# 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: