Units & Quantities

The Wolfram Language allows you to do arithmetic not only with symbols and numbers, but also with units. The Wolfram Language's integration with Wolfram|Alpha allows for a sophisticated unit system that combines the flexibility of free-form linguistics with the computational power of numerical and symbolic algorithms. The units framework integrates seamlessly with visualization, numeric and algebraic computation functions. It also supports dimensional analysis, as well as purely symbolic operations on quantities.

Unit and Quantity Input

() enter quantities and units, using free-form linguistics

Quantity the value of a physical quantity with units included

QuantityArray array of quantities with common units

QuantityDistribution probability distribution with units

Quantity Components

QuantityMagnitude give the value associated with a quantity

QuantityUnit give the unit associated with a quantity

UnitDimensions give the associated physical dimensions

QuantityQ  ▪  KnownUnitQ

Quantity Display

QuantityForm display using the specified units or abbreviations

TargetUnits target units to use for visualization and other functions

Unit Conversion

$UnitSystem default unit system for output (e.g. "Imperial" or "Metric")

UnitConvert convert between different units and unit systems

CompatibleUnitQ test whether multiple quantities are compatible

CommonUnits convert a list of quantities to a common unit

UnitSimplify convert to simpler units

Quantities with Uncertainty »

Around numbers or quantities with specified uncertainties

VectorAround  ▪  MeanAround  ▪  AroundReplace  ▪  ...

Physical Quantities

QuantityVariable a variable representing a physical quantity (e.g. for mass)

QuantityVariableIdentifier  ▪  QuantityVariablePhysicalQuantity

FormulaData common scientific formulas involving physical quantities

Dimensional Analysis

DimensionalCombinations possible combinations of dimensional physical quantities

QuantityVariableDimensions  ▪  QuantityVariableCanonicalUnit

NondimensionalizationTransform convert an equation to dimensionless form

Mixed Units

MixedUnit a mixed unit formed from a list of units (e.g. hours, minutes, seconds)

MixedMagnitude list of magnitudes corresponding to the units in a mixed unit

Currency Units

CurrencyConvert convert between currencies, using real-time data

DatedUnit  ▪  InflationAdjust

User-Defined Units & Physical Quantities

IndependentUnit represent an arbitrary user-specified unit (e.g. "foxes")

IndependentPhysicalQuantity represent a user-specified physical quantity    

IndependentUnitDimension represent a user-specified independent dimension for units