List of common physics notations

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

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Latin characters

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

Greek characters

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

Other characters

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

References

Elert, Glenn. "Special Symbols". The Physics Hypertextbook. Retrieved 4 August 2021.
NIST (16 August 2023). "SI Units". www.nist.gov. NIST.

Common mathematical notation, symbols, and formulas

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This page was last edited on 4 April 2024, at 21:57

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