrate, sodium phosphate
anhydrous, water for injections
5 ampoules BN:34901
Expires: Feb2018
3. A patient is written up for tinzaparin injection at a dose of 11,000 units.
The patient has been supplied with
Tinzaparin sodium 20,000 IU/ml
0.7mL pre-filled syringe (14,000 anti-Factor Xa IU)
For subcutaneous injection
2 syringes Manufacturer Abc
BN: 56390
What volume would you need to give the required dose?
The dose was prescribed at 175 units/kg, therefore what weight is this patient?
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5.3 Level 2 Infusions
1. A child requires a dose of 4.5g of L-arginine. It comes in vials containing 12.5% of
L-arginine. What volume would you need to give the required dose?
2. An adult patient requires 1 litre of saline over 8 hours. Calculate the flow rate in
drops/min (Calibration 20 drops/mL)
Infusion Rates
Flow rate (drops/min) =
volume fluid (mL)
total infusion time (min)
x drops/mL
3. Mr W has COAD. On the current admission, the Drs have added aminophylline to
his current therapy. This has been prescribed as an infusion of 0.56mg/minute.
The pharmacy supplies infusion bags containing 1g aminophylline per litre. What
rate (mL/hr) should the infusion be set to run at?
4. Mrs K is a 70kg patient who has been prescribed dopamine at a rate of
4micrograms/kg/minute. The pharmacy buys in pre-made syringes containing
200mg dopamine in 50mL. What rate should you set the pump at (mL/hour)?
5. Furosemide (furosemide) Infusion 250mg/25mL
These are available in boxes of 10 x 25mL ampoules.
A patient is prescribed a dose of 380mg OD.
a. Calculate how many ampoules you would need to send for 1 weeks supply
(round up to the nearest full box).
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b. The infusion should be given at a rate of 4mg/min. How long will it take to give
the 380mg dose?
c. What infusion rate would you use?
6. A 92kg patient is prescribed epoprostenol 5nanograms/kg/minute.
A 500microgram vial with 50mL diluent is available.
Calculate:
a) The prescribed dose per day
b) What volume of reconstituted solution would be used?
c) A 5 day course is indicated in the patient’s notes. How many 500microgram
vials would you need to supply?
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7. Fred is age 86 and weighs 65kg. The hospital prescribing guidance for
vancomycin is listed in table 1.
Table 1: Initial Vancomycin
LOADING Dose Actual Body
Weight (ABW)
<40kg
40-59kg
60-90kg
>90kg
Dose
Volume
(0.9% Sodium Chloride )
Duration
of infusion
250mL
250mL
500mL
500mL
1.5 hours
2 hours
3 hours
4 hours
750mg
1000mg
1500mg
2000mg
†
What initial dose of vancomycin should Fred have?
In what amount of sodium chloride should this be contained in?
Each 500mg vial of vancomycin should be made up with 10mls of water for injection.
To make up 1500mg - what volume of water for injections would need to be used?
The nurse receives the 1500mg vancomycin in 500ml of sodium chloride 0.9%. What
mg/mL is this?
The prescription states the duration of the infusion is 3 hours.
If this was to be infused using a pump -how many mLs/min should the pump be set
at?
5.4 Level 2 Renal Impairment/The Elderly
1. Unstable Angina = use clexane 1mg/kg BD.
Formulae:
Males:
Females:
1.23 x (140-Age) x weight (kg)
Serum Creatinine (micromol/L)
1.04 x (140-Age) x weight (kg)
Serum Creatinine (micromol/L)
= Creatinine Clearance mL/min
= Creatinine Clearance mL/min
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a. A 73 year old male patient weighing 82kg with a serum creatinine (SrCr) of
123 needs treating for unstable angina. Calculate the creatinine clearance,
and the dose.
b. A 55 year old female patient weighing 65kg with a SrCr of 150 needs treating
for unstable angina. Calculate the Creatinine clearance, and the dose.
2. A consultant wishes for his patients to have a bisphosphonate.
From the information in the SPCs you know that alendronate 70mg once a week is
not recommended for patients with renal impairment where GFR is less than 35
ml/min. Another bisphosphonate, risedronate sodium 30mg once a week is
contraindicated in patients with severe renal impairment (creatinine clearance lower
than 30 ml/min).
The following ‘Cockcroft Gault’ equation can be used to estimate creatinine
clearance (CrCl):
CrCl = [140-age (years)] x weight* (kg) x 1.23 (male) or 1.04 (female) (mL/min)
Δ
serum creatinine (micromol / L)
Cautions:
*Use actual body weight or maximum body weight for patient’s height, whichever is
lower. For maximum body weight see Appendix 2 or:
http://www.scottishmedicines.org.uk/files/sapg/Maximum_body_weight_table.pdf
Δ
In patients with low creatinine (<60micromol/L), use 60 micromol/L to avoid
overestimating creatinine clearance due to low muscle mass.
