Units of Measure

Remarks

Units at Runtime

Units of Measure are used only for static checking by the compiler, and are not available at runtime. They cannot be used in reflection or in methods like ToString.

For example, C# gives a double with no units for a field of type float<m> defined by and exposed from an F# library.

Conversions between units

[<Measure>] type m // meters
[<Measure>] type cm // centimeters

// Conversion factor
let cmInM = 100<cm/m>

let distanceInM = 1<m>
let distanceInCM = distanceInM * cmInM // 100<cm>

// Conversion function
let cmToM (x : int<cm>) = x / 100<cm/m>
let mToCm (x : int<m>) = x * 100<cm/m>

cmToM 100<cm> // 1<m>
mToCm 1<m> // 100<cm>

Note that the F# compiler does not know that 1<m> equals 100<cm>. As far as it cares, the units are separate types. You can write similar functions to convert from meters to kilograms, and the compiler would not care.

[<Measure>] type kg

// Valid code, invalid physics
let kgToM x = x / 100<kg/m>

It is not possible to define units of measure as multiples of other units such as

// Invalid code
[<Measure>] type m = 100<cm>

However, to define units "per something", for example Hertz, measuring frequency, is simply "per second", is quite simple.

// Valid code
[<Measure>] type s
[<Measure>] type Hz = /s

1 / 1<s> = 1 <Hz> // Evaluates to true

[<Measure>] type N = kg m/s // Newtons, measuring force. Note lack of multiplication sign.

// Usage
let mass = 1<kg>
let distance = 1<m>
let time = 1<s>

let force = mass * distance / time // Evaluates to 1<kg m/s>
force = 1<N> // Evaluates to true

Ensuring Consistent Units in Calculations

Units of measure are additional type annotations that can be added to floats or integers. They can be used to verify at compile time that calculations are using units consistently.

To define annotations:

[<Measure>] type m // meters
[<Measure>] type s // seconds
[<Measure>] type accel = m/s^2 // acceleration defined as meters per second squared

Once defined, annotations can be used to verify that an expression results in the expected type.

// Compile-time checking that this function will return meters, since (m/s^2) * (s^2) -> m
// Therefore we know units were used properly in the calculation.
let freeFallDistance (time:float<s>) : float<m> = 
    0.5 * 9.8<accel> * (time*time)    

// It is also made explicit at the call site, so we know that the parameter passed should be in seconds
let dist:float<m> = freeFallDistance 3.0<s>
printfn "%f" dist

Unit-of-measure type parameters

The [<Measure>] attribute can be used on type parameters to declare types that are generic with respect to units of measure:

type CylinderSize<[<Measure>] 'u> =
    { Radius : float<'u>
      Height : float<'u> }

Test usage:

open Microsoft.FSharp.Data.UnitSystems.SI.UnitSymbols

/// This has type CylinderSize<m>.
let testCylinder =
    { Radius = 14.<m>
      Height =  1.<m> }

Use standardized unit types to maintain compatibility

For example, types for SI units have been standardized in the F# core library, in Microsoft.FSharp.Data.UnitSystems.SI. Open the appropriate sub-namespace, UnitNames or UnitSymbols, to use them. Or, if only a few SI units are required, they can be imported with type aliases:

/// Seconds, the SI unit of time. Type abbreviation for the Microsoft standardized type.
type [<Measure>] s = Microsoft.FSharp.Data.UnitSystems.SI.UnitSymbols.s

Some users tend to do the following, which should not be done whenever a definition is already available:

/// Seconds, the SI unit of time
type [<Measure>] s // DO NOT DO THIS! THIS IS AN EXAMPLE TO EXPLAIN A PROBLEM.

The difference becomes apparent when interfacing with other code that refers to the standard SI types. Code that refers to the standard units is compatible, while code that defines its own type is incompatible with any code not using its specific definition.

Therefore, always use the standard types for SI units. It doesn't matter whether you refer to UnitNames or UnitSymbols, since equivalent names within those two refer to the same type:

open Microsoft.FSharp.Data.UnitSystems.SI

/// This is valid, since both versions refer to the same authoritative type.
let validSubtraction = 1.<UnitSymbols.s> - 0.5<UnitNames.second>

Using LanguagePrimitives to preserve or set units

When a function doesn't preserve units automatically due to lower-level operations, the LanguagePrimitives module can be used to set units on the primitives that support them:

/// This cast preserves units, while changing the underlying type
let inline castDoubleToSingle (x : float<'u>) : float32<'u> =
    LanguagePrimitives.Float32WithMeasure (float32 x)

To assign units of measure to a double-precision floating-point value, simply multiply by one with correct units:

[<Measure>]
type USD

let toMoneyImprecise (amount : float) =
   amount * 1.<USD>

To assign units of measure to a unit-less value that isn't System.Double, for example, arriving from a library written in another language, use a conversion:

open LanguagePrimitives

let toMoney amount =
   amount |> DecimalWithMeasure<'u>

Here are the function types reported by F# interactive:

val toMoney : amount:decimal -> decimal<'u>
val toMoneyImprecise : amount:float -> float<USD>