List of dimensionless quantities

This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The table also includes pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.

Name	Standard symbol	Definition	Field of application
Abbe number	V	${\displaystyle V={\frac {n_{d}-1}{n_{F}-n_{C}}}}$	optics (dispersion in optical materials)
Activity coefficient	${\displaystyle \gamma }$	${\displaystyle \gamma ={\frac {a}{x}}}$	chemistry (Proportion of "active" molecules or atoms)
Albedo	${\displaystyle \alpha }$	${\displaystyle \alpha =(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}$	climatology, astronomy (reflectivity of surfaces or bodies)
Archimedes number	Ar	${\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}$	fluid mechanics (motion of fluids due to density differences)
Arrhenius number	${\displaystyle \alpha }$	${\displaystyle \alpha ={\frac {E_{a}}{RT}}}$	chemistry (ratio of activation energy to thermal energy)[1]
Atomic weight	M		chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u)
Atwood number	A	${\displaystyle \mathrm {A} ={\frac {\rho _{1}-\rho _{2}}{\rho _{1}+\rho _{2}}}}$	fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
Bagnold number	Ba	${\displaystyle \mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}\gamma }{\mu }}}$	fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[2]
Basic reproduction number	${\displaystyle R_{0}}$	number of infections caused on average by an infectious individual over entire infectious period	epidemiology
Bejan number (fluid mechanics)	Be	${\displaystyle \mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}}$	fluid mechanics (dimensionless pressure drop along a channel)[3]
Bejan number (thermodynamics)	Be	${\displaystyle \mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}}$	thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)[4]
Bingham number	Bm	${\displaystyle \mathrm {Bm} ={\frac {\tau _{y}L}{\mu V}}}$	fluid mechanics, rheology (ratio of yield stress to viscous stress)[1]
Biot number	Bi	${\displaystyle \mathrm {Bi} ={\frac {hL_{C}}{k_{b}}}}$	heat transfer (surface vs. volume conductivity of solids)
Blake number	Bl or B	${\displaystyle \mathrm {B} ={\frac {u\rho }{\mu (1-\epsilon )D}}}$	geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
	${\displaystyle B_{\kappa }}$	${\displaystyle \mathrm {B_{\kappa }} ={\frac {t_{g}v_{f}}{l_{mf}}}}$	sport science, team sports[5]
Bodenstein number	Bo or Bd	${\displaystyle \mathrm {Bo} =vL/{\mathcal {D}}=\mathrm {Re} \,\mathrm {Sc} }$	chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)[6]
Bond number	Bo	${\displaystyle \mathrm {Bo} ={\frac {\rho aL^{2}}{\gamma }}}$	geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) [7]
Brinkman number	Br	${\displaystyle \mathrm {Br} ={\frac {\mu U^{2}}{\kappa (T_{w}-T_{0})}}}$	heat transfer, fluid mechanics (conduction from a wall to a viscous fluid)
	NBK	${\displaystyle \mathrm {N} _{\mathrm {BK} }={\frac {u\mu }{k_{\mathrm {rw} }\sigma }}}$	fluid mechanics (combination of capillary number and Bond number) [8]
Capillary number	Ca	${\displaystyle \mathrm {Ca} ={\frac {\mu V}{\gamma }}}$	porous media, fluid mechanics (viscous forces versus surface tension)
Chandrasekhar number	Q	${\displaystyle \mathrm {Q} ={\frac {{B_{0}}^{2}d^{2}}{\mu _{0}\rho \nu \lambda }}}$	magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
Colburn J factors	JM, JH, JD		turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
Coefficient of kinetic friction	${\displaystyle \mu _{k}}$		mechanics (friction of solid bodies in translational motion)
Coefficient of static friction	${\displaystyle \mu _{s}}$		mechanics (friction of solid bodies at rest)
Coefficient of determination	${\displaystyle R^{2}}$		statistics (proportion of variance explained by a statistical model)
Coefficient of variation	${\displaystyle {\frac {\sigma }{\mu }}}$	${\displaystyle {\frac {\sigma }{\mu }}}$	statistics (ratio of standard deviation to expectation)
Cohesion number	Coh	${\displaystyle Coh={\frac {1}{\rho g}}\left({\frac {\Gamma ^{5}}{{E^{*}}^{2}{R^{*}}^{8}}}\right)^{\frac {1}{3}}}$	Chemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles)[9][10]
Correlation	ρ or r	${\displaystyle {\frac {\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})]}{\sigma _{X}\sigma _{Y}}}}$	statistics (measure of linear dependence)
Cost of transport	COT	${\displaystyle \mathrm {COT} ={\frac {E}{mgd}}}$	energy efficiency, economics (ratio of energy input to kinetic motion)
Courant–Friedrich–Levy number	C or