Provide the answers to the following questions:
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a) If Sheila is 76yrs of age, weights 70kg and has a Creatinine level of 85
What is her CrCl in mLs/min?
What drug would you recommend she has?
b) Doreen is 76, weights 38kg and has a Creatine level of 85
What is her CrCl in mLs/min?
What drug would you recommend she has?
c) Ethel is 91 years of age, weights 38 kg and has a creatinine level of 56.
What is her CrCl in mLs/min?
She is currently prescribed alendronate 70mg once a week. What treatment should
Ethel have?
3. Fred is age 86 and weighs 65kg The maintenance dose of Vancomycin Fred
needs is determined by his CrCl as per Table 2 below
The following ‘Cockcroft Gault’ equation can be used to estimate creatinine
clearance (CrCl):
CrCl = [140-age (years)] x weight* (kg) x 1.23 (male) or 1.04 (female) (mL/min)
Δ
serum creatinine (micromol / L)
Cautions:
*Use actual body weight or maximum body weight for patient’s height, whichever is
lower. For maximum body weight see Appendix 2 or:
http://www.scottishmedicines.org.uk/files/sapg/Maximum_body_weight_table.pdf
Δ
In patients with low creatinine (<60micromol/L), use 60 micromol/L to avoid
overestimating creatinine clearance due to low muscle mass.
Table 2: Vancomycin MAINTENANCE dosage regimen VANCOMYCIN
PULSED INFUSION – INITIAL MAINTENANCE DOSAGE GUIDELINES
CrCl
(mL/min)
Dose
Dosing
Interval
Volume of sodium
‡
chloride 0.9%
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< 20
500mg over 1 hour
48 hours
250mL
20-29
500mg over 1 hour
24 hours
250mL
30-39
750mg over 1.5 hours
24 hours
250mL
40-54
500mg over 1 hour
12 hours
250mL
55-74
750mg over 1.5 hours
12 hours
250mL
75-89
1000mg over 2 hours
12 hours
250mL
90-110
1250mg over 2.5 hours
12 hours
250mL
>110
1500mg over 3 hours
12 hours
500mL
Fred is age 86 and weighs 65kg, what other information do you need to complete
this calculation?
Fred’s creatine level is 80
What is Fred’s CrCl?
What dose should Fred have, over what duration and in what volume of fluid?
How often should this dose be repeated?
4. Alice is age 96 and requires some clarithromycin for a chest infection
Alice is 37kg and her last Cr level was 57
The following ‘Cockcroft Gault’ equation can be used to estimate creatinine
clearance (CrCl):
CrCl = [140-age (years)] x weight* (kg) x 1.23 (male) or 1.04 (female) (mL/min)
Δ
serum creatinine (micromol / L)
Cautions:
*Use actual body weight or maximum body weight for patient’s height, whichever is
lower. For maximum body weight see Appendix 2 or:
http://www.scottishmedicines.org.uk/files/sapg/Maximum_body_weight_table.pdf
Δ
In patients with low creatinine (<60micromol/L), use 60 micromol/L to avoid
overestimating creatinine clearance due to low muscle mass.
What is Alices’ CrCl?
The SPC states that at a creatinine clearance rate of less than 30 ml/min, the
dosage should be halved to 250 mg daily or in the most severe infections to 250 mg
twice daily.
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Alice has a serious chest infection - what dose would you recommend?
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Appendix 1 Reference Sources and Further Reading
British National Formulary http://www.evidence.nhs.uk/formulary/bnf/current
British National Formulary for Children
http://www.evidence.nhs.uk/formulary/bnfc/current
Martindale: The Complete Drug Reference www.medicinescomplete.com
Introduction to Pharmaceutical Calculations 3rd edition – Judith Rees, Ian Smith and
Brian Smith (Pharmaceutical Press ISBN 978 0 85369 960 6) www.pharmpress.com/
Practical Pharmacy Calculations 2nd edition - MC Bonner, DJ Wright, 2008, (Radcliffe
Press ISBN: 9781846192517)
Electronic Medicines Compendium www.medicines.org.uk
Patient UK www.patient.co.uk
CGP Books www.cgpbooks.co.uk
Building a Safer NHS for Patients: Improving Medication Safety (Author Dr Jim Smith
Published 2004 DH)
http://webarchive.nationalarchives.gov.uk/
Safety in Doses Improving the use of medicines in the NHS. Learning from National
Reporting
2007
(National
Patient
Safety
Agency
Published
2009)
http://www.nrls.npsa.nhs.uk
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Appendix 2 Acknowledgements
We would like to thank:
Yorkshire Pharmacy Technicians Group
Children’s Services, Leeds Teaching Hospitals NHS Trust
NHS Leeds West Clinical Commissioning Group
Clinical Pharmacy Services, Humber NHS Foundation Trust
Members of the pilot review panel
All other contributors of calculations examples
Calderdale and Huddersfield NHS Foundation Trust
for their time and contribution to this training manual.
