Pharmaceutical Calculations
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Introduction
Pharmaceutical calculations dealing with:
• Expressions of concentration
• Master formulae to working quantities
• Changing concentrations
• Small quantities ( trituration)
• Solubility
• Calculations related to doses
• Reconstitution and rates of infusion
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How to minimize errors
• Write out the calculation clearly.
• Double check when transferring data from
reference.
• Write down every step
• Don’t make short cuts
• Try not to be totally dependent on your
calculator
• Double check your calculation
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Expressions of concentrations
- The metric system is the International System of Units (SI Units)
for weight, volume and length. The basic unit for weight is
kilogram (kg), for volume is liter (L) and for length is meter
(m).
- The avoirdupois ( Imperial) {pound, grain, ounces, pints and
fluid ounce & gallons).
- The apothecary system: grain, scurple, drachm, minim, fluid
drachm, fluid ounce.
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1 kilogram (Kg)= 2.2 pounds (lb)
1 grain ( Avoir. Or Apoth.) = 64.8 mg
1 teaspoonful (tsp)= 5ml
1 table spoonful = 15 ml (3 teaspoonfuls)
1 pint (pt) = 473 ml
1 gallon (gal) = 3785 ml
1 fluid ounce (oz) = 29.57 ml ( 30ml)
1 fluid ounce ( oz) = 480 minims
Example: A prescription is received for a dose of 10 grains of a drug. How
many grams is the dose?
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Expressions of concentration
Expressions of strength:
• Ratio: is the relative magnitude of two like quantities thus 1: 10
= 1 part in 10 parts or 1g in 10g.
• Ratio strength: is the expression of a concentration by means of
a ratio, e.g 1:10.
• Percentage strength: is a ratio of parts per hundred, e.g. 10%
• Percentage weight in weight ( w/w),
• Percentage weight in volume ( w/v).
• Percentage volume in volume ( v/v).
Other expressions of concentration:
• Moles & molarity
• Molality.
• Normality.
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Expression
Symbol
Definition
Molarity
M
Moles (gram molecular weights) of solute in 1
liter of solution
Normality
N
Gram equivalent weights of solute in 1 liter of
solution
Molality
m
Moles of solute in 1000g of solvent
Mole fraction
X, N
Ratio of the moles of one constituent (e.g. the
solute) of a solution to the total moles of all
constituents (solute and solvent)
Mole percent
Moles of one constituent in 100 moles of the
solution. Mole percent is obtained by multiplying
the mole fraction by 100
Percent by weight
% w/w
Grams of solute in 100g of solution
Percent by volume
% v/v
Milliliters of solute in 100mL of solution
Percent weight-involume
% w/v
Grams of solute in 100mL of solution
Milligram percent
-
Milligrams of solute in 100mL of solution
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Examples:
• Express 0.1% w/w as a ratio strength.
• Express 1:2500 as a percentage strength.
• How many grams of a drug should be used to prepare 240 grams of
a 5% w/w solution.
• If 5 g of iodine is in 250 mL of iodine tincture, calculate the
percentage of iodine in the tincture.
• Express 30g of dextrose in 600 mL of solution as a percentage,
indicating w/w , w/v, or v/v.
• Compute the percentage of the ingredients in the following
ointment: Liquid parafin 14 g, soft parafin 38g, hard parafin 12g.
• Calculate the number of milligrams of sodium hydroxide (NaOH)
to be dissolved in 1L of water to give a concentration of 10 mmol
(atomic wt: H=1, O=16, Na=23)
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Calculating quantities from a master formula
Quantities provided
by the master
formula have to
be scaled up or
down,
depending on
the quantity of
the product
required. Using
proportion or a
multiplying
factor.
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Calculating quantities from a master formula
When a combination of weights and volumes is used without indicating
the exact final volume or weight of the preparation: An excess quantity
is normally calculated for and the required amount is then measured.
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Calculations
involving
parts:
The no. of parts is
added up and the
quantity of each
ingredient
calculated by
proportion or
multiplying factor
to provide the
correct amount.
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Calculations involving percentages
Conventions which apply when dealing with
formulae which include percentages:
• A solid in a formula where the final quantity is
stated as a weight is calculated as weight in
weight (w/w).
• A solid in a formula where the final quantity is
stated as a volume is calculated as weight in
volume (w/v).
• A liquid in a formula where the final quantity is
stated as a volume is calculated as volume in
volume (v/v).
• A liquid in a formula where the final quantity is
stated as a weight is calculated as weight in
weight (w/w).
