Defining equation (physics)

For common nomenclature of base quantities used in this article, see Physical quantity. For 4-vector modifications used in relativity, see Four-vector.

Very often defining equations are in the form of a constitutive equation, since parameters of a property or effect associated matter are characteristic to the substance in question. A large number of defining equations are in that article.

In physics, defining equations are equations that define new quantities in terms of base quantities.^[1] This article uses the current SI system of units, not natural or characteristic units.

Treatment of vectors

Main Articles: Kinematics, Cross product, Unit vector

There are many forms of vector notation. In this section the following is specifically used throughout the article, closely matching standard use; upright boldface is for a vector quantity and upright boldface with a hat (circumflex) is for a unit vector.

The standard ordered vector basis for spherical polar coordinates; $\scriptstyle{\boldsymbol{\hat{r}}, \boldsymbol{\hat{\theta}}, \boldsymbol{\hat{\phi}}} \,\!$ are used with the general forms of unit vectors below.

Common general themes of unit vectors occur throughout physics:

Unit vector	Nomenclature	Diagram
Tangent vector to a curve/flux line	$\mathbf{\hat{t}}\,\!$	A normal vector $\mathbf{\hat{n}} \,\!$ to the plane containing and defined by the radial position vector $r \mathbf{\hat{r}} \,\!$ and angular tangential direction of rotation $\theta \boldsymbol{\hat{\theta}} \,\!$ is necessary so that the vector equations of angular motion hold.
Normal to a surface tangent plane/plane containing radial position component and angular tangential component	$\mathbf{\hat{n}}\,\!$ In terms of polar coordinates; $\mathbf{\hat{n}} = \mathbf{\hat{r}} \times \boldsymbol{\hat{\theta}} \,\!$
Binormal vector to tangent and normal	$\mathbf{\hat{b}} = \mathbf{\hat{t}} \times \mathbf{\hat{n}} \,\!$[2]
Parallel to some axis/line	$\mathbf{\hat{e}}_{\parallel} \,\!$	One unit vector $\mathbf{\hat{e}}_{\parallel}\,\!$ aligned parallel to a principle direction (red line), and a perpendicular unit vector $\mathbf{\hat{e}}_{\bot}\,\!$ is in any radial direction relative to the principle line.
Perpendicular to some axis/line in some radial direction	$\mathbf{\hat{e}}_{\bot} \,\!$
Possible angular deviation relative to some axis/line	$\mathbf{\hat{e}}_{\angle} \,\!$	Unit vector at acute deviation angle φ (including 0 or π/2 rad) relative to a principle direction.

Classical mechanics

Mass and inertia

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Linear, surface, volumetric mass density	λ or μ (especially in acoustics, see below) for Linear, σ for surface, ρ for volume.	$\lambda = \mathrm{d} m/\mathrm{d} x \,\!$ (or $\mu = \mathrm{d} m/\mathrm{d} x \,\!$) $\sigma = \mathrm{d}^2 m/\mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d}^2 m/\mathrm{d} S \,\!$ $\rho = \mathrm{d}^3 m/\mathrm{d} x_3 \mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d} m/\mathrm{d} V \,\!$	kg m−n, n = 1, 2, 3	[M][L]−n
Moment of mass[3]	m (No common symbol)	Point mass: $\mathbf{m} = \mathbf{r}m \,\!$ Descrete masses about an axis $x_i \,\!$: $\mathbf{m} = \sum_{i=1}^N \mathbf{r}_\mathrm{i} m_i \,\!$ Continuum of mass about an axis $x_i \,\!$: $\mathbf{m} = \int \rho \left ( \mathbf{r} \right ) x_i \mathrm{d} \mathbf{r} \,\!$	kg m	[M][L]
Centre of mass	rcom (Symbols vary)	ith moment of mass $\mathbf{m}_\mathrm{i} = \mathbf{r}_\mathrm{i} m_i \,\!$ Discrete masses: $\mathbf{r}_\mathrm{com} = \frac{1}{M}\sum_i \mathbf{r}_\mathrm{i} m_i = \frac{1}{M}\sum_i \mathbf{m}_\mathrm{i} \,\!$ Mass continuum: $\mathbf{r}_\mathrm{com} = \frac{1}{M}\int \mathrm{d}\mathbf{m} = \frac{1}{M}\int \mathbf{r} \mathrm{d}m = \frac{1}{M}\int \mathbf{r} \rho \mathrm{d}V \,\!$	m	[L]
2-Body reduced mass	m12, μ Pair of masses = m1 and m2	$\mu = \left (m_1m_2 \right )/\left ( m_1 + m_2 \right) \,\!$	kg	[M][L]2
Moment of inertia (MOI)	I	Discrete Masses: $I = \sum_i \mathbf{m}_\mathrm{i} \cdot \mathbf{r}_\mathrm{i} = \sum_i \left | \mathbf{r}_\mathrm{i} \right | ^2 m \,\!$ Mass continuum: $I = \int \left | \mathbf{r} \right | ^2 \mathrm{d} m = \int \mathbf{r} \cdot \mathrm{d} \mathbf{m} = \int \left | \mathbf{r} \right | ^2 \rho \mathrm{d}V \,\!$	kg m2 s−1	[M][L]2

Derived kinematic quantities

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Velocity	v	$\mathbf{v} = \mathrm{d} \mathbf{r}/\mathrm{d} t \,\!$	m s−1	[L][T]−1
Acceleration	a	$\mathbf{a} = \mathrm{d} \mathbf{v}/\mathrm{d} t = \mathrm{d}^2 \mathbf{r}/\mathrm{d} t^2 \,\!$	m s−2	[L][T]−2
Jerk	j	$\mathbf{j} = \mathrm{d} \mathbf{a}/\mathrm{d} t = \mathrm{d}^3 \mathbf{r}/\mathrm{d} t^3 \,\!$	m s−3	[L][T]−3
Angular velocity	ω	$\boldsymbol{\omega} = \mathbf{\hat{n}} \left ( \mathrm{d} \theta /\mathrm{d} t \right ) \,\!$	rad s−1	[T]−1
Angular Acceleration	α	$\boldsymbol{\alpha} = \mathrm{d} \boldsymbol{\omega}/\mathrm{d} t = \mathbf{\hat{n}} \left ( \mathrm{d}^2 \theta / \mathrm{d} t^2 \right ) \,\!$	rad s−2	[L][T]−2

