Flexible, statically-checked experimental library for units of measurement
Scala Python
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Flexible, statically-checked experimental library for units of measurement.

Published under MIT License.

Current version: 0.2.2


Plans for the nearest future.

Build instructions.

Available at Maven Central:

libraryDependencies += "io.github.karols" %% "units" % "0.2.2"


Reasons for creation and design goals.

Main features:

  • static, compile-time checking of units of measure

  • ability to define custom units of measure

  • unit arithmetic

  • automatic unit conversions

  • many out-of-the-box supported units and their conversions

  • support for affine spaces

A quick comparison with the units of measure support in F# is here.

Quick showcase

import io.github.karols.units._
import io.github.karols.units.defining._

type USD = DefineUnit[_U~:_S~:_D] 
type EUR = DefineUnit[_E~:_U~:_R] 

implicit val EUR_to_USD = one[EUR].contains(1.25)[USD]

import io.github.karols.units.SI._
import io.github.karols.units.USCustomary._

val priceInUSA     =  200.of[USD/square[foot]]
val priceInGermany = 1500.of[EUR/square[metre]]

val area = 200.of[centimetre] * 550.of[centimetre]

val costInUSA     = priceInUSA     * area.convert[foot × foot]
val costInGermany = priceInGermany * area.convert[metre × metre]

println(s"You can buy tiles in Germany for ${costInGermany.mkString}.")
println(s"You can buy tiles in USA for ${costInUSA.mkString}.")

if(costInUSA >~ costInGermany) {
    println("Buy in Germany.")
} else {
    println("Buy in USA.")


You can buy tiles in Germany for 16500.0 EUR.
You can buy tiles in USA for 23680.602916761392 USD.
Buy in Germany.

Quick Guide

Defining units

You define a unit using DefineUnit type constructor with a type-level string as a parameter.

import io.github.karols.units._
import io.github.karols.units.defining._

type metre = DefineUnit[_m]
type second = DefineUnit[_s]
type kilogram = DefineUnit[ _k ~: _g ]

All units are subtypes of trait MUnit. This includes the type _1, which represents the dimensionless unit 1.

This also automatically generates implicit names for those units: "m", "s", and "kg" respectively.

You can define a derived unit with operators × and / (the ASCII alternative for × is ><) and type-level functions square and cube:

type newton = (metre × kilogram) / (second × second)
type hertz  = _1 / second
type m2     = square[metre]
type m3     = cube[metre]

with implicit names "kg m s^(-2)", "s^(-1)", "m^2", and "m^3" respectively.

You can define a related unit with conversion ratio:

type centimetre = DefineUnit[_c~:_m]
type kilometre = DefineUnit[_k~:_m]

implicit val km_to_m = one[kilometre].contains(1000)[metre]
implicit val m_to_cm = one[metre].contains(100)[centimetre]

This way, you have defined conversions m→km, km→m, m→cm, cm→m, m²→km², m³→km³, km²→m² etc.

Note that this does not define a conversion from kilometres to centimetres. You can do it this way:

implicit val km_to_cm = km_to_m >> m_to_cm

You can also quickly generate conversions for kg×m→kg×cm, m/s→cm/s, J/m→J/cm, N/m²→N/cm²:

implicit val kgm_to_kgcm = m_to_cm.times[kilogram]
implicit val mps_to_cmps = m_to_cm.dividedBy[second]
implicit val Jpm_to_Jpcm = m_to_cm.dividing[joule]
implicit val Npm2_to_Npcm2 = m_to_cm.pow2.dividing[newton]

See sources for io.github.karols.units.SI and io.github.karols.units.USCustomary objects for more examples.

Using values with units

All code below assumes the following is imported:

import io.github.karols.units._

You can create a value with a unit:

val length = 2.of[metre]

This value is of type IntU[metre]. If you used a double literal, you would receive a DoubleU instance:

val length2 = 2.0.of[metre]

IntU and DoubleU are represented at runtime as an unboxed Long and Double respectively.

You can add and subtract values with the same units:

length + length2 // equals 4 m

You can multiply or divide two values:

length * length2 // equals 4 m^2

You can also compare values with the same units:

val area = 3.of[metre × metre]
area > length * length2        //equals false

If you want to extract the raw dimensionless numeric value from the value with a unit, you can use value method:

length.value // equals 2: Long

Other useful methods include raising to powers and getting roots:

length.pow2             // 4 m^2
length.pow3             // 8 m^3
area.sqrt               // 1.7... m
27.of[cube[metre]].cbrt // 3.0 m

Note that while using sqrt (respectively: cbrt) method will currently work for types with units to odd (respectively: not divisible by three) powers, but the resulting value will have some ill-defined type.

If you want to use an SI prefix without creating a separate unit for it, you can use more extension methods defined on numeric types:

20.kilo[metre]  // equals 20000 m
3.milli[second] // equals 0.003 s

Finally, to print a value with a unit, you can use mkString method:

length.mkString               // equals "4 m"
300.of[metre/second].mkString // equals "300 m s^(-1)"

It is currently not recommended though, it takes a lot of time to compile and generates awfully large classfiles. The recommended way is to use value method and append a unit symbol manually.