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some situations where the
conventions do not apply:
standard
• I. Syrup BP is a liquid-a solution of sucrose and
water. If the normal convention applied it would
be w/v, i.e. certain weight of sucrose in a final
volume of syrup
-However, in the BP formula the concentration of
sucrose is quoted as w/w. Therefore Syrup BP is:
Sucrose 66.7% w/w, Water to 100%
• 2. A gas in a solution is always calculated as
w/w, unless specified otherwise. Formaldehyde
Solution BP is a solution of 34-38% w/w
formaldehyde in water.
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Changing concentrations
• Increase or decrease the concentration by the
addition of more drug or more diluent.
The dilution equation:
C 1 V1 = C 2 V2
e.g.1 What is the final concentration if 60 ml of a 12%
w/v chlorhexidine solution is diluted to 120 ml with
water?
e.g.2 What percentage of atropine is produced when
200 mg of atropine powder is made up to 50 g with
lactose as a diluent?
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Alligation
• A method for solving the no. of parts of two or more
components of known concentration to be mixed when
the final desired concentration is known.
• Calculate the amount of a 2% w/w metronidazole cream
and of metronidazole powder required to produce 150 g
of 6% w/w metronidazole cream ( to 2 decimal places).
• Thioridazine suspension is available as 25mg/5ml ( 0.5%
w/v) and 100 mg/5ml (2% w/v).
Calculate the quantities to use to prepare 100ml of
40mg/5ml(0.8% w/v.) suspension
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Calculations where quantity of ingredients is
too small to weigh or measure accurately
• Small quantities in powder:
Trituration: when a measurable quantity of active
ingredient is diluted with an inert diluent.
Normally a 1 in 10 or 1 in 100 dilution is used.
Example:
Calculate the quantities required to make 10
powders each containing 200 micrograms of
digoxin. Assume that the balance available has a
minimum weighable quantity of 100 mg. The
convenient weight of each divided powder is 120
mg.
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Answer:
• The convenient weight of each divided powder is 120 mg. The total weight
of powder mixture required will be l0 x 120 =1200 mg= 1.2g.
• Quantities for l0 powders:
Digoxin 2 mg, lactose 1198 mg, Total 1200 mg
A 1 in l0 dilution is produced.
• Trituration A
Digoxin 100 mg, lactose 900 mg, Total 1000 mg
Each 100 mg of this mixture (A) contains l0 mg of digoxin.
• Trituration B
Mixture A 100 mg (= 10 mg digoxin), lactose 900 mg, Total 1000mg
Each 100 mg of this mixture (B) contains 1 mg of digoxin. This amount of
digoxin is less than the required amount, so mixture B can be used to give
the required quantity.
200 mg of mixture B provides the 2 mg digoxin required.
• Final trituration (C)
Mixture B 200 mg (= 2 mg digoxin) lactose (1200- 200) = 1000 mg, Total 1200
mg
Each 120 mg of this mixture (C) will contain 200 micrograms (0.2 mg) of
digoxin.
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Calculations where quantity of ingredients is too small to weigh or
measure accurately
• Small quantities in Liquids:
• Normally a 1 in 10 or 1 in 100 dilution is used.
• Example: Calculate the quantities required to prepare 100
mL of a solution containing 2.5 mg morphine
hydrochloride/5 mL. Assume that the balance available
has a minimum weighable quantity of 100 mg. The
solubility of morphine hydrochloride is 1 in 24 of water.
Quantities for 100 mL:
Morphine hydrochloride 50 mg
Chloroform water to 100 mL.
The minimum quantity of 100 mg of morphine
hydrochloride is weighed and made up to l0 mL with
chloroform water (this weight of morphine hydrochloride
will dissolve in 2.4 mL). 5 mL of this solution (A) provides
the 50 mg of morphine hydrochloride required. Take 5 mL
of solution A and make up to 100 mL with chloroform
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Calculations involving doses
• Calculating doses:
e.g. 1 The doctor prescribes orphenadrine tablets,
100 mg to be taken every 8 hrs for 28 days.
Orphenadrine is available as 50 mg tablets. How
many tablets should be supplied? (168)
e.g.2 The following prescription is received: Sodium
valproate oral solution:100 mg to be given twice
daily for 2 weeks. Note: Sodium valproate oral
solution contains sodium valproate 200 mg/5ml.
This prescription is therefore translated as:
2.5 ml to be given twice daily for 2 weeks.
The quantity to be dispensed will be:
2.5 * 2* 14= 70 ml.
Calculations involving doses
Possibility of misinterpreting the data!!!
