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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

Symbol Meaning SI unit of measure
A {\displaystyle \mathbf {A} } magnetic vector potential tesla meter (T⋅m)
A {\displaystyle A} area square meter (m)
amplitude meter
atomic mass number unitless
a {\displaystyle \mathbf {a} } acceleration meter per second squared (m/s)
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/m)
C {\displaystyle C} capacitance farad (F)
heat capacity joule per kelvin (J⋅K)
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⋅K)
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/m)
D {\displaystyle D} density kilogram per cubic meter (kg/m)
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 (m)
d V {\displaystyle dV} differential element of volume V enclosed by surface S cubic meter (m)
E {\displaystyle \mathbf {E} } electric field newton per coulomb (N⋅C), or equivalently, volt per meter (V⋅m)
E {\displaystyle E} energy joule (J)
Young's modulus pascal (Pa) or newton per square meter (N/m)
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)
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⋅m/kg)
shear modulus pascal (Pa) or newton per square meter (N/m)
g {\displaystyle \mathbf {g} } acceleration due to gravity meters per second squared (m/s), 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)
{\displaystyle \hbar } reduced Planck constant joule second (J⋅s)
I {\displaystyle I} action joule second (J⋅s)
intensity watt per square meter (W/m)
sound intensity watt per square meter (W/m)
electric current ampere (A)
moment of inertia kilogram meter squared (kg⋅m)
i {\displaystyle i} intensity watt per square meter (W/m)
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/m)
impulse kilogram meter per second (kg⋅m/s)
j {\displaystyle \mathbf {j} } jerk meter per second cubed (m/s)
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)
k {\displaystyle k} Boltzmann constant joule per kelvin (J/K)
wavenumber radian per meter (m)
stiffness newton per meter (N⋅m)
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⋅m⋅s)
L {\displaystyle L} inductance henry (H)
luminosity watt (W)
Lagrangian joule (J)
L {\displaystyle {\mathcal {L}}} Lagrangian density joule per cubic meter (J/m)
l {\displaystyle l} length meter (m)
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} atomic number unitless
n {\displaystyle n} refractive index unitless
principal quantum number unitless
amount of substance mole
P {\displaystyle P} 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)
q {\displaystyle q} electric charge coulomb (C)
R {\displaystyle R} electrical resistance ohm (Ω)
Ricci tensor reciprocal square meter (m)
radiancy meter per second
gas constant joule per mole per kelvin (J⋅mol⋅K)
r {\displaystyle \mathbf {r} } radius vector (position) meter (m)
r {\displaystyle r} radius or distance meter (m)
S {\displaystyle S} surface area square meter (m)
entropy joule per kelvin (J/K)
action joule second (J⋅s)
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 {\displaystyle u} relativistic mass kilogram (kg)
energy density joule per cubic meter (J/m)
specific energy joule per kilogram (J/kg)
V {\displaystyle V} voltage
also called electric potential difference
volt (V)
volume cubic meter (m)
shear force
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} 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/s)
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)
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)
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)
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⋅m)
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 (m/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/m)
volume charge density coulomb per cubic meter (C/m)
resistivity ohm meter (Ω⋅m)
Σ {\displaystyle \Sigma } sigma summation operator
σ {\displaystyle \sigma } area charge density coulomb per square meter (C/m)
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... () 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
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)
× {\displaystyle \nabla \times } nabla cross the curl operator
often pronounced "del cross"
per meter (m)
{\displaystyle \nabla } nabla delta (differential operator)
{\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

References

  • 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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