GENERAL UNIT CONVERSIONS
Madu Suthanan, P. Eng., FEC.
For conversion factors within the SI (International System of Units) units, you need to keep in mind of the
following prefixes:
Prefix
Symbol
Multiplying Factor
10 mm = 1 cm
tera
T
1 000 000 000 000
10 cm = 1 dm
giga
G
1 000 000 000
10 dm = 1 m
mega
M
1 000 000
10 m = 1 dam
kilo
k
1 000
10 dam = 1hm
milli
m
0.001
10 hm = 1 km
micro
µ
0.000 001
nano
n
0.000 000 001
pico
p
0.000 000 000 001
1000 mL = 1L
1000 mg = 1 g
1000 g = 1 kg
millimetre
centimetre
decimetre
metre
dekametre
hectometre
kilometre
mm
cm
dm
m
dam
hm
km
litre
gram
L
g
For example, conversion for length or distance used for various instance needs the following conversions:
1,000 m = 1km
100 cm = 1 m
1 mm = 0.001 m
Computer storage is measured in bytes and general conversions for bytes are:
1 KB = 1000 Bytes
Kilobyte (KB)
1 MB = 1000 KB
Megabyte(MB)
1 GB = 1000 MB
GigaByte (GB)
1 TB = 1000 GB
TeraByte (TB)
Note: This accuracy is “good enough” for computer storage requirements however,
1 Kilobyte ≡ 210 bytes ≡ 1 024 bytes
where ≡ means exactly equal to
There is a standard for binary multiples. Read more here: http://physics.nist.gov/cuu/Units/binary.html
SI – US Unit
Conversions between SI units and Imperial/U.S. Customary Units:
●
●
●
●
1 foot ≡0.3048 metres ≡12 inches (used to measure height)
72 points ≡ 1 inch (points are used in font sizes in computer usage)
1 Imperial Gallon (IG) = 4.5 L
1 U.S. Gallon (USG) = 3.78 L
PEOSC – STEMZ
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Buying Lumber
Jack’s dad asked him to go to Home Depot and get 2 pieces of 2x4 lumber.
“What length?” Asks Jack.
“Oh! A little longer than your height would be OK.” his dad replies.
Jack’s height is 162 cm, so Jack goes to Home Depot looking for lumber of 2 cm x 4 cm x 165 cm or more in
length. When he goes to Home Depot and asks for 2x4 lumber, the friendly associate shows him to a stack of
2x4s. They were much more than 2 cm x 4 cm!
On further enquiry, the associate explains that they sell lumber only in feet and inches, and what dad meant
was 2 inch x4 inch x 6 feet or more long lumber. So, Jack bought the lumber and dad was satisfied with the
purchase.
Jack was puzzled as to why they are selling in feet and inches when Canada has gone Metric or SI long ago.
Dad explained that still most of the older folks and the building industry (in Canada and U.S.A) use the Imperial
System, or the U.S. Customary System which measures lengths in feet (ft), weight in pounds (lb), and time in
seconds (s).
Jack finds that 1 inch is usually written as 1” and six feet as 6’. When Jack measures the 2x4 lumber beam he
bought, he found that it measured only 1½” x 3½”. He reported his finding to his Dad.
Dad, an experience handyman, smiled at him and said “2” x 4” is the Nominal size of the beam. It may not
represent any actual size, but is standardized in an industry. It is roughly the sawn size they start with. By the
time they dry it, plane it and finish it, the final size becomes 1½” to 3½” or 38mm x 89mm.”
Dad further went on to explain that many items such as pipes are also designated by nominal pipe sizes (NPS)
in inches. A ½” pipe may have various wall thickness to withstand different pressures and temperatures. You
must get the actual inside diameter (ID) and Outside diameter (OD) from tables provided by the manufacturer.
Jack decided to learn about this more later.
Question 1
What is the 2”x 4” lumber expressed in SI units, given that 1 inch = 2.54 cm.
a) 5.08cm x 10.16cm
c) 100mm x 50mm
b) 5cm x 10cm
d) 38 x 89
Sizing Fonts
Diana is working as a computer operator in a company for her volunteer experience. Her supervisor, Ms. Jane,
asks her to prepare a name board for the washroom using MS Word. She wanted the letters of the board to
be 2” high.