Variation in terminology + lack of awareness
serious consequences !!!!!
The following prescription is received:
• Verapamil tablets 160 milligrams, Send 56,
Take two tablets twice daily
There are a variety of doses quoted for verapamil in the
BNF depending on the condition being treated.
They are as follows for oral administration.
Supraventricular arrhythmias, 40- 120 mg t.i.d.
Angina, 80- 120 mg t.i.d.
Hypertension, 240-480 mg daily in 2-3 divided doses.
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Calculations involving doses
Latin
Abbreviation
English name
recipe
Rx
take
mitte
mitt.
send
signa
sig.
label
Ad
ad
to
aqua
aq.
water
bis
b.
twice
bis die
b.d.
Twice daily
bis in die
b.i.d.
Twice daily
ter in die
t.i.d.
Three times daily
ter de die
t.d.d.
Three times daily
quarter die
q.d.
Four times daily
quarter in die
q.i.d.
Four times daily
quantum sufficiat
q.s.
sufficient
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Calculation of doses by weight and surface area
• Using body weight: the dose will be expressed as
mg/kg. The total dose required is then obtained by
multiplying the weight of the patient by the dose per
kilogram.
• Body surface area is a more accurate method when
extreme accuracy is required for narrow range of
plasma concentration between the desired therapeutic
effect and severe toxicity, e.g. anticancer drugs. The
body surface area can be calculated from body weight
and height using the equation
• Body surface area (m2) =
Weight (kg)0.5378 x Height (cm)O.37 x 0.024265
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Calculations involving doses
Different doses for children, an estimation of doses. Estimation of
doses is best carried out using body weigh, but where this is not
available, there are three formulas which relate the child's dose to the
adult dose.
• Fried's rule for infants: age (months) x adult dose/150 = dose for
infant.
• Clark's rule: weight (in kg) x adult dose/75 = dose for child.
• Body surface area method (BSA):
BSA of child (m2) x adult dose/l.73 m2 (average adult BSA) =
approximate child's dose.
• The BNF also gives a percentage method for calculating paediatric
doses of drugs which have a wide therapeutic window, i.e. where
accuracy is less critical.
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Reconstitution
• What dose of antibiotic will be contained in a 5 mL
spoonful when a bottle containing 5g of penicillin V is
reconstituted to give 200 mL of syrup?
5000 mg/200 ml= 25 mg/ml
The dose in a 5 ml is 25*5= 125 mg.
• We have an ampicillin product for reconstitution. It
contains 2.5g of ampicillin to be made up to 100 mL. To
what volume should it be made to give 100 mg per 5 mL
dose?
The required dos is 100 mg/5 ml……20 mg/ml.
The required volume= 2500 mg ÷20 mg/ml= 125 ml
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Reconstitution
A child weighing 60 lb requires a dose of 8 mg/kg of ampicillin.
Given that a 5 mL dose is to be given, what volume of water
must be added when the powder is reconstituted? Instructions
on the label indicate that dilution to 150 mL (by adding 111 mL)
gives 250 mg ampicillin per 5 mL.
Conversion of weight to kg: 60/2.2 = 27.27 kg
Calculation of amount of ampicillin required:
27.27 x 8 = 218 mg
Calculation of amount of ampicillin in container:
250 mg/y mg = 5 mL/150 mL, therefore
y= 7500 mg = 7.5 g
Calculation of amount of water to add to give 21 8 mg
per 5 mL: 218 mg/7500 mg = 5 mL/ x mL,
therefore x= 172 mL
Volume occupied by powder: 150 mL -111 mL = 39 ml
Therefore, volume to be added:172 mL- 39 mL = 133 mL.
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Calculation of infusion rates
• How much drug solution to be added?
• How fast the infusion should be administered? In
terms of ml/min or drops per minute.
• An ampoule of flucloxacillin contains 250 mg of
powder with instructions to dissolve it in 5 mL of
water for infusion. What volume of this solution
should be added to 500 ml of saline infusion to
provide a dose of 175 mg? answer3.5ml.
• 100 mg of methoxamine hydrochloride are added to
500 ml of saline infusion. What should be the rate of
infusion to give a dose of 1 mg per minute? How long
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• A doctor requires an infusion of 1000 mL of 5%
dextrose to be administered over an 8-hour
period. Using an IV giving set which delivers 10
drops/ml, how many drops per minute should be
delivered to the patient?
• 20 ml of a drug solution is added to a 500 mL
infusion solution. It has to be administered to the
patient over a 5-hour period using a set giving 15
drops per millilitre, how many drops per minute
are required?
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