Physics: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 |
|---|---|---|
| [math]\displaystyle{ \mathbf{A} }[/math] | magnetic vector potential | tesla meter (T⋅m) |
| [math]\displaystyle{ A }[/math] | area | square meters (m2) |
| amplitude | meter | |
| atomic mass number | unitless | |
| [math]\displaystyle{ \mathbf{a} }[/math] | acceleration | meters per second squared (m/s2) |
| [math]\displaystyle{ \mathbf{B} }[/math] | magnetic flux density also called the magnetic field density or magnetic induction |
tesla (T), or equivalently, weber per square meter (Wb/m2) |
| [math]\displaystyle{ C }[/math] | capacitance | farad (F) |
| heat capacity | joule per kelvin (J⋅K−1) | |
| constant of integration | varied depending on context | |
| [math]\displaystyle{ c }[/math] | speed of light (in vacuum) | 299,792,458 meters per second (m/s) |
| speed of sound | meters 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) | |
| [math]\displaystyle{ \mathbf{D} }[/math] | electric displacement field also called the electric flux density |
coulomb per square meter (C/m2) |
| [math]\displaystyle{ D }[/math] | density | kilograms per cubic meter (kg/m3) |
| diameter | meter (m) | |
| [math]\displaystyle{ d }[/math] | distance | meter (m) |
| direction | unitless | |
| impact parameter | meter (m) | |
| differential (e.g. [math]\displaystyle{ dx }[/math]) | varied depending on context | |
| [math]\displaystyle{ d\mathbf{A} }[/math] | differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S | square meter (m2) |
| [math]\displaystyle{ dV }[/math] | differential element of volume V enclosed by surface S | cubic meter (m3) |
| [math]\displaystyle{ \mathbf{E} }[/math] | electric field | newton per coulomb (N⋅C−1), or equivalently, volt per meter (V⋅m−1) |
| [math]\displaystyle{ E }[/math] | energy | joule (J) |
| Young's modulus | pascal (Pa) or newton per square meter (N/m2) | |
| [math]\displaystyle{ e }[/math] | eccentricity | unitless |
| 2.71828... (base of the natural logarithm) | unitless | |
| electron | unitless | |
| elementary charge | coulomb (C) | |
| [math]\displaystyle{ \mathbf{F} }[/math] | force | newton (N) |
| [math]\displaystyle{ F }[/math] | Faraday constant | coulombs per mole (C⋅mol−1) |
| [math]\displaystyle{ f }[/math] | frequency | hertz (Hz) |
| function | ||
| friction | newton (N) | |
| [math]\displaystyle{ G }[/math] | 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) | |
| [math]\displaystyle{ \mathbf{g} }[/math] | acceleration due to gravity | meters per second squared (m/s2), or equivalently, newtons per kilogram (N/kg) |
| [math]\displaystyle{ \mathbf{H} }[/math] | magnetic field strength | ampere per meter (A/m) |
| [math]\displaystyle{ H }[/math] | Hamiltonian | joule (J) |
| enthalpy | joule (J) | |
| thermal current | watt (W) | |
| [math]\displaystyle{ h }[/math] | height | meter (m) |
| Planck constant | joule second (J⋅s) | |
| [math]\displaystyle{ \hbar }[/math] | reduced Planck constant | joule second (J⋅s) |
| [math]\displaystyle{ I }[/math] | 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) | |
| [math]\displaystyle{ i }[/math] | intensity | watt per square meter (W/m2) |
| imaginary unit | unitless | |
| electric current | ampere (A) | |
| [math]\displaystyle{ \mathbf{\hat{\imath}} }[/math] | Cartesian x-axis basis unit vector | unitless |
| [math]\displaystyle{ \mathbf{J} }[/math] | current density | ampere per square meter (A/m2) |
| impulse | kilogram meter per second (kg⋅m/s) | |
| [math]\displaystyle{ \mathbf{j} }[/math] | jerk | meters per second cubed (m/s3) |
| [math]\displaystyle{ j }[/math] | imaginary unit (electrical) | unitless |
| [math]\displaystyle{ \mathbf{\hat{\jmath}} }[/math] | Cartesian y-axis basis unit vector | unitless |
| [math]\displaystyle{ K }[/math] | kinetic energy | joule (J) |
| [math]\displaystyle{ \mathbf{k} }[/math] | wave vector | radians per meter (m−1) |
| [math]\displaystyle{ k }[/math] | Boltzmann constant | joule per kelvin (J/K) |
| wavenumber | radians per meter (m−1) | |
| stiffness | newtons per meter (N⋅m−1) | |
| [math]\displaystyle{ \mathbf{\hat{k}} }[/math] | Cartesian z-axis basis unit vector | unitless |
