Units

SI units

• International System of Units (SI, from Système international d’unités)

	SI unit	in SI base units		dimension	quantities
$\mathrm{s}$	second	base		$\mathrm{T}$	time $t$
$\mathrm{m}$	metre	base		$\mathrm{L}$	length $l,r,x$
$\mathrm{kg}$	kilogram	base		$\mathrm{M}$	mass $m$
$\mathrm{A}$	ampere	base		$\mathrm{I}$	electric current $I,i$		$I(t)=\frac{dq(t)}{dt}$
$\mathrm{K}$	kelvin	base		$\mathrm{\Theta }$	thermodynamic temperature $T$
$\mathrm{mol}$	mole	base		$\mathrm{N}$	amount of substance $n$
$\mathrm{cd}$	candela	base		$\mathrm{J}$	luminous intensity $I_{\mathrm{v}}$
$\mathrm{Hz}$	hertz	${\mathrm{s}}^{-1}$		${\mathsf{T}}^{-1}$	frequency $f$, rotational frequency $\nu$
$\mathrm{C}$	coulomb	$\mathrm{s}\cdot \mathrm{A}$		$\mathrm{TI}$	electric charge $q$
$\mathrm{Pa}\cdot \mathrm{s}$	pascal-second	$\mathrm{kg}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{s}}^{-1}$		$\mathsf{M}{\mathsf{L}}^{-1}{\mathsf{T}}^{-1}$	dynamic viscosity $\eta$
$\mathrm{Pa}$	pascal	$\mathrm{kg}\cdot {\mathrm{m}}^{-1}\cdot {\mathrm{s}}^{-2}$		$\mathsf{M}{\mathsf{L}}^{-1}{\mathsf{T}}^{-2}$	pressure $P$	$P=F/A$
		$\mathrm{kg}\cdot \mathrm{m}\cdot {\mathrm{s}}^{-1}$		$\mathrm{ML}{\mathrm{T}}^{-1}$	momentum $p$	$p=mv$
$\mathrm{N}$	newton	${\mathrm{kg}\cdot \mathrm{m}\cdot \mathrm{s}}^{-2}$		${\mathsf{MLT}}^{-2}$	force $F$, weight $W$	$F=ma$ (Newton 2nd Law)	$F(t)=\frac{dp(t)}{dt}$
$\mathrm{J}$	joule	$\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-2}$	$\mathrm{C}\cdot \mathrm{V}$	$\mathsf{M}{\mathsf{L}}^2{\mathsf{T}}^{-2}$	energy $E$, Work $W$
$\mathrm{N}\cdot \mathrm{m}$	newton-metre	$\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-2}$		$\mathsf{M}{\mathsf{L}}^2{\mathsf{T}}^{-2}$	Torque $\tau$
$\mathrm{W}$	watt	$\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-3}$		$\mathsf{M}{\mathsf{L}}^2{\mathsf{T}}^{-3}$	power $P$, electric power $P$	$P=W/t$
$\mathrm{V}$	volt	$\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-3}\cdot {\mathrm{A}}^{-1}$		$\mathsf{M}{\mathsf{L}}^2{\mathsf{T}}^{-3}{\mathsf{I}}^{-1}$	electric potential, voltage $V,U$	$V=IR$ (Ohm’s Law)
$\mathrm{\Omega }$	ohm	$\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-3}\cdot {\mathrm{A}}^{-2}$		$\mathsf{M}{\mathsf{L}}^2{\mathsf{T}}^{-3}{\mathsf{I}}^{-2}$	electric resistance $R$	$R=V/I$ (Ohm’s Law)
		$\mathrm{m}\cdot {\mathrm{s}}^{-1}$		$\mathrm{L}{\mathrm{T}}^{-1}$	velocity $v$		$v(t)=\frac{dx(t)}{dt}$
		$\mathrm{m}\cdot {\mathrm{s}}^{-2}$		$\mathrm{L}{\mathrm{T}}^{-2}$	acceleration $a$		$a(t)=\frac{dv(t)}{dt}$
		$\mathrm{m}\cdot {\mathrm{s}}^{-3}$		$\mathrm{L}{\mathrm{T}}^{-3}$	jerk $j$		$j(t)=\frac{da(t)}{dt}$
		${\mathrm{m}}^2$		${\mathrm{L}}^2$	area $A$
		${\mathrm{m}}^3$		${\mathrm{L}}^3$	volume $V$
		$\mathrm{kg}\cdot {\mathrm{m}}^{-3}$		$\mathrm{M}{\mathrm{L}}^{-3}$	density $\rho$	$\rho =m/V$
		$\mathrm{kg}\cdot {\mathrm{m}}^2$		$\mathrm{M}{\mathrm{L}}^2$	moment of inertia $I$
	volt per meter	$\mathrm{kg}\cdot \mathrm{m}\cdot {\mathrm{s}}^{-3}\cdot {\mathrm{A}}^{-1}$		$\mathrm{ML}{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}$	electric field $E$
$\mathrm{rad}$	radian	$m/m$		dimensionless	plane angle
$\mathrm{J}\cdot \mathrm{k}{\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$		${\mathrm{m}}^2\cdot {\mathrm{s}}^{-2}\cdot {\mathrm{K}}^{-1}$		${\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{\Theta }}^{-1}$	specific heat capacity $c$
$\mathrm{rad}\cdot {\mathrm{s}}^{-1}$	radian per second	${\mathrm{s}}^{-1}$		${\mathrm{T}}^{-1}$	angular frequency $\omega$	$\omega =2\pi f$
$W/{\mathrm{m}}^2$		$\mathrm{J}\cdot {\mathrm{s}}^{-1}\cdot {\mathrm{m}}^{-2}$			intensity $I$	$I=\frac{P}{A}$ (power/area)

Other units

Mass

• SI unit: $\mathrm{kg}$
• (gram, gramme) $1\mathrm{g}=10^{-3}\mathrm{kg}$
• (tonne, (in US: metric ton)) $1\mathrm{t}=10^3\mathrm{kg}$
• (short ton, tn, st, US ton, (in US: ton)) $=2000\mathrm{lb}$
• (long ton, imperial ton, displacement ton, British ton) $=2240\mathrm{lb}$
• (pound, pound-mass) $1\mathrm{lb}=0.45359237\mathrm{kg}$
  • also denoted like: $5^{\prime \prime }$ or $5\#$
• Unified atomic mass unit

Energy

• (kilowatt-hour)
  • $1\mathrm{kWh}=3.6\times 10^6\mathrm{J}$
  • the energy consumed by a 1-kilowatt appliance in 1 hour
• (electronvolt)
  • $1\mathrm{eV}=1.6\times 10^{-19}\mathrm{J}$
  • the energy acquired by a particle carrying a charge whose magnitude equals that on the electron as a result of moving through a potential difference of $1\mathsf{V}$

calorie

• in physics/chemistry: small calorie, gram calorie, thermochemical calorie
  • $1\mathrm{cal}=4.184\mathrm{J}$
• in nutrition: large calorie, kilocalorie, Calorie, kilogram calorie
  • $1\mathrm{Cal}=4.184\mathrm{kJ}$ (also $\mathrm{kcal}$)

power

• ((imperial) horsepower, HP, BHP (brake horsepower)) $1\mathrm{hp}\approx 745.7\mathsf{W}$
• (metric horsepower, CV, PS) $1\mathrm{hp}\approx 735.5\mathsf{W}\approx 75\mathsf{k}{\mathsf{g}}_{\mathsf{f}}\cdot \mathsf{m}\cdot {\mathsf{s}}^{-1}$

force

• (kilogram-force) $1\mathrm{k}{\mathrm{g}}_{\mathrm{f}}\approx 9.8\mathsf{N}$
• (pound-force) $1\mathrm{l}{\mathrm{b}}_{\mathrm{f}}\approx 4.4482\mathsf{N}$

torque

• (kilogram-force meter, (קג”מ)) $1\mathrm{k}{\mathrm{g}}_{\mathrm{f}}\cdot \mathrm{m}\approx 9.8\mathsf{N}\cdot \mathsf{m}$
• (pound-force foot) $1\mathrm{l}{\mathrm{b}}_{\mathrm{f}}\cdot \mathrm{ft}\approx 1.3558\mathsf{N}\cdot \mathsf{m}$

rotational frequency

• (revolutions per minute, $\mathrm{r}\cdot \mathrm{mi}{\mathrm{n}}^{-1}$) $1\mathrm{rpm}=\frac{1}{60}\mathsf{Hz}$

decibels

• $L=10{\log }_{10}\left(\frac{P}{P_0}\right)$
  • $P$: power level
  • $P_0$: reference power level
• Sound Intensity Level

$L_I=10{\log }_{10}\left(\frac{I}{I_0}\right)\text{dB}$