Derived dynamic quantities

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Momentum	p	$\mathbf{p}=m\mathbf{v} \,\!$	kg m s−1	[M][L][T]−1
Force	F	$\mathbf{F} = \mathrm{d} \mathbf{p}/\mathrm{d} t \,\!$	N = kg m s−2	[M][L][T]−2
Impulse	Δp, I	$\mathbf{I} = \Delta \mathbf{p} = \int_{t_1}^{t_2} \mathbf{F}\mathrm{d} t \,\!$	kg m s−1	[M][L][T]−1
Angular momentum about a position point r0,	L, J, S	$\mathbf{L} = \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{p} \,\!$ Most of the time we can set r0 = 0 if particles are orbiting about axes intersecting at a common point.	kg m2 s−1	[M][L]2[T]−1
Moment of a force about a position point r0, Torque	τ, M	$\boldsymbol{\tau} = \left ( \mathbf{r} - \mathbf{r}_0 \right ) \times \mathbf{F} = \mathrm{d} \mathbf{L}/\mathrm{d} t \,\!$	N m = kg m2 s−2	[M][L]2[T]−2
Angular impulse	ΔL (no common symbol)	$\Delta \mathbf{L} = \int_{t_1}^{t_2} \boldsymbol{\tau}\mathrm{d} t \,\!$	kg m2 s−1	[M][L]2[T]−1

General energy definitions

Main article: Mechanical energy

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Mechanical work due to a Resultant Force	W	$W = \int_C \mathbf{F} \cdot \mathrm{d} \mathbf{r} \,\!$	J = N m = kg m2 s−2	[M][L]2[T]−2
Work done ON mechanical system, Work done BY	WON, WBY	$\Delta W_\mathrm{ON} = - \Delta W_\mathrm{BY} \,\!$	J = N m = kg m2 s−2	[M][L]2[T]−2
Potential energy	φ, Φ, U, V, Ep	$\Delta W = - \Delta V \,\!$	J = N m = kg m2 s−2	[M][L]2[T]−2
Mechanical power	P	$P = \mathrm{d}E/\mathrm{d}t \,\!$	W = J s−1	[M][L]2[T]−3
Lagrangian	L	$L = T-V \,\!$	J	[M][L]2[T]−2
Hamiltonian	H	$H = T + V \,\!$	J	[M][L]2[T]−2
Action	S, $\scriptstyle{\mathcal{S}} \,\!$	$\mathcal{S} = \int_{t_1}^{t_2} L {\mathrm{d}t} \,\!$	J s	[M][L]2[T]−1

Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U:

- Wherever the force is zero, its potential energy is defined to be zero as well. - Whenever the force does work, potential energy is lost.

Transport mechanics

Here $\mathbf{\hat{t}} \,\!$ is a unit vector in the direction of the flow/current/flux.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Flow velocity vector field	u	$\mathbf{u}=\mathbf{u}\left ( \mathbf{r},t \right ) \,\!$	m s−1	[L][T]−1
Volume velocity, volume flux	φV (no standard symbol)	$\phi_V = \int_S \mathbf{u} \cdot \mathrm{d}\mathbf{A}\,\!$	m3 s−1	[L]3 [T]−1
Mass current per unit volume	s (no standard symbol)	$s = \mathrm{d}\rho / \mathrm{d}t \,\!$	kg m−3 s−1	[M] [L]−3 [T]−1
Mass current, mass flow rate	Im	$I_\mathrm{m} = \mathrm{d} m/\mathrm{d} t \,\!$	kg s−1	[M][T]−1
Mass current density	jm	$\mathbf{j}_\mathrm{m} \cdot \mathbf{\hat{n}} = \mathrm{d} I_\mathrm{m} /\mathrm{d} A = \mathrm{d}^2 m/\mathrm{d} A \mathrm{d} t \,\!$	kg m−2 s−1	[M][L]−2[T]−1
Momentum current	Ip	$I_\mathrm{p} = \mathrm{d} \left | \mathbf{p} \right |/\mathrm{d} t \,\!$	kg m s−2	[M][L][T]−2
Momentum current density	jp	$\mathbf{j}_\mathrm{p} \cdot \mathbf{\hat{n}} = \mathrm{d} I_\mathrm{p}/\mathrm{d} A = \mathrm{d}^2 \left | \mathbf{p} \right | /\mathrm{d} A \mathrm{d} t \,\!$	kg m s−2	[M][L][T]−2

Properties of matter

Stress and strain

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
General stress, Pressure	P, σ	$\sigma = F/A \,\!$ F may be any force applied to area A	Pa = N m−2	[M] [T] [L]−1
General strain	ε	$\epsilon = \Delta D / D \,\!$ D = dimension (length, area, volume) $\Delta D \,\!$ = change in dimension	dimensionless	dimensionless
General elastic modulus	Emod	$E_\mathrm{mod} = \sigma / \epsilon \,\!$	Pa = N m−2	[M] [T] [L]−1
Young's modulus	E, Y	$Y = \sigma / \left ( \Delta L/ L \right ) \,\!$	Pa = N m−2	[M] [T] [L]−1
Shear modulus	G	$G = \Delta x/L\,\!$	Pa = N m−2	[M] [T] [L]−1
Bulk modulus	B	$B = P/\left ( \Delta V / V \right ) \,\!$	Pa = N m−2	[M] [T] [L]−1
Compressibility	C	$C = 1/B \,\!$	Pa−1 = m2 N−1	[L] [M]−1 [T]−1

Thermodynamics

Thermodynamic quantities

Main articles: List of thermodynamic properties, Thermodynamic potential, Free entropy, Defining equation (physical chemistry)

