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UnitDimensions[unit]

returns a list of base dimensions associated with the specified unit.

UnitDimensions[quantity]

returns a list of base dimensions associated with the unit of the specified quantity.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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UnitDimensions

UnitDimensions[unit]

returns a list of base dimensions associated with the specified unit.

UnitDimensions[quantity]

returns a list of base dimensions associated with the unit of the specified quantity.

Details

  • UnitDimensions returns a list of ordered dimension pairs, indicating the magnitude of the unit in that dimension.
  • Physical dimensions are: "AmountUnit", "ElectricCurrentUnit", "LengthUnit", "LuminousIntensityUnit", "MassUnit", "TemperatureUnit", and "TimeUnit".
  • Additional unit dimensions include: "AngleUnit", "InformationUnit", "MoneyUnit", "PersonUnit" and "SolidAngleUnit".
  • Temperatures and temperature differences share a common unit dimension.
  • UnitDimensions accepts TimeSeries, EventSeries, and TemporalData inputs.

Examples

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Basic Examples  (2)

Get the dimensions associated with a unit:

Wolfram Language code: UnitDimensions["Meters"]
Wolfram Language code: UnitDimensions[["1 newton"]]
Wolfram Language code: UnitDimensions[["8 volts"]]

Get the dimensions associated with products of units:

Wolfram Language code: UnitDimensions["Candelas" / "Inches" ^ 2]
Wolfram Language code: UnitDimensions[Quantity[3, "DegreesFahrenheit"*"Moles"]]

Scope  (3)

Get the unit dimensions from Quantity expressions in a time series:

Wolfram Language code: data = EarthquakeData[All, {8, 10}, {{2011, 1, 1}, {2013, 1, 1}}, "Depth"]
Wolfram Language code: data[DateObject[{2012, 4, 11}]]
Wolfram Language code: UnitDimensions[data]
Wolfram Language code: %[DateObject[{2012, 4, 11}, "Day", "Gregorian", -6.]]

Get the unit dimensions from Quantity expressions in structured arrays like QuantityArray or SymmetrizedArray objects:

Wolfram Language code: UnitDimensions[QuantityArray[{1, 2, 3}, "Hectares"]]
Wolfram Language code: UnitDimensions[ SymmetrizedArray[{{1, 1} -> Quantity[2, "Liters"], {2, 1} -> Quantity[3, "Newtons"]}, {2, 2}, Symmetric[{1, 2}]]]

Get the unit dimensions from Quantity expressions in SparseArray and Association specifications:

Wolfram Language code: UnitDimensions[SparseArray[{1 -> Quantity[8, "Bits"], 2 -> Quantity[1, "Octets"]}]]
Wolfram Language code: UnitDimensions[<|"Distance" -> Quantity[260, "Miles"], "Duration" -> Quantity[3, "Hours"]|>]

Applications  (2)

Use UnitDimensions to examine the base dimension of a unit:

Wolfram Language code: UnitDimensions["Pecks"]
Wolfram Language code: UnitDimensions["OortConstantA"]
Wolfram Language code: UnitDimensions["Ostents"]

Use UnitDimensions to find the base dimension of a unit derived from SI base units:

Wolfram Language code: UnitDimensions["Atmospheres"]
Wolfram Language code: UnitDimensions["HorsepowerMechanical"]

Properties & Relations  (9)

UnitDimensions returns the base dimension of a unit:

Wolfram Language code: UnitDimensions[Quantity[3, "Spins"]]
Wolfram Language code: UnitDimensions[Quantity[7000, "WaterInches"]]

The dimension pairs are returned lexically ordered:

Wolfram Language code: UnitDimensions[Quantity[5, "Meters" * "Seconds"]]
Wolfram Language code: UnitDimensions[Quantity[5, "Seconds" * "Meters"]]

UnitDimensions returns the argument of an IndependentUnit specification together with its power:

Wolfram Language code: Quantity[3, "Kilometers" * IndependentUnit["myUnit"] ^ 2]
Wolfram Language code: UnitDimensions[%]

UnitDimensions returns one dimension pair for a MixedUnit specification:

Wolfram Language code: Quantity[MixedMagnitude[{5, 10}], MixedUnit[{"Feet", "Inches"}]]
Wolfram Language code: UnitDimensions[%]

UnitDimensions ignores the date in DatedUnit specifications:

Wolfram Language code: UnitDimensions[DatedUnit["Meters", 1889]]
Wolfram Language code: UnitDimensions[DatedUnit["USDollars", 2000]]

An empty list is returned for units without dimension:

Wolfram Language code: UnitDimensions[Quantity[72, "Percent"]]
Wolfram Language code: UnitDimensions[Quantity[98, "Scores"]]

A unit given as a prefix only is dimensionless:

Wolfram Language code: UnitDimensions[Quantity[100, "Hectometers"]]
Wolfram Language code: UnitDimensions[Quantity[100, "Hecto"]]

UnitDimensions will automatically attempt to interpret an unknown unit string:

Wolfram Language code: KnownUnitQ["feets"]
Wolfram Language code: UnitDimensions["feets"]
Wolfram Language code: KnownUnitQ["Feet"]

UnitDimensions threads over lists:

Wolfram Language code: UnitDimensions[{Quantity[7, "Meters"], Quantity[8, "Bits"], Quantity[5, "Ounces"]}]
Wolfram Language code: UnitDimensions[{Quantity[7, "Minutes"], {Quantity[2, "Radians"]}, Quantity[5, "Steradians"]}]

Possible Issues  (2)

Numerical values are considered dimensionless:

Wolfram Language code: UnitDimensions[Pi]

Temperatures and temperature differences share a common unit dimension:

Wolfram Language code: UnitDimensions["DegreesCelsius"]
Wolfram Language code: UnitDimensions["DegreesCelsiusDifference"]
Wolfram Research (2012), UnitDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/UnitDimensions.html (updated 2022).

Text

Wolfram Research (2012), UnitDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/UnitDimensions.html (updated 2022).

CMS

Wolfram Language. 2012. "UnitDimensions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/UnitDimensions.html.

APA

Wolfram Language. (2012). UnitDimensions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UnitDimensions.html

BibTeX

@misc{reference.wolfram_2026_unitdimensions, author="Wolfram Research", title="{UnitDimensions}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/UnitDimensions.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_unitdimensions, organization={Wolfram Research}, title={UnitDimensions}, year={2022}, url={https://reference.wolfram.com/language/ref/UnitDimensions.html}, note=[Accessed: 13-June-2026]}