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Appendix 3 Summary of Achievements
Medicines Optimisation Training and Assessment Schemes
Candidate’s Name
Tutor’s Name
Module Name: Calculations
Organisation:
Each of the following areas must be completed and signed by the mentor/tutor
Where *Level 1 and/or Level 2 is listed please indicate which level was taken and
using the Y/N option please indicate what sections have been included/excluded
where sections may not be relevant to candidate’s learning and role
Content
Signature
of Date
Mentor/Tutor
Section 1 Formulae
Section 2 Practice Questions
*Level 1 and/or Level 2
2.6 Moles and mmols
Section 3 Paediatric Dose Calculations
*Level 1 and/or Level 2
3.2 PICU
Section 4 Intravenous Clinical Calculations and
Activities Level 2
4.2 Adult Calculations
4.3 Child Neonatal Unit (NNU)
4.4 Children’s Paediatric Intensive Care Unit (PICU)
Section 5 Miscellaneous Calculations
*Level 1 and/or Level 2
5.3 Level 2 Infusions
5.4 Level 2 Renal Impairment/The Elderly
Calculations practice in specialist areas added to
workbook (portfolio of work)
y/n
y/n
y/n
y/n
y/n
y/n
y/n
y/n
I (print name)
confirm that the candidate:
 has completed their assessments and has successfully completed all of the above
areas of work as indicated according to their training needs.
I am satisfied that:
 the areas of work listed above have been carried out to a high standard
 procedures, policies and professional codes of conduct have been followed
 all work has been verified as the candidates own
Signed
Job title
(tutor/mentor).
Date
Please complete and send a copy of this form to [email protected]
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Appendix 4 Confirmation of Completion of Module
To be completed by Yorkshire and the Humber Pharmacy Staff working through the
Medicines Optimisation Modules.
Candidate’s Name:
Workplace Address:
Contact Telephone No.:
Name of Module:
Comments from Senior Technician/Pharmacist:
I confirm that this candidate has completed the above module and passed all
relevant assessments.
Signed (Senior Technician/Pharmacist): __________________
____________
Name (Please print):
_____________________________ Date: ___________
Signed (Candidate):
______________________________________________
Please send a copy of this form to [email protected]
A certificate of completion will be issued to Yorkshire and Humber pharmacy staff on receipt from a
recognised mentor.
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Appendix 5 Continuing Professional Development
Evaluation (Reflection on Learning)
Pharmacy staff completing this module may wish to use this form to reflect on the
learning experience and add to their GPhC CPD on-line records.
CPD No.:
_____________________________
Name of Entry:
Entry No.:
_____________
___________________________________________________
Date learning undertaken: _____/_____/_____
Time taken: _____________
Action:
U1
Please describe the activity you have undertaken
(Describe the activity you carried out, being specific about the details)
U2
To which areas of competence does this learning relate?
(If you cannot find any competences that match, write your own.)
U3
What have you learnt as a result?
(Briefly describe what you learnt from doing the activities.)
Evaluation (Reflection on learning)
U4
Please describe an example of how you have applied this learning.
(Give an example of how you have used what you have learnt.)
U5
Describe any feedback you have had.
(This might include users of your services/products, staff and colleagues. The learning may
have had an impact on you, for example by affecting your confidence or motivation, and you
should record this. Feedback may come in many forms, for example, verbally, through
surveys, or through statistics on performance.)
U6
Have you identified any learning needs as a result of undertaking this activity?
(If so, start a new CPD record that starts with Reflection)
 Yes
 No
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Appendix 6 NHS Knowledge and Skills Framework
This training may assist you in achieving:
Core 2 Personal and People Development
Level 2: Develop own skills and knowledge and provide information to others to help
their development.
The worker:
a) assesses and identifies:
 feedback from others on own work
 how s/he is applying knowledge and skills in relation to the KSF outline for
the post
 own development needs and interests in the current post
 what has been helpful in his/her learning and development to date
b) takes an active part in the development review of own work against the KSF
outline for the post with their reviewer and suggests areas for learning and
development in the coming year
c) takes responsibility for own personal development and takes an active part in
learning opportunities
d) evaluates the effectiveness of learning opportunities and alerts others to
benefits and problems
e) keeps up-to-date records of own development review process
f) offers information to others when it will help their development and/or help
them meet work demands
HWB10 Products to meet health and wellbeing needs
Level 3: Prepare and supply specialised products
The worker:
a) accurately
calculates
or
measures
the
correct
quantities
of
components/ingredients and combines and processes them correctly and in a
way which
 maintains their quality
 is consistent with legislation, policies and procedures
 minimises risks to self, others and the work environment
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