This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
Biology and medicine Name Standard symbol Definition Field of application Basic reproduction number number of infections caused on average by an infectious individual over entire infectious period epidemiology Body fat percentage total mass of fat divided by total body mass, multiplied by 100 biology Kt/V Kt/V medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time) Waist–hip ratio waist circumference divided by hip circumference biology Waist-to-chest ratio waist circumference divided by chest circumference biology Waist-to-height ratio waist circumference divided by height biology
Chemistry Name Standard symbol DefinitionNamed after Field of application Activity coefficient chemistry (Proportion of "active" molecules or atoms) Arrhenius number Svante Arrhenius chemistry (ratio of activation energy to thermal energy) Atomic weight M chemistry (mass of one atom divided by the atomic mass constant, ) Bodenstein number Bo or Bd Max Bodenstein chemistry (residence-time distribution; similar to the axial mass transfer Peclet number) Damköhler numbers Da Gerhard Damköhler chemistry (reaction time scales vs. residence time) Hatta number Ha Shirôji Hatta (1895–1973) chemical engineering (adsorption enhancement due to chemical reaction) Jakob number Ja chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change) pH chemistry (the measure of the acidity or basicity of an aqueous solution) van 't Hoff factor i Jacobus Henricus van 't Hoff quantitative analysis (Kf and Kb) Wagner number Wa electrochemistry (ratio of kinetic polarization resistance to solution ohmic resistance in an electrochemical cell) Weaver flame speed number Wea combustion (laminar burning velocity relative to hydrogen gas)
Physics
Physical constants
Fluids and heat transfer
Solids Name Standard symbol DefinitionNamed after Field of application Coefficient of kinetic friction mechanics (friction of solid bodies in translational motion) Coefficient of static friction mechanics (friction of solid bodies at rest) Föppl–von Kármán number August Föppl and Theodore von Kármán virology, solid mechanics (thin-shell buckling) Rockwell scale – Hugh M. (1890–1957) and Stanley P. (1886–1940) Rockwell mechanical hardness (indentation hardness of a material) Rolling resistance coefficient Crr vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)
Optics Name Standard symbol DefinitionNamed after Field of application Abbe number V Ernst Abbe optics (dispersion in optical materials) f-number N optics, photography (ratio of focal length to diameter of aperture) Fresnel number F Augustin-Jean Fresnel optics (slit diffraction)Fresnel number Refractive index n electromagnetism, optics (speed of light in vacuum over speed of light in a material) Transmittance T optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample)
Other Name Standard symbol DefinitionNamed after Field of application Fine-structure constant quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction) Havnes parameter O. Havnes In dusty plasma physics, ratio of the total charge carried by the dust particles to the charge carried by the ions , with the number density of particles Helmholtz number Hermann von Helmholtz The most important parameter in duct acoustics. If is the dimensional frequency, then is the corresponding free field wavenumber and is the corresponding dimensionless frequency S.W. RIENSTRA, 2015, Fundamentals of Duct Acoustics, Von Karman Institute Lecture Notes Lundquist number S Stig Lundqvist plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma) Perveance K charged particle transport (measure of the strength of space charge in a charged particle beam) Pierce parameter Traveling wave tube Beta Plasma and fusion power. Ratio of plasma thermal pressure to magnetic pressure, controlling the level of turbulence in a magnetised plasma. Poisson's ratio elasticity (strain in transverse and longitudinal direction) Q factor Q physics, engineering (Damping ratio of oscillator or resonator; energy stored versus energy lost) Relative density RD hydrometers, material comparisons (ratio of density of a material to a reference material—usually water) Relative permeability magnetostatics (ratio of the permeability of a specific medium to free space) Relative permittivity electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum) Specific gravity SG (same as Relative density) Stefan number Ste Josef Stefan phase change, thermodynamics (ratio of sensible heat to latent heat) Strain materials science, elasticity (displacement between particles in the body relative to a reference length) Erlang Agner Krarup Erlang telephony (a measure of offered load on a telephone circuit)
Mathematics and statistics
Geography, geology and geophysics Name Standard symbol DefinitionNamed after Field of application Albedo climatology, astronomy (reflectivity of surfaces or bodies)Dieterich–Ruina–Rice numberJames H. Dieterich, Andy Ruina, and James R. Ricemechanics, friction, rheology, geophysics (stiffness ratio for frictional contacts) Love numbers h, k, lAugustus Edward Hough Love geophysics (solidity of earth and other planets) Porosity geology, porous media (void fraction of the medium) Rossby number Ro Carl-Gustav Arvid Rossby geophysics (ratio of inertial to Coriolis force)
Sport Name Standard symbol Definition Field of application Blondeau number sport science, team sports Gain ratio – bicycling (system of representing gearing; length traveled over length pedaled)Gain Ratio – Sheldon Brown Runs Per Wicket Ratio RpW ratio cricket Winning percentage – Various, e.g. or Various sports
Other fields
Name Standard symbol Definition Field of application Capacity factor energyCohesion numberCohChemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles) Cost of transport COT energy efficiency, economics (ratio of energy input to kinetic motion) Damping ratio mechanics, electrical engineering (the level of damping in a system) Decibel dB acoustics, electronics, control theory (ratio of two intensities or powers of a wave) Elasticity(economics) E economics (response of demand or supply to price changes) Gain – electronics (signal output to signal input) Load factor energy Peel number NP coating (adhesion of microstructures with substrate) Pixel px digital imaging (smallest addressable unit) Power factor pf electrical (real power to apparent power) Power number Np fluid mechanics, power consumption by rotary agitators; resistance force versus inertia force) Prater number β reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet) Relative density RD hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)Lift CoefficientCLAerodynamics, fluid dynamics, hydrodynamicsDrag CoefficientCDAerodynamics, fluid dynamics, hydrodynamics
References
Bibliography