# QuantityVariableDimensions

QuantityVariableDimensions[quantityvariable]

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

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## Basic Examples(2)

Find the physical dimensions of a QuantityVariable:

Use the single-argument form of QuantityVariable:

## Scope(3)

Find the physical dimensions of a combination of QuantityVariable objects:

Determine the physical dimensions of the Derivative of a QuantityVariable:

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

## Applications(2)

Find the dimensional coefficients of a sampling of electrical physical quantities:

Check equations for dimensional consistency:

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

Check that the formula is dimensionally correct:

## Properties & Relations(2)

The dimensions of "PhysicalQuantity" entities can also be determined:

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

## Possible Issues(2)

Some physical quantities are dimensionless:

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

Find the dimensions of derivatives:

## Neat Examples(2)

Explore the space of common physical quantities of mechanics:

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

Find the dimensions of these physical quantities:

Write dimensional equations for the physical quantities involved:

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

Form and solve linear equations for the exponents:

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

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).

#### CMS

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

#### BibTeX

@misc{reference.wolfram_2024_quantityvariabledimensions, author="Wolfram Research", title="{QuantityVariableDimensions}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}", note=[Accessed: 25-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_quantityvariabledimensions, organization={Wolfram Research}, title={QuantityVariableDimensions}, year={2018}, url={https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}, note=[Accessed: 25-June-2024 ]}