General fundamental quantities

Quantity (common name/s)	(Common) symbol/s	SI units	Dimension
Number of molecules	N	dimensionless	dimensionless
Number of moles	n	mol	[N]
Temperature	T	K	[Θ]
Heat energy	Q, q	J	[M][L]2[T]−2
Latent heat	QL	J	[M][L]2[T]−2
Entropy	S	J K−1	[M][L]2[T]−2 [Θ]−1
Negentropy	J	J K−1	[M][L]2[T]−2 [Θ]−1

Thermal properties of matter

Main Articles: Heat capacity, Thermal expansion

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
General heat/thermal capacity	C	$C = \partial Q/\partial T\,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Heat capacity (isobaric)	Cp	$C_{p} = \partial Q/\partial T\,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Specific heat capacity (isobaric)	Cmp	$C_{mp} = \partial^2 Q/\partial m \partial T \,\!$	J kg−1 K−1	[L]2[T]−2 [Θ]−1
Molar specific heat Capacity (isobaric)	Cnp	$C_{np} = \partial^2 Q/\partial n \partial T \,\!$	J K −1 mol−1	[M][L]2[T]−2 [Θ]−1 [N]−1
Heat capacity (isochoric/volumetric)	CV	$C_{V} = \partial Q/\partial T \,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Specific heat capacity (isochoric)	CmV	$C_{mV} = \partial^2 Q/\partial m \partial T \,\!$	J kg−1 K−1	[L]2[T]−2 [Θ]−1
Molar specific heat capacity (isochoric)	CnV	$C_{nV} = \partial^2 Q/\partial n \partial T \,\!$	J K −1 mol−1	[M][L]2[T]−2 [Θ]−1 [N]−1
Specific latent heat	L	$L = \partial Q/ \partial m \,\!$	J kg−1	[L]2[T]−2
Ratio of isobaric to isochoric heat capacity, Heat capacity ratio, adiabatic index	γ	$\gamma = C_p/C_V = c_p/c_V = C_{mp}/C_{mV} \,\!$	dimensionless	dimensionless

Thermal transfer

Main article: Thermal conductivity

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Temperature gradient	No standard symbol	$\nabla T \,\!$	K m−1	[Θ][L]−1
Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer	P	$P = \mathrm{d} q/\mathrm{d} t \,\!$	W = J s−1	[M] [L]2 [T]−2
Thermal intensity	I	$I = \mathrm{d} P/\mathrm{d} A= \mathrm{d}^2 q/\mathrm{d} A \mathrm{d} t \,\!$	W m−2	[M] [T]−3
Thermal/heat flux density (vector analogue of thermal intensity above)	q	$\mathbf{q} \cdot \mathbf{\hat{t}} = I = \mathrm{d}^2 q/\mathrm{d} A \mathrm{d} t \,\!$	W m−2	[M] [T]−3

Waves

General fundamental quantities

A wave can be longnitudinal where the oscillations are parallel (or antiparallel) to the propagation direction, or transverse where the oscillations are perpendicular to the propagation direction. These oscillations are characterized by a periodically time-varying displacement in the parallel or perpendicular direction, and so the instantaneous velocity and acceleration are also periodic and time varying in these directions. But the wave profile (the apparent motion of the wave due to the successive oscillations of particles or fields about their equilibrium positions) propagates at the phase and group velocities parallel or antiparallel to the propagation direction, which is common to longitudinal and transverse waves. Below oscillatory displacement, velocity and acceleration refer to the kinematics in the oscillating directions of the wave - transverse or longitudinal (mathematical description is identical), the group and phase velocities are separate.

Main articles: Transverse wave, Longitudinal wave

Quantity (common name/s)	(Common) symbol/s	SI units	Dimension
Number of wave cycles	N	dimensionless	dimensionless
(Oscillatory) displacement	Symbol of any quantity which varies periodically, such as h, x, y (mechanical waves), x, s, η (longitudinal waves) I, V, E, B, H, D (electromagnetism), u, U (luminal waves), ψ, Ψ, Φ (quantum mechanics). Most general purposes use y, ψ, Ψ. For generality here, A is used and can be replaced by any other symbol, since others have specific, common uses. $\mathbf{A} = A \mathbf{\hat{e}}_{\parallel} \,\!$ for longitudinal waves, $\mathbf{A} = A \mathbf{\hat{e}}_{\bot} \,\!$ for transverse waves.	m	[L]
(Oscillatory) displacement amplitude	Any quantity symbol typically subscripted with 0, m or max, or the capitalized letter (if displacement was in lower case). Here for generality A0 is used and can be replaced.	m	[L]
(Oscillatory) velocity amplitude	V, v0, vm. Here v0 is used.	m s−1	[L][T]−1
(Oscillatory) acceleration amplitude	A, a0, am. Here a0 is used.	m s−2	[L][T]−2
Spatial position Position of a point in space, not necessarily a point on the wave profile or any line of propagation	d, r	m	[M]
Wave profile displacement Along propagation direction, distance travelled (path length) by one wave from the source point r0 to any point in space d (for longitudinal or transverse waves)	L, d, r $\mathbf{r} \equiv r \mathbf{\hat{e}}_{\parallel} \equiv \mathbf{d} - \mathbf{r}_0 \,\!$	m	[L]
Phase angle	δ, ε, φ	rad	dimensionless