| [math]\displaystyle{ \mathbf{L} }[/math] | angular momentum | newton meter second (N⋅m⋅s or kg⋅m2⋅s−1) |
| [math]\displaystyle{ L }[/math] | inductance | henry (H) |
| luminosity | watt (W) | |
| Lagrangian | joule (J) | |
| [math]\displaystyle{ l }[/math] | length | meter (m) |
| ℓ | azimuthal quantum number | unitless |
| [math]\displaystyle{ \mathbf{M} }[/math] | magnetization | amperes per meter (A/m) |
| [math]\displaystyle{ M }[/math] | moment of force often simply called moment or torque |
newton meter (N⋅m) |
| [math]\displaystyle{ m }[/math] | mass | kilogram (kg) |
| [math]\displaystyle{ \mathbf{N} }[/math] | normal vector | unit varies depending on context |
| [math]\displaystyle{ N }[/math] | atomic number | unitless |
| [math]\displaystyle{ n }[/math] | refractive index | unitless |
| principal quantum number | unitless | |
| amount of substance | mole | |
| [math]\displaystyle{ P }[/math] | power | watt (W) |
| probability | unitless | |
| [math]\displaystyle{ \mathbf{p} }[/math] | momentum | kilogram meter per second (kg⋅m/s) |
| [math]\displaystyle{ p }[/math] | pressure | pascal (Pa) |
| [math]\displaystyle{ Q }[/math] | electric charge | coulomb (C) |
| heat | joule (J) | |
| [math]\displaystyle{ q }[/math] | electric charge | coulomb (C) |
| [math]\displaystyle{ R }[/math] | 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) | |
| [math]\displaystyle{ \mathbf{r} }[/math] | radius vector (position) | meter (m) |
| [math]\displaystyle{ r }[/math] | radius or distance | meter (m) |
| [math]\displaystyle{ S }[/math] | surface area | m2 |
| entropy | joule per kelvin (J/K) | |
| action | joule second (J⋅s) | |
| [math]\displaystyle{ \mathbf{s} }[/math] | displacement | meter (m) |
| [math]\displaystyle{ s }[/math] | arc length | meter (m) |
| distance | meter (m) | |
| [math]\displaystyle{ T }[/math] | period | second (s) |
| temperature | kelvin (K) or Celsius (C) | |
| kinetic energy | joule (J) | |
| [math]\displaystyle{ t }[/math] | time | second (s) |
| [math]\displaystyle{ \mathbf{U} }[/math] | four-velocity | meter per second (m/s) |
| [math]\displaystyle{ U }[/math] | potential energy | joule (J) |
| internal energy | joule (J) | |
| [math]\displaystyle{ u }[/math] | relativistic mass | kilogram (kg) |
| energy density | joule per cubic meter (J/m3) | |
| specific energy | joule per kilogram (J/kg) | |
| [math]\displaystyle{ V }[/math] | voltage also called electric potential difference |
volt (V) |
| volume | cubic meter (m3) | |
| shear force | ||
| [math]\displaystyle{ \mathbf{v} }[/math] | velocity | meter per second (m/s) |
| [math]\displaystyle{ W }[/math] | weight | newton (N) |
| mechanical work | joule (J) | |
| [math]\displaystyle{ w }[/math] | width | meter (m) |
| [math]\displaystyle{ X }[/math] | electrical reactance | ohm (Ω) |
| [math]\displaystyle{ \mathbf{x} }[/math] | position vector | meter (m) |
| displacement | meter (m) | |
| [math]\displaystyle{ x }[/math] | a generic unknown | varied depending on context |
| [math]\displaystyle{ Y }[/math] | admittance | siemens (S) |
| [math]\displaystyle{ Z }[/math] | compressibility factor | unitless |
| electrical impedance | ohm (Ω) | |
| [math]\displaystyle{ Z_0 }[/math] | impedance of free space | ohm (Ω) |
Greek characters
| Symbol | Name | Meaning | SI unit of measure |
|---|---|---|---|
| [math]\displaystyle{ \alpha }[/math] | alpha | alpha particle | |
| angular acceleration | radian per second squared (rad/s2) | ||
| fine-structure constant | unitless | ||
| [math]\displaystyle{ \beta }[/math] | beta | velocity in terms of the speed of light c | unitless |
| beta particle | |||
| [math]\displaystyle{ \gamma }[/math] | gamma | Lorentz factor | unitless |
| photon | |||
| gamma ray | |||
| shear strain | radian | ||
| heat capacity ratio | unitless | ||
| surface tension | newton per meter (N/m) | ||
| [math]\displaystyle{ \Delta }[/math] | delta | change in a variable (e.g. [math]\displaystyle{ \Delta x }[/math]) | unitless |
| Laplace operator | per square meter (m−2) | ||
| [math]\displaystyle{ \delta }[/math] | displacement (usually small) | meter (m) | |
| Dirac delta function | |||