Diana is used to using only “points” for Font size in the computer and she asks Jane, “How many points do
you want the Font size to be”. Jane does not understand points, and Diana does not know how to convert
Inches to Points. Therefore, Diana uses the internet to find the conversion factor and finds that 1” = 72 points.
PEOSC – STEMZ
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Question 2
When you want to print Fonts to 2” high, what is the point size to be used in a computer?
a) 36
b) 72
c) 144
d) None of the above
Furnishing your Room
Daniel’s parents are interested in buying a new house. They collect many brochures of the house plans that
the Builders and Real Estate agents provide. Daniel selects a nice room as his bedroom/study room. Daniel
finds that all the house plans give the size of the rooms in feet and inches. He gets annoyed as he has learned
to use dimensions in metres, centimetres and other metric (SI) units. How does he convert feet and inches to
SI units? Fortunately, he could find the conversion factors from the Internet. What a boon Internet is!
He finds that 1 foot = 12 inches, and 1 inch = 25.4 mm.
Question 3
Daniel selects a room which is 10ft x 12 ft in size for his bedroom/study room. He measures his bed as 200
cm x 120 cm. and his study table as 120 cm x 75 cm. He wishes to place the table and bed along a 12 ft size
wall. How many centimetres will be free along that wall after placing the bed and study table with their long
sides along the wall? Give the answer to the nearest cm.
Answer:
Room Length 12 ft = 366 cm
Bed Length = 200 cm
Table Length = 120 cm
Free Space = 366 – 200 – 120 = 46 cm
Obey the Traffic Laws!
Edward has got a new car where the speed is nicely shown in large numbers in the digital format. He is very
proud of his car. His sister Stella and mother wants to go to Buffalo U.S.A. for shopping. He readily agrees to
take them as it would give him a chance to try out his car on a long trip. He drives carefully observing all the
speed limits on the road.
They set out on the trip from Scarborough, Ontario. After they cross the Lewiston-Queenston bridge and enter
the U.S.A., Edward finds that the speed limit now is 65 and not 100 as in Canada! So he slows down. Stella
tells Edward to go faster as the 65 is in miles per hour (mph) and not kilometres per hour (km/h), as in Canada.
He knew that his car speedometer can be set to read in mph: but he has not learned how. Stella checks on
internet with her smartphone and finds the conversion factor. 1 mile = 1.6 km.
Question 4
If the speed limit in the highway is 65 mph, at what speed in km/h should you drive? 1 mile = 1.6 km.
a) 104 km/h
PEOSC – STEMZ
b) 40.6 km/h
c) 65 km/h
d) Non of the above
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Fuel Consumption in Cars
The traditional way of stating the fuel consumption in cars in the Imperial System was miles/gallon. After
metrification (the conversion from the Imperial System to the Metric System), the standard was to state the
fuel consumption in litres used per 100 km. When Shaun went to the showrooms to help his dad to buy a
fuel-efficient car, he found that in the Energuide labels attached to each car, the fuel consumption was given
in litres/100 km as well as in miles per gallon. He was surprised to find that the efficiency given in miles/gallon
was very high compared to the SI values. He was puzzled. When he asked the salesman, he had no answer
except to say it is correct. On later inquiry, Edward found that the gallon given in Imperial Gallon, whereas in
Canada we usually use the U.S. Gallon. 1 U.S. gallon = 3.78 litres, whereas 1 Imperial Gallon = 4.5 litres. So
when Imperial Gallons is used, it gives a larger value for the miles per gallon. But this is legally correct as it is
the recommended method given by Natural Resources Canada. Many of us tend to think of the gallon as a
U.S. Gallon.
Question 5
The Energuide label on a new 2016 car is given as: 31 mpg. (miles per Imperial gallon). How much is this in
litres/100 km. Give the answer to 1 decimal place.
1 U.S. gallon = 3.7854 litres, 1 Imperial Gallon = 4.5461 litres. 1 mile = 1.60934 km.
31 mpg = 7.6 L/100 km
Epilogue to Question 5
We have to be very careful of the correct interpretation of values given in sales brochures and other
documents. In this case if you mistake the Imperial Gallon to U.S. Gallon, you think the car is very efficient.
Sales propaganda always try to give a favourable amount to boost the sales as many of the customers are
ignorant or do not care to verify the details of what is advertised.
PEOSC – STEMZ
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