Engineering Statics/Appendices/SI Units Used in Mechanics

SI Units Used in Mechanics

Quantity Unit SI Symbol
(Base Units)
Length meter* m
Mass kilogram kg
Time second s
(Derived Units)
Acceleration, linear meter/second2 m/s2
Acceleration, angular radian/second2 rad/s2
Area meter2 m2
Density kilogram/meter3 kg/m3
Force newton N (= kg-m/s2)
Frequency hertz Hz (= 1/s)
Impulse, linear newton-second N-s
Impulse, angular newton-meter-second N-m-s
Moment of force newton-meter N-m
Moment of inertia, area meter4 m4
Moment of inertia, mass kilogram-meter2 kg-m2
Momentum, linear kilogram-meter/second kg-m/s (= N-s)
Moment, angular kilogram-meter2/second kg-m2/s (= N-m-s)
Power watt W (= J/s = N-m/s)
Pressure, stress pascal Pa (= N/m2)
Product of inertia, area meter4 m4
Product of inertia, mass kilogram-meter2 kg-m2
Spring constant newton/meter N/m
Velocity, linear meter/second m/s
Velocity, angular radian/second rad/s
Volume meter3 m3
Work, energy joule J (= N-m)
(Supplementary and Other Acceptable Units)
Distance (navigation) nautical mile (= 1,852 km)
Mass ton (metric) t (= 1,000 kg)
Plane angle degrees (decimal) °
Plane angle radian —
Speed knot (1.852 km/h)
Time day d
Time hour h
Time minute min
* Also spelled metre
Metric prefixes
Prefix Symbol 1000m 10n Decimal Short scale Long scale Since[n 1]
yotta Y 10008 1024 1,000,000,000,000,000,000,000,000 Septillion Quadrillion 1991
zetta Z 10007 1021 1,000,000,000,000,000,000,000 Sextillion Trilliard 1991
exa E 10006 1018 1,000,000,000,000,000,000 Quintillion Trillion 1975
peta P 10005 1015 1,000,000,000,000,000 Quadrillion Billiard 1975
tera T 10004 1012 1,000,000,000,000 Trillion Billion 1960
giga G 10003 109 1,000,000,000 Billion Milliard 1960
mega M 10002 106 1,000,000 Million 1960
kilo k 10001 103 1000 Thousand 1795
hecto h 10002/3 102 100 Hundred 1795
deca da 10001/3 101 10 Ten 1795
10000 100 1 One –
deci d 1000−1/3 10−1 0.1 Tenth 1795
centi c 1000−2/3 10−2 0.01 Hundredth 1795
milli m 1000−1 10−3 0.001 Thousandth 1795
micro μ 1000−2 10−6 0.000001 Millionth 1960
nano n 1000−3 10−9 0.000000001 Billionth Milliardth 1960
pico p 1000−4 10−12 {0.000000000001 Trillionth Billionth 1960
femto f 1000−5 10−15 0.000000000000001 Quadrillionth Billiardth 1964
atto a 1000−6 10−18 0.000000000000000001 Quintillionth Trillionth 1964
zepto z 1000−7 10−21 0.000000000000000000001 Sextillionth Trilliardth 1991
yocto y 1000−8 10−24 0.000000000000000000000001 Septillionth Quadrillionth 1991
  1. ↑ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.

Selected Rules for Writing Metric Quantities

  • For readability, use unit prefixes such that the number is between 0.1 and 1000.
  • The most common prefixes in engineering are giga, mega, kilo, centi, milli, and micro. Prefixes like hecto, deka, and deci make for awkward numbers.
  • Unit combinations should only use prefixes in the numerator (write kJ/s instead of J/ms), with the exception of kg.
  • Do not double up the prefixes, e.g. write GW not kMW.
  • Use a dot to multiply units (write N•m not Nm)
  • Avoid the ambiguity of multiple divisions (write N/m3 not N/m/m/m)
  • Exponents refer to the entire unit symbol (mm2 means (mm)2)
  • Use spaces instead of commas to make long numbers easier to read (e.g. 1 210 000 000.001 W), ignore for numbers of four digits.
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