# 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$^2$
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$$10^{-6} nanon10^{-9} picop10^{-12} femtof10^{-15} attoa10^{-18} #### 1.4.1 Length: 1m in other units of length UnitAbbreviationValue Millimetresmm1\;000 Centimetrescm100 Metresm1 Kilometreskm0.001 Inchesin39.37008 Feetft3.28084 Yardsyd0.093613 Milesmi0.000621 #### 1.4.2 Area: 1 m^2 in other units of area UnitAbbreviationValue Millimetre^2mm^2$$1\;000\;000$
Centimetre$^2$cm$^2$$10\;000 Metre^2m^2$$1$
Inch$^2$in$^2$$1\;550.003 Foot^2ft^2^10.76391 Yard^2yd^2$$1.19599$

#### 1.4.3 Volume: 1 m$^3$ in other units of volume

UnitAbbreviationValue
Centimetre$^3$cm$^3$$1\;000\;000 Metre^3m^3$$1$
LitreLtr$1\;000$
Inch$^3$in$^3$$61\;024 Foot^3ft^3$$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$$1 Pound/foot^3lb/ft^3$$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 ($K$)$(^\circ C +273.15)$
$\displaystyle{\frac{(^\circ F + 459.67)}{1.8}}$