--- title: "QuantityVariable" language: "en" type: "Symbol" summary: "QuantityVariable[var, pq] represents a variable with the label var and the corresponding physical quantity pq. QuantityVariable[pq] represents the unlabeled physical quantity pq." keywords: - DimensionalVariable - Quantity - FormulaVariable canonical_url: "https://reference.wolfram.com/language/ref/QuantityVariable.html" source: "Wolfram Language Documentation" related_guides: - title: "Units & Quantities" link: "https://reference.wolfram.com/language/guide/Units.en.md" - title: "Formulas" link: "https://reference.wolfram.com/language/guide/Formulas.en.md" - title: "Scientific Models" link: "https://reference.wolfram.com/language/guide/ScientificModels.en.md" - title: "Scientific Data Analysis" link: "https://reference.wolfram.com/language/guide/ScientificDataAnalysis.en.md" related_functions: - title: "QuantityVariableIdentifier" link: "https://reference.wolfram.com/language/ref/QuantityVariableIdentifier.en.md" - title: "QuantityVariablePhysicalQuantity" link: "https://reference.wolfram.com/language/ref/QuantityVariablePhysicalQuantity.en.md" - title: "QuantityVariableDimensions" link: "https://reference.wolfram.com/language/ref/QuantityVariableDimensions.en.md" - title: "QuantityVariableCanonicalUnit" link: "https://reference.wolfram.com/language/ref/QuantityVariableCanonicalUnit.en.md" - title: "FormulaData" link: "https://reference.wolfram.com/language/ref/FormulaData.en.md" - title: "IndependentPhysicalQuantity" link: "https://reference.wolfram.com/language/ref/IndependentPhysicalQuantity.en.md" --- # QuantityVariable QuantityVariable[var, "pq"] represents a variable with the label var and the corresponding physical quantity "pq". QuantityVariable["pq"] represents the unlabeled physical quantity "pq". ## Details * Supported physical quantities include both physical and chemical quantities such as ``"Length"``, ``"ElectricCurrent"``, and ``"ChemicalPotential"``, as well as mathematical and financial quantities such as ``"Angle"`` and ``"Money"``. * Combinations of physical quantities are also supported, as well as ``"PhysicalQuantity"`` entities. * ``pq`` can also be specified using a list of ordered dimension pairs (such as returned by ``QuantityVariableDimensions``), indicating the magnitude of the ``pq`` in that dimension. * ``Information`` of a ``QuantityVariable`` may include the following properties: | | | | ------------------ | -------------------------------------------- | | "Identifier" | identifier associated with quantity variable | | "PhysicalQuantity" | physical quantity | | "UnitDimensions" | physical dimensions | | "CanonicalUnit" | canonical units | ## Examples (12) ### Basic Examples (2) A ``QuantityVariable`` represents a variable associated with a particular physical quantity: ```wl In[1]:= QuantityVariable["V", "ElectricPotential"] Out[1]= V ``` --- ``QuantityVariable`` can be used to specify values in ``FormulaData`` : ```wl In[1]:= FormulaData["KineticEnergy", {QuantityVariable["K", "Energy"] -> Quantity[10, "Joules"], QuantityVariable["m", "Mass"] -> Quantity[10, "Grams"]}] Out[1]= v == Quantity[-20 Sqrt[5], ("Meters"/"Seconds")] || v == Quantity[20 Sqrt[5], ("Meters"/"Seconds")] ``` ### Scope (2) ``QuantityVariable`` objects can be constructed using free-form input (ctrl+=): ```wl In[1]:= \[FreeformPrompt]["electrical potential"] Out[1]= ElectricPotential ``` --- Create a ``QuantityVariable`` using a combination of physical quantities: ```wl In[1]:= QuantityVariable["x", "Mass" * "Distance"] Out[1]= x ``` Use a list of unit dimensions to set a physical quantity instead: ```wl In[2]:= QuantityVariable["y", {{"LengthUnit", 2}, {"MassUnit", -1}}] Out[2]= y ``` ### Properties & Relations (8) ``QuantityVariableIdentifier`` can be used to extract the symbol from a ``QuantityVariable`` : ```wl In[1]:= var = QuantityVariable["I", "Current"] Out[1]= I In[2]:= QuantityVariableIdentifier[var] Out[2]= "I" ``` The physical quantity can be recovered with ``QuantityVariablePhysicalQuantity`` : ```wl In[3]:= QuantityVariablePhysicalQuantity[var] Out[3]= "Current" ``` --- ``FormulaData`` returns ``QuantityVariable`` objects: ```wl