General derived quantities

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Wavelength	λ	General definition (allows for FM): $\lambda = \mathrm{d} r/\mathrm{d} N \,\!$ For non-FM waves this reduces to: $\lambda = \Delta r/\Delta N \,\!$	m	[L]
Wavenumber, k-vector, Wave vector	k, σ	Two definitions are in use: $\mathbf{k} = \left ( 2\pi/\lambda \right ) \mathbf{\hat{e}}_{\angle} \,\!$ $\mathbf{k} = \left ( 1/\lambda \right ) \mathbf{\hat{e}}_{\angle} \,\!$	m−1	[L]−1
Frequency	f, ν	General definition (allows for FM): $f = \mathrm{d} N/\mathrm{d} t \,\!$ For non-FM waves this reduces to: $f = \Delta N/\Delta t \,\!$ In practice N is set to 1 cycle and t = T = time period for 1 cycle, to obtain the more useful relation: $f = 1/T \,\!$	Hz = s−1	[T]−1
Angular frequency/ pulsatance	ω	$\omega = 2\pi f = 2\pi / T \,\!$	Hz = s−1	[T]−1
Oscillatory velocity	v, vt, v	Longitudinal waves: $\mathbf{v} = \mathbf{\hat{e}}_{\parallel} \left ( \partial A/\partial t \right ) \,\!$ Transverse waves: $\mathbf{v} = \mathbf{\hat{e}}_{\bot} \left ( \partial A/\partial t \right ) \,\!$	m s−1	[L][T]−1
Oscillatory acceleration	a, at	Longitudinal waves: $\mathbf{a} = \mathbf{\hat{e}}_{\parallel} \left ( \partial^2 A/\partial t^2 \right ) \,\!$ Transverse waves: $\mathbf{a} = \mathbf{\hat{e}}_{\bot} \left ( \partial^2 A/\partial t^2 \right ) \,\!$	m s−2	[L][T]−2
Path length difference between two waves	L, ΔL, Δx, Δr	$\mathbf{r} = \mathbf{r}_2 - \mathbf{r}_1 \,\!$	m	[L]
Phase velocity	vp	General definition: $\mathbf{v}_\mathrm{p} = \mathbf{\hat{e}}_{\parallel} \left ( \Delta r /\Delta t \right ) \,\!$ In practice reduces to the useful form: $\mathbf{v}_\mathrm{p} = \lambda f \mathbf{\hat{e}}_{\parallel} = \left ( \omega/k \right ) \mathbf{\hat{e}}_{\parallel} \,\!$	m s−1	[L][T]−1
(Longitudinal) group velocity	vg	$\mathbf{v}_\mathrm{g} = \mathbf{\hat{e}}_{\parallel} \left ( \partial \omega /\partial k \right ) \,\!$	m s−1	[L][T]−1
Time delay, time lag/lead	Δt	$\Delta t = t_2 - t_1 \,\!$	s	[T]
Phase difference	δ, Δε, Δϕ	$\Delta \phi = \phi_2 - \phi_1 \,\!$	rad	dimensionless
Phase	No standard symbol	$\mathbf{k} \cdot \mathbf{r} \mp \omega t + \phi= 2\pi N \,\!$ Physically; upper sign: wave propagation in +r direction lower sign: wave propagation in −r direction Phase angle can lag if: ϕ > 0 or lead if: ϕ < 0.	rad	dimensionless

Relation between space, time, angle analogues used to describe the phase:

$\frac{\Delta r}{\lambda} = \frac{\Delta t}{T} = \frac{\phi}{2\pi} \,\!$

Modulation indicies

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
AM index:	h, hAM	$h_{AM} = A/A_m \,\!$ A = carrier amplitude Am = peak amplitude of a component in the modulating signal	dimensionless	dimensionless
FM index:	hFM	$h_{FM} = \Delta f/f_m \,\!$ Δf = max. deviation of the instantaneous frequency from the carrier frequency fm = peak frequency of a component in the modulating signal	dimensionless	dimensionless
PM index:	hPM	$h_{PM} = \Delta \phi \,\!$ Δϕ = peak phase deviation	dimensionless	dimensionless

Acoustics

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Acoustic impedance	Z	$Z = \rho v\,\!$ v = speed of sound, ρ = volume density of medium	kg m−2 s−1	[M] [L]−2 [T]−1
Specific acoustic impedance	z	$z = ZS\,\!$ S = surface area	kg s−1	[M] [T]−1
Sound Level	β	$\beta = \left ( \mathrm{dB} \right ) 10 \log \left | \frac{I}{I_0} \right | \,\!$	dimensionless	dimensionless

Gravitation

A common misconseption occurs between centre of mass and centre of gravity. They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical descrition of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts. They are only equal if and only if the external gravitational field is uniform.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Centre of gravity	rcog (symbols vary)	ith moment of mass $\mathbf{m}_i = \mathbf{r}_i m_i \,\!$ Centre of gravity for a descrete masses: $\begin{align} \mathbf{r}_\mathrm{cog} & = \frac{1}{M \left | \mathbf{g} \left ( \mathbf{r}_i \right ) \right |}\sum_i \mathbf{m}_i \left | \mathbf{g} \left ( \mathbf{r}_i \right ) \right | \\ & = \frac{1}{M \left | \mathbf{g} \left ( \mathbf{r}_\mathrm{cog} \right ) \right |}\sum_i \mathbf{r}_i m_i \left | \mathbf{g} \left ( \mathbf{r}_i \right ) \right | \end{align}\,\!$ Centre of a gravity for a continuum of mass: $\begin{align} \mathbf{r}_\mathrm{cog} & = \frac{1}{M \left | \mathbf{g} \left ( \mathbf{r}_\mathrm{cog} \right ) \right |}\int \left | \mathbf{g} \left ( \mathbf{r} \right ) \right |\mathrm{d}\mathbf{m} \\ & = \frac{1}{M \left | \mathbf{g} \left ( \mathbf{r}_\mathrm{cog} \right ) \right |}\int \mathbf{r} \left | \mathbf{g} \left ( \mathbf{r} \right ) \right | \mathrm{d}^n m \\ & = \frac{1}{M \left | \mathbf{g} \left ( \mathbf{r}_\mathrm{cog} \right ) \right |}\int \mathbf{r} \rho_n \left | \mathbf{g} \left ( \mathbf{r} \right ) \right | \mathrm{d}^n x \end{align} \,\!$	m	[L]
Standard gravitational parameter of a mass	μ	$\mu = Gm \,\!$	N m2 kg−1	[L]3 [T]−2
Gravitational field, field strength, potential gradient, acceleration	g	$\mathbf{g} = \mathbf{F}/m \,\!$	N kg−1 = m s−2	[L][T]−2
Gravitational flux	ΦG	$\Phi_G = \int_S \mathbf{g} \cdot \mathrm{d}\mathbf{A} \,\!$	m3 s−2	[L]3[T]−2
Absolute gravitational potential	Φ, φ, U, V	$U = - \frac{W_{\infty r}}{m} = - \frac{1}{m} \int_\infty^{r} \mathbf{F} \cdot \mathrm{d}\mathbf{r} = - \int_\infty^{r} \mathbf{g} \cdot \mathrm{d}\mathbf{r} \,\!$	J kg−1	[L]2[T]−2
Gravitational potential difference	ΔΦ, Δφ, ΔU, ΔV	$\Delta U = - \frac{W}{m} = - \frac{1}{m} \int_{r_1}^{r_2} \mathbf{F} \cdot \mathrm{d}\mathbf{r} = - \int_{r_1}^{r_2} \mathbf{g} \cdot \mathrm{d}\mathbf{r} \,\!$	J kg−1	[L]2[T]−2
Gravitational potential energy	Ep	$E_p = - W_{\infty r} \,\!$	J	[M][L]2[T]−2
Gravitational torsion field	Ω	$\boldsymbol{\Omega} = 2 \boldsymbol{\xi} \,\!$	Hz = s−1	[T]−1
Gravitational torsion flux	ΦΩ	$\Phi_\Omega = \int_S \boldsymbol{\Omega} \cdot \mathrm{d}\mathbf{A} \,\!$	N m s kg−1 = m2 s−1	[M]2 [T]−1
Gravitomagnetic field	H, Bg, B, ξ	$\mathbf{F} = m \left ( \mathbf{v} \times 2 \boldsymbol{\xi} \right ) \,\!$	Hz = s−1	[T]−1
Gravitomagnetic flux	Φξ	$\Phi_\xi = \int_S \boldsymbol{\xi} \cdot \mathrm{d}\mathbf{A} \,\!$	N m s kg−1 = m2 s−1	[M]2 [T]−1
Gravitomagnetic vector potential [4]	h	$\mathbf{\xi} = \nabla \times \mathbf{h} \,\!$	m s−1	[M] [T]−1

