List of physical quantities

This article consists of tables outlining a number of physical quantities.

The first table lists the fundamental quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. The second table lists the derived physical quantities. Derived quantities can be expressed in terms of the base quantities.

Note that neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magnetic B-field which is known as the magnetic flux density, the magnetic induction or simply as the magnetic field depending on the context. Similarly, surface tension can be denoted by either σ, γ or T. The table usually lists only one name and symbol that is most commonly used.

The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved.

Fundamental

Fundamental quantities
Base quantity	Symbol	Description	SI base unit	Dimension	Comments
Amount of substance	n	The quantity proportional to the number of particles in a sample, with the Avogadro constant as the proportionality constant	mole (mol)	N	extensive, scalar
Length	l	The one-dimensional extent of an object	metre (m)	L	extensive
Time	t	The duration of an event	second (s)	T	scalar, intensive, extensive
Mass	m	A measure of resistance to acceleration	kilogram (kg)	M	extensive, scalar
Temperature	T	Average kinetic energy per degree of freedom of a system	kelvin (K)	Θ or [K]	intensive, scalar
Electric Current	I	Rate of flow of electrical charge per unit time	ampere (A)	I	extensive, scalar
Angle	∠	the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.	radian (rad)	∠ BAC	extensive, scalar
Luminous intensity	I_v	Wavelength-weighted power of emitted light per unit solid angle	candela (cd)	J	scalar

