returns the possible combinations of the list of physical quantities pqi that are dimensionless.


returns the possible combinations of the list of physical quantities pqi that match the dimensions of physical quantity dim.

Details and Options

  • Physical quantities can be valid QuantityVariable objects or physical quantity strings.
  • dim can be a QuantityVariable object. It can also be a combination of QuantityVariable objects or their derivatives.
  • Solutions are determined by the physical quantity components in unit dimensions purely mathematically and have no guarantee of physical significance.
  • Physical dimensions include: "AmountUnit", "AngleUnit", "ElectricCurrentUnit", "InformationUnit", "LengthUnit", "LuminousIntensityUnit", "MassUnit", "MoneyUnit", "SolidAngleUnit", "TemperatureDifferenceUnit", "TemperatureUnit", and "TimeUnit".
  • Dimensionless physical quantities will not be used in the solution.
  • The following options can be given:
  • GeneratedParametersChow to name parameters that are generated
    IncludeQuantities{}additional quantities to include
  • GeneratedParameters takes the option None, which returns a list of parameter-free solutions.
  • IncludeQuantities allows quantity values and constants to be included in the combinations.
  • The setting "PhysicalConstants" for IncludeQuantities includes the quantities Quantity["BoltzmannConstant"], Quantity["ElectricConstant"], Quantity["GravitationalConstant"], Quantity["MagneticConstant"], Quantity["PlanckConstant"], and Quantity["SpeedOfLight"].


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Basic Examples  (1)

Determine the combination of physical quantities that are dimensionally equivalent to energy:

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Find all combinations of physical quantities that result in a dimensionless expression:

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Discover if a dimensionless expression is possible with a set of physical quantities:

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Scope  (2)

Options  (5)

Applications  (4)

Properties & Relations  (1)

Possible Issues  (5)

Interactive Examples  (1)

Neat Examples  (2)

Introduced in 2014
Updated in 2018