Electromagnetism

Here subscripts e and m are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q_m(Wb) = μ₀ q_m(Am).

Initial quantities

Quantity (common name/s)	(Common) symbol/s	SI units	Dimension
Electric charge	qe, q, Q	C = As	[I][T]
Monopole strength, magnetic charge	qm, g, p	Wb or Am	[L]2[M][T]−2 [I]−1 (Wb) [I][L] (Am)

Electric quantities

Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues.

Electric transport

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Linear, surface, volumetric charge density	λe for Linear, σe for surface, ρe for volume.	$\lambda_e = \mathrm{d} q_e/\mathrm{d} x \,\!$ $\sigma_e = \mathrm{d}^2 q_e/\mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d}^2 m/\mathrm{d} S \,\!$ $\rho_e = \mathrm{d}^3 q_e/\mathrm{d} x_3 \mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d} m/\mathrm{d} V \,\!$	C m−n, n = 1, 2, 3	[I][T][L]−n
Capacitance	C	$C = \mathrm{d}q/\mathrm{d}V\,\!$ V = voltage, not volume.	F = C V−1	[I][T]3[L]−2[M]−1
Electric current	I	$I = \mathrm{d}q/\mathrm{d}t \,\!$	A	[I]
Electric current density	J	$\mathbf{J} \cdot \mathbf{\hat{n}} = \mathrm{d} I/\mathrm{d} A \,\!$	A m−2	[I][L]−2
Displacement current density	Jd	$\mathbf{J}_\mathrm{d} = \epsilon_0 \left ( \partial \mathbf{E} / \partial t \right ) = \partial \mathbf{D} / \partial t \,\!$	Am−2	[I][L]m−2
Convection current density	Jc	$\mathbf{J}_\mathrm{c} = \rho \mathbf{v} \,\!$	A m−2	[I] [L]m−2

Electric fields

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Electric field, field strength, flux density, potential gradient	E	$\mathbf{E} =\mathbf{F}/q\,\!$	N C−1 = V m−1	[M][L][T]−3[I]−1
Electric flux	ΦE	$\Phi_E = \int_S \mathbf{E} \cdot \mathrm{d} \mathbf{A}\,\!$	N m2 C−1	[M][L]3[T]−3[I]−1
Absolute permittivity;	ε	$\epsilon = \epsilon_r \epsilon_0\,\!$	F m−1	[I]2 [T]4 [M]−1 [L]−3
Electric displacement field	D	$\mathbf{D} =\mathbf{E}/\epsilon\,\!$	C m−2	[I][T][L]−2
Electric displacement flux	ΦD	$\Phi_D = \int_S \mathbf{D} \cdot \mathrm{d} \mathbf{A}\,\!$	C	[I][T]
Electric dipole moment	p	$\mathbf{p} = 2q\mathbf{a}\,\!$ a = charge separation directed from -ve to +ve charge	C m	[I][T][L]
Electric Polarization, polarization density	P	$\mathbf{P} = \mathrm{d} \langle \mathbf{p} \rangle /\mathrm{d} V \,\!$	C m−2	[I][T][L]−2
Absolute electric potential, EM scalar potential relative to point $r_0 \,\!$ Theoretical: $r_0 = \infty \,\!$ Practical: $r_0 = R_\mathrm{earth} \,\!$ (Earth's radius)	φ ,V	$V = -\frac{W_{\infty r }}{q} = -\frac{1}{q}\int_\infty^r \mathbf{F} \cdot \mathrm{d} \mathbf{r} = -\int_{r_1}^{r_2} \mathbf{E} \cdot \mathrm{d} \mathbf{r}\,\!$	V = J C−1	[M] [L] [T]−3 [I]−1
Voltage, Electric potential difference	Δφ,ΔV	$\Delta V = -\frac{\Delta W}{q} = -\frac{1}{q}\int_{r_1}^{r_2} \mathbf{F} \cdot \mathrm{d} \mathbf{r} = -\int_{r_1}^{r_2} \mathbf{E} \cdot \mathrm{d} \mathbf{r} \,\!$	V = J C−1	[M] [L] [T]−3 [I]−1
Electric potential energy	U	$U = - W\,\!$	J	[M][L]2[T]2

