Dimensionless quantity

Dimensionless quantities, or quantities of dimension one, are quantities <a href="/facts/Implicitly_defined/UJmQ2Cyk">implicitly defined</a> in a manner that prevents their aggregation into <a href="/facts/Unit_of_measurement/pvTpWbmC">units of measurement</a>. Typically expressed as <a href="/facts/Ratio/mFmhQt7T">ratios</a> that align with another system, these quantities do not necessitate explicitly defined <a href="/facts/Unit_of_measurement/pvTpWbmC">units</a>. For instance, <a href="/facts/Alcohol_by_volume/FeFdzl8v">alcohol by volume</a> (ABV) represents a <a href="/facts/Volumetric_ratio/nj2akBNM">volumetric ratio</a>; its value remains independent of the specific <a href="/facts/Unit_of_volume/q0pRQd4e">units of volume</a> used, such as in <a href="/facts/Milliliter/QKwbQz8I">milliliters</a> per milliliter (mL/mL).
The <a href="/facts/1/d6SoCnze">number one</a> is recognized as a dimensionless <a href="/facts/Base_unit_of_measurement/7d7Uqd9N">base quantity</a>. <a href="/facts/Radian/Srd38Sxa">Radians</a> serve as dimensionless units for <a href="/facts/Angle/gFUTEQYq">angular measurements</a>, derived from the universal ratio of 2π times the <a href="/facts/Radius/9Gr9deYD">radius</a> of a circle being equal to its circumference.
Dimensionless quantities play a crucial role serving as <a href="/facts/Parameter/zFvVFMv9">parameters</a> in <a href="/facts/Differential_equation/9MGbE3Ca">differential equations</a> in various technical disciplines. In <a href="/facts/Calculus/MEmUTYoz">calculus</a>, concepts like the unitless ratios in <a href="/facts/Limits_of_integration/nyhHNKLM">limits</a> or <a href="/facts/Derivative/7Ito70Dh">derivatives</a> often involve dimensionless quantities. In <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the <a href="/facts/Reynolds_number/4sdungsf">Reynolds number</a> in <a href="/facts/Fluid_dynamics/y7uzSCfg">fluid dynamics</a>, the <a href="/facts/Fine-structure_constant/zyzpmTJV">fine-structure constant</a> in <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, and the <a href="/facts/Lorentz_factor/s5uyKNsA">Lorentz factor</a> in <a href="/facts/Special_relativity/vsFFc63E">relativity</a>. In <a href="/facts/Chemistry/SrNqkGVm">chemistry</a>, <a href="/facts/Equation_of_state/tLILkepz">state properties</a> and ratios such as <a href="/facts/Mole_fraction/nW4EepmJ">mole fractions</a> <a href="/facts/Concentration_ratio/tu5fvV1p">concentration ratios</a> are dimensionless.

Dimensionless quantity open-in-new

Dimensionless quantity