List of common physics notations

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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

[edit ]

Symbol	Meaning	SI unit of measure
$\mathbf {A}$ {\displaystyle \mathbf {A} }	magnetic vector potential	tesla meter (T⋅m)
$A$ {\displaystyle A}	area	square meter (m²)
	amplitude	meter
	atomic mass number	unitless
$\mathbf {a}$ {\displaystyle \mathbf {a} }	acceleration	meter per second squared (m/s²)
$\mathbf {B}$ {\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)
$\mathbf {D}$ {\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)
$D$ {\displaystyle D}	diameter	meter (m)
$d$ {\displaystyle d}	distance	meter (m)
	direction	unitless
	impact parameter	meter (m)
	differential (e.g. $dx$ {\displaystyle dx})	varied depending on context
$d\mathbf {A}$ {\displaystyle d\mathbf {A} }	differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S	square meter (m²)
$dV$ {\displaystyle dV}	differential element of volume V enclosed by surface S	cubic meter (m³)
$\mathbf {E}$ {\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)
$E$ {\displaystyle E}	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)
$\mathbf {F}$ {\displaystyle \mathbf {F} }	force	newton (N)
$F$ {\displaystyle F}	Faraday constant	coulombs per mole (C⋅mol⁻¹)
$f$ {\displaystyle f}	frequency	hertz (Hz)
	function
	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)
$\mathbf {g}$ {\displaystyle \mathbf {g} }	acceleration due to gravity	meters per second squared (m/s²), or equivalently, newtons per kilogram (N/kg)
$\mathbf {H}$ {\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)
$h$ {\displaystyle h}	Planck constant	joule second (J⋅s)
$\hbar$ {\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)
$\mathbf {\hat {\imath }}$ {\displaystyle \mathbf {\hat {\imath }} }	Cartesian x-axis basis unit vector	unitless
$\mathbf {J}$ {\displaystyle \mathbf {J} }	current density	ampere per square meter (A/m²)
$\mathbf {J}$ {\displaystyle \mathbf {J} }	impulse	kilogram meter per second (kg⋅m/s)
$\mathbf {j}$ {\displaystyle \mathbf {j} }	jerk	meter per second cubed (m/s³)
$j$ {\displaystyle j}	imaginary unit (electrical)	unitless
$\mathbf {\hat {\jmath }}$ {\displaystyle \mathbf {\hat {\jmath }} }	Cartesian y-axis basis unit vector	unitless
$K$ {\displaystyle K}	kinetic energy	joule (J)
$\mathbf {k}$ {\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)
$\mathbf {\hat {k}}$ {\displaystyle \mathbf {\hat {k}} }	Cartesian z-axis basis unit vector	unitless
$\mathbf {L}$ {\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)
${\mathcal {L}}$ {\displaystyle {\mathcal {L}}}	Lagrangian density	joule per cubic meter (J/m³)
$l$ {\displaystyle l}	length	meter (m)
l	azimuthal quantum number	unitless
$\mathbf {M}$ {\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)
$\mathbf {N}$ {\displaystyle \mathbf {N} }	normal vector	unit varies depending on context
$N$ {\displaystyle N}	atomic 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
$\mathbf {p}$ {\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 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)
$\mathbf {r}$ {\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)
$\mathbf {s}$ {\displaystyle \mathbf {s} }	displacement	meter (m)
$s$ {\displaystyle s}	arc length	meter (m)
$s$ {\displaystyle s}	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)
$\mathbf {U}$ {\displaystyle \mathbf {U} }	four-velocity	meter per second (m/s)
$U$ {\displaystyle U}	potential energy	joule (J)
$U$ {\displaystyle U}	internal energy	joule (J)
$u$ {\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
$\mathbf {v}$ {\displaystyle \mathbf {v} }	velocity	meter per second (m/s)
$W$ {\displaystyle W}	weight	newton (N)
$W$ {\displaystyle W}	mechanical work	joule (J)
$w$ {\displaystyle w}	width	meter (m)
$X$ {\displaystyle X}	electrical reactance	ohm (Ω)
$\mathbf {x}$ {\displaystyle \mathbf {x} }	position vector	meter (m)
$\mathbf {x}$ {\displaystyle \mathbf {x} }	displacement	meter (m)
$x$ {\displaystyle x}	a generic unknown	varied depending on context
$Y$ {\displaystyle Y}	admittance	siemens (S)
$Z$ {\displaystyle Z}	compressibility factor	unitless
$Z$ {\displaystyle Z}	electrical impedance	ohm (Ω)
$Z_{0}$ {\displaystyle Z_{0}}	impedance of free space	ohm (Ω)

Greek characters

[edit ]

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

Other characters

[edit ]

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

References

[edit ]

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

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