Magnetic quantities

Magnetic transport

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Linear, surface, volumetric pole density	λm for Linear, σm for surface, ρm for volume.	$\lambda_m = \mathrm{d} q_m/\mathrm{d} x \,\!$ $\sigma_m = \mathrm{d}^2 q_m/\mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d}^2 m/\mathrm{d} S \,\!$ $\rho_m = \mathrm{d}^3 q_m/\mathrm{d} x_3 \mathrm{d} x_2 \mathrm{d} x_1 = \mathrm{d} m/\mathrm{d} V \,\!$	Wb m−n A m−(n + 1), n = 1, 2, 3	[L]2[M][T]−2 [I]−1 (Wb) [I][L] (Am)
Monopole current	Im	$I_m = \mathrm{d}q_m/\mathrm{d}t \,\!$	Wb s−1 A m s−1	[L]2[M][T]−3 [I]−1 (Wb) [I][L][T]−1 (Am)
Monopole current density	Jm	$\mathbf{J}_\mathrm{m} \cdot \mathbf{\hat{n}} = \mathrm{d} I/\mathrm{d} A \,\!$	Wb s−1 m−2 A m−1 s−1	[M][T]−3 [I]−1 (Wb) [I][L]−1[T]−1 (Am)

Magnetic fields

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Magnetic field, field strength, flux density, induction field	B	$\mathbf{F} =q_e \left ( \mathbf{v}\times\mathbf{B} \right ) \,\!$	T = N A−1 m−1 = Wb m2	[M][T]−2[I]−1
Magnetic potential, EM vector potential	A	$\mathbf{B} = \nabla \times \mathbf{A}$	T m = N A−1 = Wb m3	[M][L][T]−2[I]−1
Magnetic flux	ΦB	$\Phi_B = \int_S \mathbf{B} \cdot \mathrm{d} \mathbf{A}\,\!$	Wb = T m−2	[L]2[M][T]−2[I]−1
Magnetic field intensity, (AKA field strength)	H	$\mathbf{H} = \mathbf{B}/\mu \,\!$	A m−1	[I] [L]−1
Magnetic moment, magnetic dipole moment	m, μ, Π	Two definitions are possible: using pole strengths, $\mathbf{m} = q_m \mathbf{a}\,\!$ using currents: $\mathbf{m} = NIA\mathbf{\hat{n}}\,\!$ a = pole separation N is the number of turns of conductor	A m2	[I][L]2
Magnetization	M	$\mathbf{M} = \mathrm{d} \langle \mathbf{m} \rangle /\mathrm{d} V \,\!$	A m2	[I] [L]−1
Intensity of magnetization, magnetic polarization	I, J	$\mathbf{I} = \mu \mathbf{M} \,\!$	T = N A−1 m−1 = Wb m2	[M][T]−2[I]−1
Self Inductance	L	Two equivalent definitions are possible: $L=N\left ( \mathrm{d} \Phi/\mathrm{d} I \right )\,\!$ $L\left ( \mathrm{d} I/\mathrm{d} t \right )=-NV\,\!$	H = Wb A−1	[L]2 [M] [T]−2 [I]−2
Mutual inductance	M	Again two equivalent definitions are possible: $M_1=N\left ( \mathrm{d} \Phi_2/\mathrm{d} I_1 \right )\,\!$ $M\left ( \mathrm{d} I_2/\mathrm{d} t \right )=-NV_1\,\!$ 1,2 subscripts refer to two conductors/inductors mutually inducing voltage/ linking magnetic flux though each other. They can be interchanged for the required conductor/inductor; $M_2=N\left ( \mathrm{d} \Phi_1/\mathrm{d} I_2 \right )\,\!$ $M\left ( \mathrm{d} I_1/\mathrm{d} t \right )=-NV_2\,\!$	H = Wb A−1	[L]2 [M] [T]−2 [I]−2
Gyromagnetic ratio (for charged particles in a magnetic field)	γ	$\omega = \gamma B \,\!$	Hz T−1	[M]−1[T][I]

Electric circuits

DC circuits, general definitions

Main article: Direct current

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Terminal Voltage for Power Supply	Vter		V = J C−1	[M] [L]2 [T]−3 [I]−1
Load Voltage for Circuit	Vload		V = J C−1	[M] [L]2 [T]−3 [I]−1
Internal resistance of power supply	Rint	$R_\mathrm{int} = V_\mathrm{ter}/I \,\!$	Ω = V A−1 = J s C−2	[M][L]2 [T]−3 [I]−2
Load resistance of circuit	Rext	$R_\mathrm{ext} = V_\mathrm{load}/I \,\!$	Ω = V A−1 = J s C−2	[M][L]2 [T]−3 [I]−2
Electromotive force (emf), voltage across entire circuit including power supply, external components and conductors	E	$\mathcal{E} = V_\mathrm{ter} + V_\mathrm{load} \,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1

AC circuits

Main articles: Alternating current, Resonance

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Resistive load voltage	VR	$V_R = I_R R \,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
Capacitive load coltage	VC	$V_C = I_C X_C\,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
Inductive load coltage	VL	$V_L = I_L X_L\,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
Capacitive reactance	XC	$X_C = \frac{1}{\omega_\mathrm{d} C} \,\!$	Ω−1 m−1	[I]2 [T]3 [M]−2 [L]−2
Inductive reactance	XL	$X_L = \omega_d L \,\!$	Ω−1 m−1	[I]2 [T]3 [M]−2 [L]−2
AC electrical impedance	Z	$V = I Z\,\!$ $Z = \sqrt{R^2 + \left ( X_L - X_C \right )^2 } \,\!$	Ω−1 m−1	[I]2 [T]3 [M]−2 [L]−2
Phase constant	δ, φ	$\tan\phi= \frac{X_L - X_C}{R}\,\!$	dimensionless	dimensionless
AC peak current	I0	$I_0 = I_\mathrm{rms} \sqrt{2}\,\!$	A	[I]
AC root mean square current	Irms	$I_\mathrm{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} \left [ I \left ( t \right ) \right ]^2 \mathrm{d} t} \,\!$	A	[I]
AC peak voltage	V0	$V_0 = V_\mathrm{rms} \sqrt{2} \,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
AC root mean square voltage	Vrms	$V_\mathrm{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} \left [ V \left ( t \right ) \right ]^2 \mathrm{d} t} \,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
AC emf, root mean square	$\mathcal{E}_\mathrm{rms}, \sqrt{\langle \mathcal{E} \rangle} \,\!$	$\mathcal{E}_\mathrm{rms}=\mathcal{E}_\mathrm{m}/\sqrt{2}\,\!$	V = J C−1	[M] [L]2 [T]−3 [I]−1
AC average power	$\langle P \rangle \,\!$	$\langle P \rangle =\mathcal{E}I_\mathrm{rms}\cos\phi\,\!$	W = J s−1	[M] [L]2 [T]−3
Capacitive time constant	τC	$\tau_C = RC\,\!$	s	[T]
Inductive time constant	τL	$\tau_L = L/R\,\!$	s	[T]

