Variables commonly used in physics

This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector.

Latin characters

Symbol	Meaning	SI unit of measure
A {\displaystyle \mathbf {A} }	magnetic vector potential	tesla meter (T⋅m)
A {\displaystyle A}	area	square meter (m2)
	amplitude	meter
	atomic mass number	unitless
a {\displaystyle \mathbf {a} }	acceleration	meter per second squared (m/s2)
B {\displaystyle \mathbf {B} }	magnetic flux density also called the magnetic field density or magnetic induction	tesla (T), or equivalently, weber per square meter (Wb/m2)
C {\displaystyle C}	capacitance	farad (F)
	heat capacity	joule per kelvin (J⋅K−1)
	constant of integration	varied depending on context
c {\displaystyle c}	speed of light (in vacuum)	299,792,458 meters per second (m/s)
	speed of sound	meter per second (m/s)
	specific heat capacity	joule per kilogram per kelvin (J⋅kg−1⋅K−1)
	viscous damping coefficient	kilogram per second (kg/s)
D {\displaystyle \mathbf {D} }	electric displacement field also called the electric flux density	coulomb per square meter (C/m2)
D {\displaystyle D}	density	kilogram per cubic meter (kg/m3)
	diameter	meter (m)
d {\displaystyle d}	distance	meter (m)
	direction	unitless
	impact parameter	meter (m)
	differential (e.g. d x {\displaystyle dx} )	varied depending on context
d A {\displaystyle d\mathbf {A} }	differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S	square meter (m2)
d V {\displaystyle dV}	differential element of volume V enclosed by surface S	cubic meter (m3)
E {\displaystyle \mathbf {E} }	electric field	newton per coulomb (N⋅C−1), or equivalently, volt per meter (V⋅m−1)
E {\displaystyle E}	energy	joule (J)
	Young's modulus	pascal (Pa) or newton per square meter (N/m2)
e {\displaystyle e}	eccentricity	unitless
	Euler's number (2.71828, base of the natural logarithm)	unitless
	electron	unitless
	elementary charge	coulomb (C)
F {\displaystyle \mathbf {F} }	force	newton (N)
F {\displaystyle F}	Faraday constant	coulombs per mole (C⋅mol−1)
f {\displaystyle f}	frequency	hertz (Hz)
	function	unitless
	friction	newton (N)
G {\displaystyle G}	electrical conductance	siemens (S)
	universal gravitational constant	newton meter squared per kilogram squared (N⋅m2/kg2)
	shear modulus	pascal (Pa) or newton per square meter (N/m2)
	gluon field strength tensor	inverse length squared (1/m2)
g {\displaystyle \mathbf {g} }	acceleration due to gravity	meters per second squared (m/s2), or equivalently, newtons per kilogram (N/kg)
H {\displaystyle \mathbf {H} }	magnetic field strength	ampere per meter (A/m)
H {\displaystyle H}	Hamiltonian	joule (J)
	enthalpy	joule (J)
	thermal current	watt (W)
h {\displaystyle h}	height	meter (m)
	Planck constant	joule second (J⋅s)
ℏ {\displaystyle \hbar }	reduced Planck constant	joule second (J⋅s)
I {\displaystyle I}	action	joule second (J⋅s)
	intensity	watt per square meter (W/m2)
	sound intensity	watt per square meter (W/m2)
	electric current	ampere (A)
	moment of inertia	kilogram meter squared (kg⋅m2)
i {\displaystyle i}	intensity	watt per square meter (W/m2)
	imaginary unit	unitless
	electric current	ampere (A)
ı ^ {\displaystyle \mathbf {\hat {\imath }} }	Cartesian x-axis basis unit vector	unitless
J {\displaystyle \mathbf {J} }	current density	ampere per square meter (A/m2)
	impulse	kilogram meter per second (kg⋅m/s)
j {\displaystyle \mathbf {j} }	jerk	meter per second cubed (m/s3)
