QuantityVariableDimensions
returns a list of base dimensions associated with the specified quantityvariable.
Details

- QuantityVariableDimensions returns a list of ordered dimension pairs, indicating the magnitude of the quantityvariable in that physical dimension.
- quantityvariable can be a QuantityVariable, a combination of QuantityVariable objects, or the Derivative of a QuantityVariable. quantityvariable can also include "PhysicalQuantity" entities.
- Physical dimensions include: "AmountUnit", "AngleUnit", "ElectricCurrentUnit", "InformationUnit", "LengthUnit", "LuminousIntensityUnit", "MassUnit", "MoneyUnit", "SolidAngleUnit", "TemperatureDifferenceUnit", "TemperatureUnit", and "TimeUnit".
- Electromagnetic dimensions follow the SI convention.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Find the physical dimensions of a QuantityVariable:

https://wolfram.com/xid/0bc69podhl1izg0-o5jmgd

Use the single-argument form of QuantityVariable:

https://wolfram.com/xid/0bc69podhl1izg0-stv9jt


https://wolfram.com/xid/0bc69podhl1izg0-1hdv6u


https://wolfram.com/xid/0bc69podhl1izg0-kytxmk

Scope (3)Survey of the scope of standard use cases
Find the physical dimensions of a combination of QuantityVariable objects:

https://wolfram.com/xid/0bc69podhl1izg0-fqh20z


https://wolfram.com/xid/0bc69podhl1izg0-xp71hg

Determine the physical dimensions of the Derivative of a QuantityVariable:

https://wolfram.com/xid/0bc69podhl1izg0-llzegr


https://wolfram.com/xid/0bc69podhl1izg0-zmw2xa

Discover the dimensions of an arbitrary combination of QuantityVariable objects and their derivatives:

https://wolfram.com/xid/0bc69podhl1izg0-w9swam

Applications (2)Sample problems that can be solved with this function
Find the dimensional coefficients of a sampling of electrical physical quantities:

https://wolfram.com/xid/0bc69podhl1izg0-uhak7c

Check equations for dimensional consistency:

https://wolfram.com/xid/0bc69podhl1izg0-glvd02


https://wolfram.com/xid/0bc69podhl1izg0-2bu5qy

Define the variables in a standard format based on their dimensions:

https://wolfram.com/xid/0bc69podhl1izg0-qjics8
Check that the formula is dimensionally correct:

https://wolfram.com/xid/0bc69podhl1izg0-7tqtlw

Properties & Relations (2)Properties of the function, and connections to other functions
The dimensions of "PhysicalQuantity" entities can also be determined:

https://wolfram.com/xid/0bc69podhl1izg0-gxh3ew

Use the ResourceFunction "PhysicalQuantityLookup" to find physical quantities from unit dimensions:

https://wolfram.com/xid/0bc69podhl1izg0-0vlnt4

Possible Issues (2)Common pitfalls and unexpected behavior
Some physical quantities are dimensionless:

https://wolfram.com/xid/0bc69podhl1izg0-xon4ap

For functions of QuantityVariable, dimensions are only returned for the head:

https://wolfram.com/xid/0bc69podhl1izg0-bj3toh

Find the dimensions of derivatives:

https://wolfram.com/xid/0bc69podhl1izg0-t7dag7

Neat Examples (2)Surprising or curious use cases
Explore the space of common physical quantities of mechanics:

https://wolfram.com/xid/0bc69podhl1izg0-jiach6

Estimating the power of a bomb blast based on dimensional analysis, using only these physical quantities:

https://wolfram.com/xid/0bc69podhl1izg0-0rmceb
Find the dimensions of these physical quantities:

https://wolfram.com/xid/0bc69podhl1izg0-fs5dqj

https://wolfram.com/xid/0bc69podhl1izg0-enix2f

Write dimensional equations for the physical quantities involved:

https://wolfram.com/xid/0bc69podhl1izg0-z4f0xp

Make an ansatz for the energy as a function of radius, mass, time, and mass density:

https://wolfram.com/xid/0bc69podhl1izg0-dc19s8

Form and solve linear equations for the exponents:

https://wolfram.com/xid/0bc69podhl1izg0-dbu4bf


https://wolfram.com/xid/0bc69podhl1izg0-ivz415


https://wolfram.com/xid/0bc69podhl1izg0-wor23x

Given the inputs of the parameters at a given time, estimate the energy of an explosion:

https://wolfram.com/xid/0bc69podhl1izg0-ynw5r6

https://wolfram.com/xid/0bc69podhl1izg0-1u0p8e


https://wolfram.com/xid/0bc69podhl1izg0-d3n3zx

Wolfram Research (2014), QuantityVariableDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html (updated 2018).
Text
Wolfram Research (2014), QuantityVariableDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html (updated 2018).
Wolfram Research (2014), QuantityVariableDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html (updated 2018).
CMS
Wolfram Language. 2014. "QuantityVariableDimensions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html.
Wolfram Language. 2014. "QuantityVariableDimensions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html.
APA
Wolfram Language. (2014). QuantityVariableDimensions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html
Wolfram Language. (2014). QuantityVariableDimensions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html
BibTeX
@misc{reference.wolfram_2025_quantityvariabledimensions, author="Wolfram Research", title="{QuantityVariableDimensions}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}", note=[Accessed: 09-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_quantityvariabledimensions, organization={Wolfram Research}, title={QuantityVariableDimensions}, year={2018}, url={https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}, note=[Accessed: 09-July-2025
]}