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 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

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.