Magnetic circuits

Main article: Magnetic circuits

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Magnetomotive force, mmf	F, $\mathcal{F}, \mathcal{M}$	$\mathcal{M} = NI$ N = number of turns of conductor	A	[I]

Photonics

Geometric optics (luminal rays)

Main article: Geometrical optics

General fundamental quantities

Quantity (common name/s)	(Common) symbol/s	SI units	Dimension
Object distance	x, s, d, u, x1, s1, d1, u1	m	[L]
Image distance	x', s', d', v, x2, s2, d2, v2	m	[L]
Object height	y, h, y1, h1	m	[L]
Image height	y', h', H, y2, h2, H2	m	[L]
Angle subtended by object	θ, θo, θ1	rad	dimensionless
Angle subtended by image	θ', θi, θ2	rad	dimensionless
Curvature radius of lens/mirror	r, R	m	[L]
Focal length	f	m	[L]

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Lens power	P	$P = 1/f \,\!$	m−1 = D (dioptre)	[L]−1
Lateral magnification	m	$m = - x_2/x_1 = y_2/y_1 \,\!$	dimensionless	dimensionless
Angular magnification	m	$m = \theta_2/\theta_1 \,\!$	dimensionless	dimensionless

Physical optics (EM luminal waves)

Main article: Physical optics

There are different forms of the Poynting vector, the most common are in terms of the E and B or E and H fields.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Poynting vector	S, N	$\mathbf{N} = \frac{1}{\mu_0}\mathbf{E}\times\mathbf{B} = \mathbf{E}\times\mathbf{H} \,\!$	W m−2	[M][T]−3
Poynting flux, EM field power flow	ΦS, ΦN	$\Phi_N = \int_S \mathbf{N} \cdot \mathrm{d}\mathbf{S} \,\!$	W	[M][L]2[T]−3
RMS Electric field of Light	Erms	$E_\mathrm{rms} = \sqrt{\langle E^2 \rangle} = E/\sqrt{2}\,\!$	N C−1 = V m−1	[M][L][T]−3[I]−1
Radiation momentum	p, pEM, pr	$p_{EM} = U/c\,\!$	J s m−1	[M][L][T]−1
Radiation pressure	Pr, pr, PEM	$P_{EM} = I/c = p_{EM}/At \,\!$	W m−2	[M][T]−3

Radiometry

Main article: Radiometry

Visulization of flux through differential area and solid angle. As always $\mathbf{\hat{n}} \,\!$ is the unit normal to the incidant surface A, $\mathrm{d} \mathbf{A} = \mathbf{\hat{n}}\mathrm{d}A \,\!$, and $\mathbf{\hat{e}}_{\angle} \,\!$ is a unit vector in the direction of incident flux on the area element, θ is the angle between them. The factor $\mathbf{\hat{n}} \cdot \mathbf{\hat{e}}_{\angle} \mathrm{d}A = \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} = \cos \theta \mathrm{d}A \,\!$ arises when the flux is not normal to the surface element, so the area normal to the flux is reduced.

For spectral quantities two definitions are in use to refer to the same quantity, in terms of frequency or wavelength.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Radiant energy	Q, E, Qe, Ee		J	[M][L]2[T]−2
Radiant exposure	He	$H_e = \mathrm{d} Q/\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \,\!$	J m−2	[M][T]−3
Radiant energy density	ωe	$\omega_e = \mathrm{d} Q/\mathrm{d}V \,\!$	J m−3	[M][L]−3
Radiant flux, radiant power	Φ, Φe	$\Phi = \mathrm{d} Q/\mathrm{d} t \,\!$	W	[M][L]2[T]−3
Radiant intensity	I, Ie	$I = \mathrm{d} \Phi/\mathrm{d} \Omega \,\!$	W sr−1	[M][L]2[T]−3
Radiance, intensity	L, Le	$L = \mathrm{d}^2 \Phi/\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega \,\!$	W sr−1 m−2	[M][T]−3
Irradiance	E, I, Ee, Ie	$E = \mathrm{d} \Phi/\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \,\!$	W m−2	[M][T]−3
Radiant exitance, radiant emittance	M, Me	$M = \mathrm{d} \Phi/\left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \,\!$	W m−2	[M][T]−3
Radiosity	J, Jν, Je, Jeν	$J = E + M \,\!$	W m−2	[M][T]−3
Spectral radiant flux, spectral radiant power	Φλ, Φν, Φeλ, Φeν	$\Phi_\lambda = \frac{\mathrm{d}^2 Q}{\mathrm{d} \lambda \mathrm{d} t} , \quad \Phi_\nu = \frac{\mathrm{d}^2 Q}{\mathrm{d} \nu \mathrm{d} t } \,\!$	W m−1 (Φλ) W Hz−1 = J (Φν)	[M][L]−3[T]−3 (Φλ) [M][L]−2[T]−2 (Φν)
Spectral radiant intensity	Iλ, Iν, Ieλ, Ieν	$I_\lambda = \frac{\mathrm{d}^2 \Phi}{\mathrm{d} \lambda \mathrm{d} \Omega} , \quad I_\nu = \frac{\mathrm{d}^2 \Phi}{\mathrm{d} \nu \mathrm{d} \Omega} \,\!$	W sr−1 m−1 (Iλ) W sr−1 Hz−1 (Iν)	[M][L]−3[T]−3 (Iλ) [M][L]2[T]−2 (Iν)
Spectral radiance	Lλ, Lν, Leλ, Leν	$L_\lambda = \frac{\mathrm{d}^3 \Phi}{\mathrm{d} \lambda \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega} , \quad L_\nu = \frac{\mathrm{d}^3 \Phi}{\mathrm{d} \nu \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) \mathrm{d} \Omega} \,\!$	W sr−1 m−3 (Lλ) W sr−1 m−2 Hz−1 (Lν)	[M][L]−1[T]−3 (Lλ) [M][L]−2[T]−2 (Lν)
Spectral irradiance	Eλ, Eν, Eeλ, Eeν	$E_\lambda = \frac{\mathrm{d}^2 \Phi}{\mathrm{d} \lambda \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right ) } , \quad E_\nu = \frac{\mathrm{d}^2 \Phi}{\mathrm{d} \nu \left ( \mathbf{\hat{e}}_{\angle} \cdot \mathrm{d}\mathbf{A} \right )} \,\!$	W m−3 (Eλ) W m−2 Hz−1 (Eν)	[M][L]−1[T]−3 (Eλ) [M][L]−2[T]−2 (Eν)