In[1]:= InputForm[FormulaData["OhmsLaw"]] ``` Out[1]= QuantityVariable["V", "ElectricPotential"] == QuantityVariable["I", "ElectricCurrent"]\*QuantityVariable["R", "ElectricResistance"] --- The physical quantities used within ``QuantityVariable`` can be used to search for formulas using ``FormulaLookup`` : ```wl In[1]:= FormulaLookup[All, 5, RequiredPhysicalQuantities -> {"Volume", "Mass", "Speed"}] Out[1]= {{"MeanFreePath", "Volume", "Diameter"}, {"MeanFreePath", "Volume", "Radius"}} ``` --- Any symbol can be used with any physical quantity without restriction: ```wl In[1]:= QuantityVariable["I", "ElectricPotential"] Out[1]= I ``` --- ``QuantityVariable`` can be used in symbolic results: ```wl In[1]:= EntityValue[\[FreeformPrompt]["pendulum system"], "Lagrangian"] Out[1]= Cos[θ[t]] g l m + (1/2) l^2 m Derivative[1][θ][t]^2 In[2]:= EntityValue[\[FreeformPrompt]["pendulum system"], "Lagrangian"]//InputForm ``` Out[2]//InputForm= Cos[QuantityVariable["θ", "Angle"][QuantityVariable["t", "Time"]]]\* QuantityVariable["g", "GravitationalAcceleration"]\*QuantityVariable["l", "Length"]\* QuantityVariable["m", "Mass"] + (QuantityVariable["l", "Length"]^2\*QuantityVariable["m", "Mass"]\* Derivative[1][QuantityVariable["θ", "Angle"]][QuantityVariable["t", "Time"]]^2)/2 --- Use ``QuantityVariable`` in functions such as ``DSolve`` : ```wl In[1]:= DSolve[{Derivative[1][x][t] == Quantity[5, ("Meters"/"Seconds")]}, x[t], t] Out[1]= {{x[t] -> C[1] + (Quantity[5, "Meters"/"Seconds"]) t}} In[2]:= DSolveValue[{Derivative[2][x][t] == Quantity[5, ("Meters"/"Seconds"^2)], x[Quantity[0, "Seconds"]] == Quantity[3, "Meters"], Derivative[1][x][Quantity[0, "Seconds"]] == Quantity[7, ("Meters"/"Seconds")]}, x[t], t] Out[2]= Quantity[3, "Meters"] + (Quantity[7, ("Meters"/"Seconds")]) t + (Quantity[(5/2), ("Meters"/"Seconds"^2)]) t^2 ``` --- ``"PhysicalQuantity"`` entities can be used as arguments for ``QuantityVariable`` : ```wl In[1]:= QuantityVariable["x", Entity["PhysicalQuantity", "Length"]] Out[1]= x ``` --- Use the ``ResourceFunction`` ``"PhysicalQuantityLookup"`` to find physical quantities and quantity variables from units and quantities: ```wl In[1]:= ResourceFunction["PhysicalQuantityLookup"]["Kilograms", "QuantityVariable"] Out[1]= {B, m, Δ, μ, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, Subscript[m, 0], Subscript[M, J], m^ * , {}, Biomass, FabricMass, FoodMass, m, {}, {}, {}, {}, {}, {}, {}, {}, Subscript[m, a]} In[2]:= ResourceFunction["PhysicalQuantityLookup"][Quantity[2, "Miles" / "Hours" ^ 2], "Entity"] Out[2]= {Entity["PhysicalQuantity", "Acceleration"], Entity["PhysicalQuantity", "CentrifugalAcceleration"], Entity["PhysicalQuantity", "CentripetalAcceleration"], Entity["PhysicalQuantity", "CoriolisAcceleration"], Entity["PhysicalQuantity", "CoriolisDecel ... onalFieldStrength"], Entity["PhysicalQuantity", "SpecificForce"], Entity["PhysicalQuantity", "PiezoelectricAccelerometerStrainSensitivity"], Entity["PhysicalQuantity", "SoundParticleAcceleration"], Entity["PhysicalQuantity", "TransportationCost"]} ``` ## See Also * [`QuantityVariableIdentifier`](https://reference.wolfram.com/language/ref/QuantityVariableIdentifier.en.md) * [`QuantityVariablePhysicalQuantity`](https://reference.wolfram.com/language/ref/QuantityVariablePhysicalQuantity.en.md) * [`QuantityVariableDimensions`](https://reference.wolfram.com/language/ref/QuantityVariableDimensions.en.md) * [`QuantityVariableCanonicalUnit`](https://reference.wolfram.com/language/ref/QuantityVariableCanonicalUnit.en.md) * [`FormulaData`](https://reference.wolfram.com/language/ref/FormulaData.en.md) * [`IndependentPhysicalQuantity`](https://reference.wolfram.com/language/ref/IndependentPhysicalQuantity.en.md) ## Related Guides * [Units & Quantities](https://reference.wolfram.com/language/guide/Units.en.md) * [`Formulas`](https://reference.wolfram.com/language/guide/Formulas.en.md) * [Scientific Models](https://reference.wolfram.com/language/guide/ScientificModels.en.md) * [Scientific Data Analysis](https://reference.wolfram.com/language/guide/ScientificDataAnalysis.en.md) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) \| [Updated in 2017 (11.2)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn112.en.md) ▪ [2019 (12.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn120.en.md)