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

QuantityDimensionsUnits
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

PrefixSymbolEquivalent
exaE$10^{18}$
petaP$10^{15}$
teraT$10^{12}$
gigaG$10^9$
megaM$10^6$
kilok$10^3$
hectoh$10^2$
decada$10$
decid$10^{-1}$
centic$10^{-2}$
millim$10^{-3}$
micro$\mu$$10^{-6}$
nanon$10^{-9}$
picop$10^{-12}$
femtof$10^{-15}$
attoa$10^{-18}$

1.4.1 Length: 1m in other units of length

UnitAbbreviationValue
Millimetresmm$1\;000$
Centimetrescm$100$
Metresm$1$
Kilometreskm$0.001$
Inchesin$39.37008$
Feetft$3.28084$
Yardsyd$0.093613$
Milesmi$0.000621$

1.4.2 Area: 1 m$^2$ in other units of area

UnitAbbreviationValue
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

UnitAbbreviationValue
Centimetre$^3$cm$^3$$1\;000\;000$
Metre$^3$m$^3$$1$
LitreLtr$1\;000$
Inch$^3$in$^3$$61\;024$
Foot$^3$ft$^3$$35$

1.4.4 Mass: 1 kg in other units of mass

UnitAbbreviationValue
Gramsg$1\;000$
Kilogramskg$1$
Metric tonnesTonne$0.001$
Poundslb$2.204586$
Ouncesoz$35.27337$

1.4.5 Density

UnitAbbreviationValue
Gram/millilitreg/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

UnitAbbreviationValue
Metre/Secondm/s$1$
Kilometre/hourkm/hr$3.599712$
Feet/secondft/s$3.28084$
Miles/hourmi/hr$2.237136$

1.4.7 Torque

UnitAbbreviationValue
Newton-metreNm$1$
Kilogram force-metrekgfm$0.101972$
Foot-poundftlb$0.737561$
Inch-poundinlb$8.850732$

1.4.8 Temperature conversion formulas

UnitConversion 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 ($K$)$(^\circ C +273.15)$
 $\displaystyle{\frac{(^\circ F + 459.67)}{1.8}}$

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