gives the equations for the formula name.


solves or simplifies equations using the specified values quantityi for the variables vari.


gives the value of the specified property for the formula name.

Details and Options

  • FormulaData returns algebraic equations for formulas using standard names such as "OhmsLaw" or "LawOfSines".
  • The variables returned by FormulaData are expressed with the QuantityVariable wrapper.
  • Specified values for vari can be entered as a List or Association.
  • When specifying a list of values to insert into an equation, an input variable value can be specified with var->value; var can be a string or QuantityVariable, and value can be a number, symbol, or Quantity.
  • If the number of unspecified variables equals the number of equations, FormulaData will attempt to solve for the remaining variables for a real-valued solution. Otherwise it will replace all specified variables with the supplied values.
  • FormulaData[] returns a list of all available formulas.
  • FormulaData["Properties"] returns all available properties for formulas.
  • Properties include:
  • "Classes"what classes contain this formula
    "ExternalIdentifiers"source information for the formula
    "Formula"equations for the formula
    "QuantityVariableDimensions"list of base dimensions for all variables
    "QuantityVariableNames"English names for all variables
    "QuantityVariablePhysicalQuantities"physical quantities for all variables
    "QuantityVariables"list of all variables in the formula
    "QuantityVariableTable"details on all variables for the formula
  • "Classes" include general categories such as "Physics" or "Chemistry" as well as subcategorizations such as {"Physics", "Mechanics"}.
  • "Association" can be specified as a second or third argument to alter output to Association. FormulaData[name, "Association"] returns the equation or equations as an Association with the left-hand side of the equations as keys. FormulaData[name,{var1quantity1,var2quantity2,},"Association"] returns the solution to the formula or simplified equations as an Association. FormulaData[name,"property","Association"] returns an Association instead of a List.
  • FormulaData takes the UnitSystem option with the default value $UnitSystem. This option determines the unit system in which results are returned.


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Basic Examples  (7)

Find the equation for a formula:

Include values to solve for formula variables:

Formula names can be found with FormulaLookup:

Formula values can be inserted using free-form input ():

Some formulas have multiple equations:

Formulas with multiple equations will be solved for all variables if possible:

Some formula standard names are specified as lists, such as the different forms of Planck's radiation law:

Scope  (13)

Usage  (9)

Find all formulas used by FormulaData:

Find all properties supported by FormulaData:

Get all instances of QuantityVariable in the equations:

Find the physical quantities for the equation variables:

Learn the variable names for the equation:

Find the dimensions of physical quantities for the equation:

Display all the properties of the formula variables:

Find source information for formulas:

Find what classes a formula belongs to:

Variable Specification  (4)

Formula variables can be specified with QuantityVariable:

The symbol component of QuantityVariable can also be used:

Variables are valid inputs for a formula variable:

Pure numbers are also valid:

Association can be used to specify formula variables:

Options  (1)

UnitSystem  (1)

Use UnitSystem to control the units for results:

Applications  (1)

Formula equations can be used in subsequent calculations:

Integrate over temperature:

Plot the behavior of the equation:

Properties & Relations  (2)

Use FormulaLookup to find formulas by class or name:

Classes include strings and more specific lists of strings:

Get a list of available classes:

Find classes for a specific formula:

Possible Issues  (3)

Use FormulaLookup to find the names of formulas:

Input quantities should have appropriate dimensions:

If there are fewer unspecified variables than equations in the formula, then the system is overdetermined:

Neat Examples  (2)

Common Physical Constants  (1)

Find all formulas that contain both the speed of light and Planck's constant as parameters:

Explore Fundamental Physics Formulas  (1)

Select all formulas that contain Planck's constant, speed of light, or gravitational constant as a parameter:

Construct a network of formulas based on related physical quantities:

Wolfram Research (2014), FormulaData, Wolfram Language function, (updated 2019).


Wolfram Research (2014), FormulaData, Wolfram Language function, (updated 2019).


Wolfram Language. 2014. "FormulaData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019.


Wolfram Language. (2014). FormulaData. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_formuladata, author="Wolfram Research", title="{FormulaData}", year="2019", howpublished="\url{}", note=[Accessed: 24-June-2024 ]}


@online{reference.wolfram_2024_formuladata, organization={Wolfram Research}, title={FormulaData}, year={2019}, url={}, note=[Accessed: 24-June-2024 ]}