j {\displaystyle j}	imaginary unit (electrical)	unitless
ȷ ^ {\displaystyle \mathbf {\hat {\jmath }} }	Cartesian y-axis basis unit vector	unitless
K {\displaystyle K}	kinetic energy	joule (J)
k {\displaystyle \mathbf {k} }	wave vector	radian per meter (m−1)
k {\displaystyle k}	Boltzmann constant	joule per kelvin (J/K)
	wavenumber	radian per meter (m−1)
	stiffness	newton per meter (N⋅m−1)
k ^ {\displaystyle \mathbf {\hat {k}} }	Cartesian z-axis basis unit vector	unitless
L {\displaystyle \mathbf {L} }	angular momentum	newton meter second (N⋅m⋅s or kg⋅m2⋅s−1)
L {\displaystyle L}	inductance	henry (H)
	luminosity	watt (W)
	Lagrangian	joule (J)
L {\displaystyle {\mathcal {L}}}	Lagrangian density	joule per cubic meter (J/m3)
l {\displaystyle l}	length	meter (m)
ℓ	azimuthal quantum number	unitless
M {\displaystyle \mathbf {M} }	magnetization	ampere per meter (A/m)
M {\displaystyle M}	moment of force often simply called moment or torque	newton meter (N⋅m)
m {\displaystyle m}	mass	kilogram (kg)
N {\displaystyle \mathbf {N} }	normal vector	unit varies depending on context
N {\displaystyle N}	neutron number	unitless
n {\displaystyle n}	refractive index	unitless
	principal quantum number	unitless
	amount of substance	mole
P {\displaystyle P}	power	watt (W)
	active power (real power)	watt (W)
	probability	unitless
p {\displaystyle \mathbf {p} }	momentum	kilogram meter per second (kg⋅m/s)
p {\displaystyle p}	pressure	pascal (Pa)
Q {\displaystyle Q}	electric charge	coulomb (C)
	heat	joule (J)
	Reactive Power	volt-ampere reactive (var)
q {\displaystyle \mathbf {q} }	Generalized coordinates	varied depending on context (sometimes meter (m) or radian (rad))
q {\displaystyle q}	electric charge	coulomb (C)
R {\displaystyle R}	electrical resistance	ohm (Ω)
	Ricci tensor	reciprocal square meter (m−2)
	radiancy	meter per second
	gas constant	joule per mole per kelvin (J⋅mol−1⋅K−1)
r {\displaystyle \mathbf {r} }	radius vector (position)	meter (m)
r {\displaystyle r}	radius or distance	meter (m)
S {\displaystyle S}	surface area	square meter (m2)
	entropy	joule per kelvin (J/K)
	action	joule second (J⋅s)
	apparent power (complex power)	Volt-Ampere (VA)
s {\displaystyle \mathbf {s} }	displacement	meter (m)
s {\displaystyle s}	arc length	meter (m)
	distance	meter (m)
T {\displaystyle T}	period	second (s)
	temperature	kelvin (K) or Celsius (C)
	kinetic energy	joule (J)
t {\displaystyle t}	time	second (s)
U {\displaystyle \mathbf {U} }	four-velocity	meter per second (m/s)
U {\displaystyle U}	potential energy	joule (J)
	internal energy	joule (J)
u	initial velocity	meter per second (m/s)
u {\displaystyle u}	relativistic mass	kilogram (kg)
	energy density	joule per cubic meter (J/m3)
	specific energy	joule per kilogram (J/kg)
V {\displaystyle V}	voltage also called electric potential difference	volt (V)
	volume	cubic meter (m3)
	shear force	newton (N)
v {\displaystyle \mathbf {v} }	velocity	meter per second (m/s)
W {\displaystyle W}	weight	newton (N)
	mechanical work	joule (J)
w {\displaystyle w}	width	meter (m)
X {\displaystyle X}	electrical reactance	ohm (Ω)
x {\displaystyle \mathbf {x} }	position vector	meter (m)
	displacement	meter (m)
x {\displaystyle x}	a generic unknown	varied depending on context
Y {\displaystyle Y}	admittance	siemens (S)
Z {\displaystyle Z}	atomic number	unitless
	compressibility factor	unitless
	electrical impedance	ohm (Ω)
Z 0 {\displaystyle Z_{0}}	impedance of free space	ohm (Ω)