Scalar

Scalar quantities
Derived quantity	Symbol	Description	SI derived unit	Dimension	Comments
Absorbed dose rate	D	Absorbed dose received per unit of time	Gy/s	L² T⁻³
Action	S	Momentum of particle multiplied by distance travelled	J/Hz	L² M T⁻¹	scalar
Angular acceleration	ω_a	Change in angular velocity per unit time	rad/s²	T⁻²
Area	A	Extent of a surface	m²	L²	extensive, bivector or scalar
Area density	ρ_A	Mass per unit area	kg⋅m⁻²	L⁻² M	intensive
Capacitance	C	Stored charge per unit electric potential	farad (F = C/V)	L⁻² M⁻¹ T⁴ I²	scalar
Catalytic activity concentration		Change in reaction rate due to presence of a catalyst per unit volume of the system	kat⋅m⁻³	L⁻³ T⁻¹ N	intensive
Chemical potential	μ	Energy per unit change in amount of substance	J/mol	L² M T⁻² N⁻¹	intensive
Dose equivalent	H	Received radiation adjusted for the effect on biological tissue	sievert (Sv = J/kg)	L² T⁻²	intensive
Electric charge	Q	The force per unit electric field strength	coulomb (C = A⋅s)	T I	extensive, conserved
Electric charge density	ρ_Q	Electric charge per unit volume	C/m³	L⁻³ T I	intensive
Electrical conductance	G	Measure for how easily current flows through a material	siemens (S = Ω⁻¹)	L⁻² M⁻¹ T³ I²	scalar
Electrical conductivity	σ	Measure of a material's ability to conduct an electric current	S/m	L⁻³ M⁻¹ T³ I²	scalar
Electric potential	φ	Energy required to move a unit charge through an electric field from a reference point	volt (V = J/C)	L² M T⁻³ I⁻¹	extensive, scalar
Electrical resistance	R	Electric potential per unit electric current	ohm (Ω = V/A)	L² M T⁻³ I⁻²	extensive, scalar, assumes linearity
Electrical resistivity	ρ_e	Bulk property equivalent of electrical resistance	ohm-metre (Ω⋅m)	L³ M T⁻³ I⁻²	extensive, scalar, conserved
Energy	E	Energy	joule (J)	L² M T⁻²
Energy density	?	Energy per volume	J⋅m⁻³	L⁻¹ M T⁻²	intensive
Entropy	S	Logarithmic measure of the number of available states of a system	J/K	L² M T⁻² Θ⁻¹	extensive, scalar
Force	$F$ →	Transfer of momentum per unit time	newton (N = kg⋅m⋅s⁻²)	L M T⁻²	extensive, vector
Frequency	f	Number of (periodic) occurrences per unit time	hertz (Hz = s⁻¹)	T⁻¹	scalar
Half-life	t_1/2	Time for a quantity to decay to half its initial value	s	T
Heat	Q	Thermal energy	joule (J)	L² M T⁻²
Heat capacity	C_p	Energy per unit temperature change	J/K	L² M T⁻² Θ⁻¹	extensive
Heat flux density	ϕ_Q	Heat flow per unit time per unit surface area	W/m²	M T⁻³
Illuminance	E_v	Wavelength-weighted luminous flux per unit surface area	lux (lx = cd⋅sr/m²)	L⁻² J
Impedance	Z	Resistance to an alternating current of a given frequency, including effect on phase	ohm (Ω)	L² M T⁻³ I⁻²	complex scalar
Inductance	L	Magnetic flux generated per unit current through a circuit	henry (H)	L² M T⁻² I⁻²	scalar
Irradiance	E	Electromagnetic radiation power per unit surface area	W/m²	M T⁻³	intensive
Intensity	I	Power per unit cross sectional area	W/m²	M T⁻³	intensive
Linear density	ρ_l	Mass per unit length	kg⋅m⁻¹	L⁻¹ M
Luminous flux (or luminous power)	F	Perceived power of a light source	lumen (lm = cd⋅sr)	J
Mach number (or mach)	M	Ratio of flow velocity to the local speed of sound	unitless	1
Magnetic flux	Φ	Measure of magnetism, taking account of the strength and the extent of a magnetic field	weber (Wb)	L² M T⁻² I⁻¹	scalar
Mass fraction	x	Mass of a substance as a fraction of the total mass	kg/kg	1	intensive
(Mass) Density (or volume density)	ρ	Mass per unit volume	kg/m³	L⁻³ M	intensive
Mean lifetime	τ	Average time for a particle of a substance to decay	s	T	intensive
Molar concentration	C	Amount of substance per unit volume	mol⋅m⁻³	L⁻³ N	intensive
Molar energy	J/mol	Amount of energy present in a system per unit amount of substance	J/mol	L² M T⁻² N⁻¹	intensive
Molar entropy	S°	Entropy per unit amount of substance	J/(K⋅mol)	L² M T⁻² Θ⁻¹ N⁻¹	intensive
Molar heat capacity	c	Heat capacity of a material per unit amount of substance	J/(K⋅mol)	L² M T⁻² Θ⁻¹ N⁻¹	intensive
Moment of inertia	I	Inertia of an object with respect to angular acceleration	kg⋅m²	L² M	extensive, tensor, scalar
Optical power	P	Measure of the effective curvature of a lens or curved mirror; inverse of focal length	dioptre (dpt = m⁻¹)	L⁻¹
Permeability	μ_s	Measure for how the magnetization of material is affected by the application of an external magnetic field	H/m	L M T⁻² I⁻²	intensive
Permittivity	ε_s	Measure for how the polarization of a material is affected by the application of an external electric field	F/m	L⁻³ M⁻¹ T⁴ I²	intensive
Plane angle	θ	Ratio of circular arc length to radius	radian (rad)	1
Power	P	Rate of transfer of energy per unit time	watt (W)	L² MT⁻³	extensive, scalar
Pressure	p	Force per unit area	pascal (Pa = N/m²)	L⁻¹ MT⁻²	intensive, scalar
(Radioactivity) Activity	A	Number of particles decaying per unit time	becquerel (Bq = Hz)	T⁻¹	extensive, scalar
(Radiation) Dose	D	Ionizing radiation energy absorbed per unit mass	gray (Gy = J/kg)	L² T⁻²
Radiance	L	Power of emitted electromagnetic radiation per unit solid angle per emitting source area	W/(m²⋅sr)	M T⁻³
Radiant intensity	I	Power of emitted electromagnetic radiation per unit solid angle	W/sr	L² M T⁻³	scalar
Reaction rate	r	Rate of a chemical reaction for unit time	mol/(m³⋅s)	L⁻³ T⁻¹ N	intensive, scalar
Refractive index	n	Factor by which the phase velocity of light is reduced in a medium	unitless	1	intensive, scalar
Reluctance	${\mathcal {R}}$	resistance to the flow of magnetic flux	H⁻¹	L⁻² M⁻¹ T² I²	scalar
Solid angle	Ω	Ratio of area on a sphere to its radius squared	steradian (sr)	∠²
Specific energy	$e$	Energy density per unit mass	J⋅kg⁻¹	L² T⁻²	intensive
Specific heat capacity	c	Heat capacity per unit mass	J/(K⋅kg)	L² T⁻² Θ⁻¹	intensive
Specific volume	v	Volume per unit mass (reciprocal of density)	m³⋅kg⁻¹	L³ M⁻¹	intensive
Spin	S	Quantum-mechanically defined angular momentum of a particle	kg⋅m²⋅s⁻¹	L² M T⁻¹
Strain	ε	Extension per unit length	unitless	1
Stress	σ	Force per unit oriented surface area	Pa	L⁻¹ M T⁻²	order 2 tensor
Surface tension	γ	Energy change per unit change in surface area	N/m or J/m²	M T⁻²
Thermal conductance	κ (or) λ	Measure for the ease with which an object conducts heat	W/K	L² M T⁻³ Θ⁻¹	extensive
Thermal conductivity	λ	Measure for the ease with which a material conducts heat	W/(m⋅K)	L M T⁻³ Θ⁻¹	intensive
Thermal resistance	R	Measure for the ease with which an object resists conduction of heat	K/W	L⁻² M⁻¹ T³ Θ	extensive
Thermal resistivity	R_λ	Measure for the ease with which a material resists conduction of heat	K⋅m/W	L⁻¹ M⁻¹ T³ Θ	intensive
Viscosity	η	The measure of the internal friction in a fluid	Pa⋅s	L^-1 M T^-1	intensive, scalar
Volume	V	Three dimensional extent of an object	m³	L³	extensive, scalar
Volumetric flow rate	Q	Rate of change of volume with respect to time	m³⋅s⁻¹	L³ T⁻¹	extensive, scalar
Wavelength	λ	Perpendicular distance between repeating units of a wave	m	L
Wavenumber	k	Repetency or spatial frequency: the number of cycles per unit distance	m⁻¹	L⁻¹	scalar
Work	W	Transferred energy	joule (J)	L² M T⁻²	scalar
Young's modulus	E	Ratio of stress to strain	pascal (Pa = N/m²)	L⁻¹ M T⁻²	scalar; assumes isotropic linear material
spring constant	k	k is the torsional constant (measured in N·m/radian), which characterizes the stiffness of the torsional spring or the resistance to angular displacement.	N/m	M T⁻²	scalar