Atomic/nuclear physics

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Number of atoms	N = Number of atoms remaining at time t N0 = Initial number of atoms at time t = 0 ND = Number of atoms decayed at time t	$N_0 = N + N_D \,\!$	dimensionless	dimensionless
Decay rate, activity of a radioisotope	A	$A = \mathrm{d} N /\mathrm{d} t \,\!$	Bq = Hz = s−1	[T]−1
Decay constant	λ	$\lambda = A/N \,\!$	Bq = Hz = s−1	[T]−1
Half-life of a radioisotope	t1/2, T1/2	Time taken for half the number of atoms present to decay $t \rightarrow t + T_{1/2} \,\!$ $N \rightarrow N / 2 \,\!$	s	[T]
Number of half-lives	n (no standard symbol)	$n = t / T_{1/2} \,\!$	dimensionless	dimensionless
Radioisotope time constant, mean lifetime of an atom before decay	τ (no standard symbol)	$\tau = 1 / \lambda \,\!$	s	[T]
Absorbed dose, total ionizing dose (total energy of radiation transferred to unit mass)	D can only be found experimentally	N/A	Sv = J kg−1 (Sievert)	[L]2[T]−2
Equivalent dose	H	$H = DQ \,\!$ Q = radiation quality factor (dimensionless)	Sv = J kg−1 (Sievert)	[L]2[T]−2
Effective dose	E	$E = \sum_j H_jW_j \,\!$ Wj = weighting factors corresponding to radiosensitivities of matter (dimensionless) $\sum_j W_j = 1 \,\!$	Sv = J kg−1 (Sievert)	[L]2[T]−2

Quantum mechanics

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Wave function	ψ, Ψ	To solve from the Schrödinger equation	varies with situation and number of particles
Threshold frequency	f0, ν0	Can only be found by experiment/calculated from work function below.	Hz = s−1	[T]−1
Work function	φ, Φ	$\phi = hf_0\,\!$	J	[M][L]2[T]−2
Wavefunction probability density	ρ	$\rho = \left | \Psi \right |^2 = \Psi^* \Psi$	m−3	[L]−3
Wavefunction probability current	j	Non-relativistic, no external field: $\mathbf{j} = \frac{-i\hbar}{2m}\left(\Psi^* \nabla \Psi - \Psi \nabla \Psi^*\right)$ $= \frac\hbar m \mathrm{Im}(\Psi^*\nabla\Psi)=\mathrm{Re}(\Psi^* \frac{\hbar}{im} \nabla \Psi)$ star * is complex conjugate	m−2 s−1	[T]−1 [L]−2

Astrophysics

In astrophysics, L is used for luminosity (energy per unit time, equivalent to power) and F is used for energy flux (energy per unit time per unit area, equivalent to intensity in terms of area, not solid angle). They are not new quantities, simply different names.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Comoving transverse distance	DM		pc (parsecs)	[L]
Luminosity distance	DL	$D_L = \sqrt{\frac{L}{4\pi F}} \,$	pc (parsecs)	[L]
Apparent magnitude in band j (UV, visible and IR parts of EM spectrum) (Bolometric)	m	$m_j= -\frac{5}{2} \log_{10} \left | \frac {F_j}{F_j^0} \right | \,$	dimensionless	dimensionless
Absolute magnitude (Bolometric)	M	$M = m - 5 \left [ \left ( \log_{10}{D_L} \right ) - 1 \right ]\!\,$	dimensionless	dimensionless
Distance modulus	μ	$\mu = m - M \!\,$	dimensionless	dimensionless
Colour indices	(No standard symbols)	$U-B = M_U - M_B\!\,$ $B-V = M_B - M_V\!\,$	dimensionless	dimensionless
Bolometric correction	Cbol (No standard symbol)	$\begin{align} C_\mathrm{bol} & = m_\mathrm{bol} - V \\ & = M_\mathrm{bol} - M_V \end{align} \!\,$	dimensionless	dimensionless

See also

List of physics formulae
Defining equation (physical chemistry)

Footnotes

1. ^ Warlimont, pp 12–13
2. ^ Vector Analysis (2nd Edition), Schaum's Outlines Series, M. R. Spiegel, S. Lipschutz, D. Spellman, Mc Graw Hill, ISBN 978 0 07 161545 7
3. ^ http://www.ltcconline.net/greenl/courses/202/multipleIntegration/MassMoments.htm, Section: Moments and center of mass
4. ^ Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995, ISBN 0-691-03323-4

References

• Dynamics and Relativity, J.R. Forshaw, A.G. Smith, Wiley, 2009, ISBN 978 0 470 01460 8
• Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, ISBN 0 7195 3382 1
• Encyclopaedia of Physics, R.G. Lerner, G.L. Trigg, 2nd Edition, VHC Publishers, Hans Warlimont, Springer, 2005, pp 12–13
• Physics for Scientists and Engineers: With Modern Physics (6th Edition), P.A. Tipler, G. Mosca, W.H. Freeman and Co, 2008, 9-781429-202657