| Kronecker delta (e.g [math]\displaystyle{ \delta_{ij} }[/math]) | |||
| [math]\displaystyle{ \epsilon }[/math] | epsilon | permittivity | farad per meter (F/m) |
| strain | unitless | ||
| [math]\displaystyle{ \varepsilon_0 }[/math] | epsilon nought | vacuum permittivity constant | farad per meter (F/m) |
| [math]\displaystyle{ \zeta }[/math] | zeta | damping ratio | unitless |
| [math]\displaystyle{ \eta }[/math] | eta | angular jerk | radians per second cubed (rad⋅s−3) |
| energy efficiency | unitless | ||
| (dynamic) viscosity (also [math]\displaystyle{ \mu }[/math]) | pascal second (Pa⋅s) | ||
| [math]\displaystyle{ \theta }[/math] | theta | angular displacement | radian (rad) |
| [math]\displaystyle{ \kappa }[/math] | kappa | torsion coefficient also called torsion constant |
newton meter per radian (N⋅m/rad) |
| [math]\displaystyle{ \Lambda }[/math] | lambda | cosmological constant | per second squared (s−2) |
| [math]\displaystyle{ \lambda }[/math] | wavelength | meter (m) | |
| linear charge density | coulomb per meter (C/m) | ||
| eigenvalue | non-zero vector | ||
| [math]\displaystyle{ \mathbf{\mu} }[/math] | mu | magnetic moment | ampere square meter (A⋅m2) |
| coefficient of friction | unitless | ||
| (dynamic) viscosity (also [math]\displaystyle{ \eta }[/math]) | pascal second (Pa⋅s) | ||
| permeability (electromagnetism) | henry per meter (H/m) | ||
| reduced mass | kilogram (kg) | ||
| gravitational parameter | cubic meter per second squared | ||
| [math]\displaystyle{ \mathbf{\mu}_0 }[/math] | mu nought | vacuum permeability constant or magnetic constant | henry per meter (H/m) |
| [math]\displaystyle{ \nu }[/math] | nu | frequency | hertz (Hz) |
| kinematic viscosity | meters squared per second (m2/s) | ||
| neutrino | |||
| [math]\displaystyle{ \xi }[/math] | xi | electromotive force | volt (V) |
| [math]\displaystyle{ \pi }[/math] | pi | 3.14159... (irrational number) | unitless |
| [math]\displaystyle{ \rho }[/math] | 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) | ||
| [math]\displaystyle{ \Sigma }[/math] | sigma | summation operator | |
| [math]\displaystyle{ \sigma }[/math] | 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) | ||
| [math]\displaystyle{ \tau }[/math] | tau | torque | newton meter (N⋅m) |
| shear stress | pascal (Pa) | ||
| time constant | second (s) | ||
| 6.28318... (2π) | unitless | ||
| [math]\displaystyle{ \Phi }[/math] | phi | field strength | unit varies depending on context |
| magnetic flux | weber (Wb) | ||
| [math]\displaystyle{ \phi }[/math] | electric potential | volt (V) | |
| Higgs field work function | |||
| [math]\displaystyle{ \Psi }[/math] | psi | wave function | m−3/2 |
| [math]\displaystyle{ \Omega }[/math] | omega | electric resistance | ohm |
| [math]\displaystyle{ \omega }[/math] | angular frequency | radian per second (rad/s) | |
| angular velocity | radian per second (rad/s) | ||
| ∫ | integral | the inverse of the derivative. | unitless |
Other characters
| Symbol | Name | Meaning | SI unit of measure |
|---|---|---|---|
| [math]\displaystyle{ \nabla\cdot }[/math] | nabla dot | the divergence operator often pronounced "del dot" |
per meter (m−1) |
| [math]\displaystyle{ \nabla\times }[/math] | nabla cross | the curl operator often pronounced "del cross" |
per meter (m−1) |
| [math]\displaystyle{ \nabla }[/math] | nabla | delta (differential operator) | |
| [math]\displaystyle{ \partial }[/math] | "der", "dow", "die", "partial" or simply "d" | partial derivative (e.g. [math]\displaystyle{ \partial y/\partial x }[/math]) | |
| [math]\displaystyle{ \Box }[/math] | D'Alembert operator | [math]\displaystyle{ \nabla^2-\partial_t^2 }[/math] | |
| [math]\displaystyle{ \langle \, \, \rangle }[/math] | angle brackets | average
sometimes over Maxwell–Boltzmann distribution |
|
| [math]\displaystyle{ \langle \ | \ \rangle }[/math] | Dirac notation |
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
- Elert, Glenn. "Special Symbols". https://physics.info/symbols/.
- NIST (16 August 2023). "SI Units". NIST. https://www.nist.gov/pml/owm/metric-si/si-units.
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