Learning Futures
-
Teaching Support
- - Technology-Enabled Learning
- - WOS Studio
- - MESH
- - Smart Assessment Design Toolkit
- - Placements Hub
- - Digital Learning
- - Academic Integrity
- - Academic Integrity Research
- - Academic integrity quick guide
- Professional Learning @ Western
- Learning Transformations
- The 21C Project
- Contact Us
- Engaged Teaching
Units and Conversions
The following tables of units and conversions are useful for reference. A PDF file of this information can be downloaded here.
1.1 Commonly used mechanical units
Quantity | CGS (Centimetre-Gram-Second) | SI (International System of units) |
---|---|---|
Length | Centimetre (cm) | Metre (m) |
Mass | Gram (g) | Kilogram (kg) |
Time | Second (s) | Second (s) |
Force | Dyne (dyn) | Newton (N) = kilogram -metre/(second)$^2$ |
Work, Energy | Erg (erg) | Joule (J) = Newton-metre |
Power | Watt (W) = Joule/second |
1.2 Mechanical quantities, fundamental units of dimensions MLT (mass, length, time) and their SI units
Quantity | Dimensions | Units |
---|---|---|
Acceleration | LT$^{-2}$ | Metre/second$^2$ |
Angle | Radian | |
Angular acceleration | T$^{-2}$ | Radian/second$^2$ |
Angular momentum | ML$^2$T$^{-1}$ | Kilogram-metre$^2$/second |
Angular velocity | T$^{-1}$ | Radian/second |
Area | L$^2$ | Metre$^2$ |
Energy | ML$^2$T$^{-2}$ | Joule |
Force | MLT$^{-2}$ | Newton |
Frequency | T$^{-1}$ | Cycle/second (Hertz) |
Gravitational field strength | LT$^{-2}$ | Newton/kilogram |
Mass density | ML$^{-3}$ | Kilogram/metre$^2$ |
Momentum | MLT$^{-1}$ | Kilogram-metre/second |
Power | ML$^2$T$^{-3}$ | Watt |
Pressure | ML$^{-1$}T$^{-2}$ | Newton/metre$^2$ |
Torque | ML$^2$T$^{-2}$ | Newton/metre |
Velocity | LT$^{-1}$ | Metre/second |
Work | ML$^2$T$^{-2}$ | Joule |
1.3 Multiples and sub-multiples of SI units
Prefix | Symbol | Equivalent |
---|---|---|
exa | E | $10^{18}$ |
peta | P | $10^{15}$ |
tera | T | $10^{12}$ |
giga | G | $10^9$ |
mega | M | $10^6$ |
kilo | k | $10^3$ |
hecto | h | $10^2$ |
deca | da | $10$ |
deci | d | $10^{-1}$ |
centi | c | $10^{-2}$ |
milli | m | $10^{-3}$ |
micro | $\mu$ | $10^{-6}$ |
nano | n | $10^{-9}$ |
pico | p | $10^{-12}$ |
femto | f | $10^{-15}$ |
atto | a | $10^{-18}$ |
1.4.1 Length: 1m in other units of length
Unit | Abbreviation | Value |
---|---|---|
Millimetres | mm | $1\;000$ |
Centimetres | cm | $100$ |
Metres | m | $1$ |
Kilometres | km | $0.001$ |
Inches | in | $39.37008$ |
Feet | ft | $3.28084$ |
Yards | yd | $0.093613$ |
Miles | mi | $0.000621$ |
1.4.2 Area: 1 m$^2$ in other units of area
Unit | Abbreviation | Value |
---|---|---|
Millimetre$^2$ | mm$^2$ | $1\;000\;000$ |
Centimetre$^2$ | cm$^2$ | $10\;000$ |
Metre$^2$ | m$^2$ | $1$ |
Inch$^2$ | in$^2$ | $1\;550.003$ |
Foot$^2$ | ft$^2^ | $10.76391$ |
Yard$^2$ | yd$^2$ | $1.19599$ |
1.4.3 Volume: 1 m$^3$ in other units of volume
Unit | Abbreviation | Value |
---|---|---|
Centimetre$^3$ | cm$^3$ | $1\;000\;000$ |
Metre$^3$ | m$^3$ | $1$ |
Litre | Ltr | $1\;000$ |
Inch$^3$ | in$^3$ | $61\;024$ |
Foot$^3$ | ft$^3$ | $35$ |
1.4.4 Mass: 1 kg in other units of mass
Unit | Abbreviation | Value |
---|---|---|
Grams | g | $1\;000$ |
Kilograms | kg | $1$ |
Metric tonnes | Tonne | $0.001$ |
Pounds | lb | $2.204586$ |
Ounces | oz | $35.27337$ |
1.4.5 Density
Unit | Abbreviation | Value |
---|---|---|
Gram/millilitre | g/ml | $0.001$ |
Kilogram/metre$^3$ | kg/m$^3$ | $1$ |
Pound/foot$^3$ | lb/ft$^3$ | $0.062422$ |
Pound/inch$^3$ | lb/in$^3$ | $0.000036$ |
1.4.6 Speed
Unit | Abbreviation | Value |
---|---|---|
Metre/Second | m/s | $1$ |
Kilometre/hour | km/hr | $3.599712$ |
Feet/second | ft/s | $3.28084$ |
Miles/hour | mi/hr | $2.237136$ |
1.4.7 Torque
Unit | Abbreviation | Value |
---|---|---|
Newton-metre | Nm | $1$ |
Kilogram force-metre | kgfm | $0.101972$ |
Foot-pound | ftlb | $0.737561$ |
Inch-pound | inlb | $8.850732$ |
1.4.8 Temperature conversion formulas
Unit | Conversion formulae |
---|---|
Degree Celsius ($^\circ C$) | $(^\circ F - 32)\times\frac59$ |
$(K - 273.15)$ | |
Degree Fahrenheit ($^\circ F$) | $(^\circ C\times\frac95 )+32$ |
$(1.8\times K)-459.67$ | |
Degree Kelvin ($K$) | $(^\circ C +273.15)$ |
$\displaystyle{\frac{(^\circ F + 459.67)}{1.8}}$ |
Additional Resources
- International Society of Automation Conversion Tables - an extended version of the above tables
- JPL Conversion Tables - an even more extended version from the Jet Propulsion Labs at Caltech
- Understanding Conversion Factors - video describing the concepts
- Converting Units with Conversion Factors - video giving practical examples of simple conversions
- Converting Units with Multiple Conversion Factors - similar to above with more complicated example
- Multiple Conversions Part 2 - continuation of the above video
- Converting Units in the Metric System - video from Khan Academy
- Relationships of SI Derived Units - a diagram showing relationships between most SI units.
Mobile options: