Appendix A: Units

Table A1 Units Used in Physics (Fundamental units in bold)
Quantity	Common Symbol	Unit	Unit in Terms of Base SI Units
Acceleration	$\vec{a}$	m/s²	m/s²
Amount of substance	n	mole	mol
Angle	$θ, ϕ$	radian (rad)
Angular acceleration	$\vec{α}$	rad/s²	s⁻²
Angular frequency	$ω$	rad/s	s⁻¹
Angular momentum	$\vec{L}$	$kg \cdot m^{2} /s$	$kg \cdot m^{2} /s$
Angular velocity	$\vec{ω}$	rad/s	s⁻¹
Area	A	m²	m²
Atomic number	Z
Capacitance	C	farad (F)	$A^{2} \cdot s^{4} / kg \cdot m^{2}$
Charge	q, Q, e	coulomb (C)	$A \cdot s$
Charge density:
Line	$λ$	C/m	$A \cdot s/m$
Surface	$σ$	C/m²	$A \cdot {s/m}^{2}$
Volume	$ρ$	C/m³	$A \cdot {s/m}^{3}$
Conductivity	$σ$	$1/ Ω \cdot m$	$A^{2} \cdot s^{3} /kg \cdot m^{3}$
Current	I	ampere	A
Current density	$\vec{J}$	A/m²	A/m²
Density	$ρ$	kg/m³	kg/m³
Dielectric constant	$κ$
Electric dipole moment	$\vec{p}$	$C \cdot m$	$A \cdot s \cdot m$
Electric field	$\vec{E}$	N/C	$kg \cdot m/A \cdot s^{3}$
Electric flux	$Φ$	$N \cdot m^{2} / C$	$kg \cdot m^{3} /A \cdot s^{3}$
Electromotive force	$ε$	volt (V)	$kg \cdot m^{2} /A \cdot s^{3}$
Energy	E,U,K	joule (J)	$kg \cdot m^{2} {/s}^{2}$
Entropy	S	J/K	$kg \cdot m^{2} {/s}^{2} \cdot K$
Force	$\vec{F}$	newton (N)	$kg \cdot {m/s}^{2}$
Frequency	f	hertz (Hz)	s⁻¹
Heat	Q	joule (J)	$kg \cdot m^{2} {/s}^{2}$
Inductance	L	henry (H)	$kg \cdot m^{2} {/A}^{2} \cdot s^{2}$
Length:	$ℓ, L$	meter	m
Displacement	$Δ x, Δ \vec{r}$
Distance	d, h
Position	$x, y, z, \vec{r}$
Magnetic dipole moment	$\vec{μ}$	$N \cdot J/T$	$A \cdot m^{2}$
Magnetic field	$\vec{B}$	tesla (T) $= ({Wb/m}^{2})$	$kg/A \cdot s^{2}$
Magnetic flux	$Φ_{m}$	weber (Wb)	$kg \cdot m^{2} /A \cdot s^{2}$
Mass	m, M	kilogram	kg
Molar specific heat	C	$J/mol \cdot K$	$kg \cdot m^{2} {/s}^{2} \cdot mol \cdot K$
Moment of inertia	I	$kg \cdot m^{2}$	$kg \cdot m^{2}$
Momentum	$\vec{p}$	$kg \cdot m/s$	$kg \cdot m/s$
Period	T	s	s
Permeability of free space	$μ_{0}$	${N/A}^{2} = (H/m)$	$kg \cdot {m/A}^{2} \cdot s^{2}$
Permittivity of free space	$ε_{0}$	$C^{2} /N \cdot m^{2} = (F/m)$	$A^{2} \cdot s^{4} /kg \cdot m^{3}$
Potential	V	volt (V) $= (J/C)$	$kg \cdot m^{2} /A \cdot s^{3}$
Power	P	watt (W) $= (J/s)$	$kg \cdot m^{2} {/s}^{3}$
Pressure	p	pascal (P) $= ({N/m}^{2})$	$kg/m \cdot s^{2}$
Resistance	R	ohm (Ω) $= (V/A)$	$kg \cdot m^{2} {/A}^{2} \cdot s^{3}$
Specific heat	c	$J/kg \cdot K$	$m^{2} {/s}^{2} \cdot K$
Speed	$ν$	m/s	m/s
Temperature	T	kelvin	K
Time	t	second	s
Torque	$\vec{τ}$	$N \cdot m$	$kg \cdot m^{2} {/s}^{2}$
Velocity	$\vec{v}$	m/s	m/s
Volume	V	m³	m³
Wavelength	$λ$	m	m
Work	W	joule (J) $= (N \cdot m)$	$kg \cdot m^{2} {/s}^{2}$

This table has four columns, labeled: Quantity, Common Symbol, Unit and Unit in Terms of Base SI Units. Each row describes one quantity as follows: Acceleration, vector a, meters per second squared, meters per second squared; Amount of substance, n mole, mol; Angle, theta or phi, radian; Angular acceleration, vector alpha, radians per second squared, s raised to minus 2; Angular frequency, omega, radians per second, second raised to minus 1; Angular momentum, vector L, kg meter squared per second, kg meter squared per second; Angular velocity, vector omega, radians per second, second raised to minus 1; Area, A, meter squared, meter squared; Atomic number, Z; Capacitance, C, farad, A squared s to the power 4 by kg meter squared; Charge, q or Q or e, coulomb, A into s; Charge density of Line, lambda, C by m, A into s by m; Charge density of Surface, sigma, C by m squared, A into s by m squared; Charge density of Volume, rho, C by m cubed, A into s by m cubed; Conductivity, sigma, 1 by ohm meter, A squared into s cubed by kg meter cubed; Current, I, ampere, A; Current density, vector J, A by m square, A by m squared; Density, rho, kg per meter cubed, kg per meter cubed; Dielectric constant, , kappa; Electric dipole moment, vector p, C into m, A into s into m; Electric field, vector e, V by m, kg meter by A s cubed; Electric flux, phi, V m, kg meter cubed by A s cubed; Electromotive force, epsilon, volt V, kg meter squared by A s cubed; Energy, E or U or K, joule J, kg meter squared per second squared; Entropy, S, J by K, kg meter squared by second squared K; Force, vector F, newton N, kg into m per second squared; Frequency, f, hertz Hz, s to the power minus 1; Heat, joule J, kg meter squared per second squared; Inductance, L, henry H, kg meter squared by A squared s squared; Length, l or L, meter, m; Length Displacement, delta x or delta vector r; Length Distance, d, h; Length Position, x, y, z, vector r; Magnetic dipole moment, vector mu, N m by T, A into m squared; Magnetic field, vector B, tesla T equal to Wb by m squared, kg by A s squared; Magnetic flux, phi subscript m, weber Wb, kg m squared by A s squared; Mass, m or M, kilogram, kg; Molar specific heat, C, J by mol K, kg meter squared by s squared mole k; Moment of inertia, I, kg meter squared, kg meter squared; Momentum, vector p, kg m per second, kg meter per second; Period, T, s, s; Permeability of free space, mu subscript 0, N by A squared equal to H by m; kg into meter by A squared s squared; Permittivity of free space, epsilon subscript 0, C squared by N m squared equal to F by m, A squared s to the power 4 by kg meter cubed; Potential, V, volt V equal to J by C, kg meter squared by A s cubed; Power, P, watt W equal to J by s, kg meter squared by second cubed; Pressure, p, pascal Pa equal to N by m squared, kg per meter second squared; Resistance, R ohm omega equal to V by A, kg meter squared by A squared s cubed; Specific heat, C, J by kg K, m squared by s squared K; Speed, v, m by s, m by s; Temperature, T, Kelvin, K; Time, T, second, s; Torque, vector tau, N m, kg meter squared per second squared; Velocity, vector v, m by s, m by s; Volume, V, m cubed, m cubed; Wavelength, lambda, m, m; Work, W, joule J equal to N m, kg meter squared per second squared.