Greek characters

Symbol	Name	Meaning	SI unit of measure
α {\displaystyle \alpha }	alpha	alpha particle
		angular acceleration	radian per second squared (rad/s2)
		fine-structure constant	unitless
β {\displaystyle \beta }	beta	velocity in terms of the speed of light c	unitless
		beta particle
γ {\displaystyle \gamma }	gamma	Lorentz factor	unitless
		photon
		gamma ray
		shear strain	radian
		heat capacity ratio	unitless
		surface tension	newton per meter (N/m)
Δ {\displaystyle \Delta }	delta	change in a variable (e.g. Δ x {\displaystyle \Delta x} )	unitless
		Laplace operator	per square meter (m−2)
δ {\displaystyle \delta }		displacement (usually small)	meter (m)
		Dirac delta function
		Kronecker delta (e.g δ i j {\displaystyle \delta _{ij}} )
ϵ {\displaystyle \epsilon }	epsilon	permittivity	farad per meter (F/m)
		strain	unitless
ε 0 {\displaystyle \varepsilon _{0}}	epsilon nought	Vacuum permittivity	farad per meter (F/m)
ζ {\displaystyle \zeta }	zeta	damping ratio	unitless
η {\displaystyle \eta }	eta	angular jerk	radian per second cubed (rad⋅s−3)
		energy efficiency	unitless
		(dynamic) viscosity (also μ {\displaystyle \mu } )	pascal second (Pa⋅s)
θ {\displaystyle \theta }	theta	angular displacement	radian (rad)
κ {\displaystyle \kappa }	kappa	torsion coefficient also called torsion constant	newton meter per radian (N⋅m/rad)
Λ {\displaystyle \Lambda }	lambda	cosmological constant	per second squared (s−2)
λ {\displaystyle \lambda }		wavelength	meter (m)
		linear charge density	coulomb per meter (C/m)
		eigenvalue	non-zero vector
μ {\displaystyle \mathbf {\mu } }	mu	magnetic moment	ampere square meter (A⋅m2)
		coefficient of friction	unitless
		(dynamic) viscosity (also η {\displaystyle \eta } )	pascal second (Pa⋅s)
		permeability (electromagnetism)	henry per meter (H/m)
		reduced mass	kilogram (kg)
		Standard gravitational parameter	cubic meter per second squared
μ 0 {\displaystyle \mathbf {\mu } _{0}}	mu nought	Vacuum permeability or the magnetic constant	henry per meter (H/m)
ν {\displaystyle \nu }	nu	frequency	hertz (Hz)
		kinematic viscosity	meter squared per second (m2/s)
		neutrino
ξ {\displaystyle \xi }	xi	electromotive force	volt (V)
π {\displaystyle \pi }	pi	3.14159... (irrational number)	unitless
ρ {\displaystyle \rho }	rho	mass density usually simply called density	kilogram per cubic meter (kg/m3)
		volume charge density	coulomb per cubic meter (C/m3)
		resistivity	ohm meter (Ω⋅m)
Σ {\displaystyle \Sigma }	sigma	summation operator
σ {\displaystyle \sigma }		area charge density	coulomb per square meter (C/m2)
		electrical conductivity	siemens per meter (S/m)
		normal stress	pascal (Pa)
		scattering cross section	barn (10^-28 m^2)
		surface tension	newton per meter (N/m)
τ {\displaystyle \tau }	tau	torque	newton meter (N⋅m)
		shear stress	pascal (Pa)
		time constant	second (s)
		6.28318... (2π)	unitless
Φ {\displaystyle \Phi }	phi	field strength	unit varies depending on context
		magnetic flux	weber (Wb)
ϕ {\displaystyle \phi }		electric potential	volt (V)
		Higgs field work function
Ψ {\displaystyle \Psi }	psi	wave function	m−3/2
Ω {\displaystyle \Omega }	omega	electric resistance	ohm
ω {\displaystyle \omega }		angular frequency	radian per second (rad/s)
		angular velocity	radian per second (rad/s)

Other characters

Symbol	Name	Meaning	SI unit of measure
∇ ⋅ {\displaystyle \nabla \cdot }	nabla dot	the divergence operator often pronounced "del dot"	per meter (m−1)
∇ × {\displaystyle \nabla \times }	nabla cross	the curl operator often pronounced "del cross"	per meter (m−1)
∇ {\displaystyle \nabla }	nabla	the gradient operator	per meter (m−1)
∂ {\displaystyle \partial }	"der", "dow", "die", "partial" or simply "d"	partial derivative (e.g. ∂ y / ∂ x {\displaystyle \partial y/\partial x} )
◻ {\displaystyle \Box }	D'Alembert operator	∇ 2 − ∂ t 2 {\displaystyle \nabla ^{2}-\partial _{t}^{2}}
⟨ ⟩ {\displaystyle \langle \,\,\rangle }	angle brackets	average sometimes over Maxwell–Boltzmann distribution
⟨   |   ⟩ {\displaystyle \langle \ |\ \rangle }		Dirac notation
∫ {\displaystyle \int }	integral	the inverse of the derivative.	unitless

See also

• List of letters used in mathematics and science
• Glossary of mathematical symbols
• List of mathematical uses of Latin letters
• Greek letters used in mathematics, science, and engineering
• Physical constant
• Physical quantity
• International System of Units
• ISO 31

References