Vector

Vector quantities
Derived quantity	Symbol	Description	SI derived unit	Dimension	Comments
Absement	A	Measure of sustained displacement: the first integral with respect to time of displacement	m⋅s	L T	vector
Acceleration	$a$ →	Rate of change of velocity per unit time: the second time derivative of position	m/s²	L T⁻²	vector
Angular acceleration	ω_a	Change in angular velocity per unit time	rad/s²	T⁻²	pseudovector
Angular momentum	L	Measure of the extent and direction an object rotates about a reference point	kg⋅m²/s	L² M T⁻¹	conserved, bivector
Angular velocity	ω	The angle incremented in a plane by a segment connecting an object and a reference point per unit time	rad/s	T⁻¹	bivector
Area	A	Extent of a surface	m²	L²	extensive, bivector or scalar
Centrifugal force	F_c	Inertial force that appears to act on all objects when viewed in a rotating frame of reference	N⋅rad = kg⋅m⋅rad⋅s⁻²	L M T⁻²	bivector
Crackle	$c$ →	Change of jounce per unit time: the fifth time derivative of position	m/s⁵	L T⁻⁵	vector
Current density	$J \to$	Electric current per unit cross-section area	A/m²	L⁻² I	conserved, intensive, vector
Electric dipole moment	p	Measure of the separation of equal and opposite electric charges	C⋅m	L T I	vector
Electric displacement field	$D \to$	Strength of the electric displacement	C/m²	L⁻² T I	vector field
Electric field strength	$E \to$	Strength of the electric field	V/m, N/C	L M T⁻³ I⁻¹	vector field
Force	$F$ →	Transfer of momentum per unit time	newton (N = kg⋅m⋅s⁻²)	L M T⁻²	extensive, vector
Impulse	J	Transferred momentum	newton-second (N⋅s = kg⋅m/s)	L M T⁻¹	vector
Jerk	$j$ →	Change of acceleration per unit time: the third time derivative of position	m/s³	L T⁻³	vector
Jounce (or snap)	$s$ →	Change of jerk per unit time: the fourth time derivative of position	m/s⁴	L T⁻⁴	vector
Magnetic field strength	H	Strength of a magnetic field	A/m	L⁻¹ I	vector field
Magnetic flux density	B	Measure for the strength of the magnetic field	tesla (T = Wb/m²)	M T⁻² I⁻¹	pseudovector field
Magnetic moment (or magnetic dipole moment)	m	The component of magnetic strength and orientation that can be represented by an equivalent magnetic dipole	N⋅m/T	L² I	vector
Magnetization	M	Amount of magnetic moment per unit volume	A/m	L⁻¹ I	vector field
Momentum	$p$ →	Product of an object's mass and velocity	kg⋅m/s	L M T⁻¹	vector, extensive
Pop	$p$ →	Rate of change of crackle per unit time: the sixth time derivative of position	m/s⁶	L T⁻⁶	vector
Pressure gradient	$\nabla p$	Pressure per unit distance	pascal/m	L⁻² M¹ T⁻²	vector
Temperature gradient	$\nabla T$	steepest rate of temperature change at a particular location	K/m	L⁻¹ Θ	vector
Torque	τ	Product of a force and the perpendicular distance of the force from the point about which it is exerted	newton-metre (N⋅m)	L² M T⁻²	bivector (or pseudovector in 3D)
Velocity	$v$ →	Moved distance per unit time: the first time derivative of position	m/s	L T⁻¹	vector
Wavevector	$k \to$	Repetency or spatial frequency vector: the number of cycles per unit distance	m⁻¹	L⁻¹	vector
Weight	w	Gravitational force on an object	newton (N = kg⋅m/s²)	L M T⁻²	vector

Tensor

Scalar quantities
Derived quantity	Symbol	Description	SI derived unit	Dimension	Comments
Moment of inertia	I	Inertia of an object with respect to angular acceleration	kg⋅m²	L² M	extensive, tensor, scalar
Stress	σ	Force per unit oriented surface area	Pa	L⁻¹ M T⁻²	order 2 tensor

Fundamental

Scalar

Vector

Tensor

See also