Section about using custom numeric types with units has been moved here.

Manual unit conversion

You can convert a value to another unit, provided there is an implicit conversion ratio in scope:

val length = 2.of[metre]
length.convert[centimetre]          // equals 200.0 cm

If you are converting an integer value from a unit to its subunit, you can get the results as an IntU:

length.convertToInt[centimetre]     // equals 200 cm

You can apply the conversion ratio to a more complicated unit in order to replace one unit with another:

length.represent[metre, centimetre] // equals 200.0 cm
area.represent[metre, centimetre]   // equals 300.0 cm×m
1.represent[metre, centimetre]      // equals 100.0 cm/m

Finally, you can apply the conversion to all occurrences of a unit inside another. The only restriction is that the unit you are converting from is a basic unit, defined with DefineUnit:

area.representAll[metre, centimetre]                              // equals 30000.0 cm^2
1.representAll[metre, centimetre]                                 // equals 1.0
2.of[metre/second].representAll[metre, centimetre]                // equals 200.0 cm/s
2.of[square[metre]/second].representAll[metre, centimetre]        // equals 20000.0 cm^2/s
30000000.of[kilogram/cube[metre]].representAll[metre, centimetre] // equals 30.0 kg/cm^3

Automatic unit conversion

Units are automatically converted in comparisons when using operators ending with a tilde:

399.of[centimetre] >=~ 4.of[metre]   // false

If there is an integer conversion ratio between two units, then adding/subtracting two values with those units converts the sum/difference to the smaller unit:

14.of[centimetre] + 3.of[metre]  // equals 314 cm, not 3.14 m

Affine spaces

Affine space is a space of quantities which cannot be multiplied or added, only subtracted. The reason for that is that the zero is chosen arbitrarily. Affine spaces are used to represent temperatures, timestamps, Cartesian coordinates, potential energy, electric potential, and more. See this article for more info.


val freezeC = 0.at[CelsiusScale] // temperature at which water freezes
0.of[celsius_deg]                // zero difference of temperatures

Affine values have types DoubleA[A] and IntA[A], where A is an affine space.

The reason that you can't add affine values is that this operation makes no sense.

val freezeF = freezeC.convert[FahrenheitScale] // equals 32°F
freezeC + freezeC                              // 0°C + 0°C == does not compile
freezeF + freezeF                              // 32°F + 32°F == does not compile

In the above case, if we assumed naïvely that we can add temperatures, the first sum would end up being 0°C, and the second one would be 64°F – clearly two different results.

You can add/subtract normal values to/from affine values:

val temperatureIncreaseC = 5.of[celsius_deg]                            // equals +5°C
val temperatureIncreaseF = temperatureIncreaseC.convert[fahrenheit_deg] // equals +9°F

freezeC + temperatureIncreaseC  // equals 5°C
freezeF + temperatureIncreaseF  // equals 41°F == 5°C
freezeC - temperatureIncreaseC  // equals -5°C
freezeF - temperatureIncreaseF  // equals 23°F == -5°C

You can also calculate a difference between two affine values, which yields a normal value:

val boilC = 100.at[CelsiusScale] // equals 100°C == 212°F
val diffC = boilC -- freezeC     // equals +100°C == +180°F

The operator name is double minus sign, because single minus sign was used for subtracting a normal value and Scala compiler cannot overload that method due to type erasure for value classes.

Defining affine spaces

AffineSpace is defined as a pair containing a zero point and a unit.

import io.github.karols.units._
import io.github.karols.units.defining._

type celsius_deg = DefineUnit[_deg~:_C]
sealed trait CelsiusZero

type CelsiusScale = DefineAffineSpace[CelsiusZero, celsius_deg]

Unlike normal values, affine spaces currently require conversion functions in both directions.

implicit val fromCelsiusToFahrenheit = convertAffineSpace[CelsiusScale,FahrenheitScale]{ 
    x => x * (9/5.0) + 32  // (Double => Double)
implicit val fromFahrenheitToCelsius = convertAffineSpace[FahrenheitScale,CelsiusScale]{ 
    x => (x - 32) * (5/9.0)

If two affine spaces only differ by their unit, you can use changeUnit method to convert between them:

sealed trait UnixEpoch
type UnixEpochSeconds = DefineAffineSpace[UnixEpoch, second]
type UnixEpochMillis = DefineAffineSpace[UnixEpoch, millisecond]

val timestamp = 123456789.at[UnixEpochSeconds] // equals 123456789 s from Unix Epoch
timestamp.changeUnit[millisecond]              // equals 123456789000 ms from Unix Epoch

Affine values can be compared with relational operators, similarly to normal values.

Writing polymorphic functions using units of measure

This section has been moved to a separate document.

Using arrays

This section has been moved to a separate document.

2D and 3D vectors

This section has been moved to a separate document.

Implementation details

The implementation started with a pretty common type-level implementation of boolean and integers.

Type-level strings are either a cons of a char and a string, a single char, or an empty string. Each char is implemented currently as a triple of members of Z/5Z, so only 125 different characters are allowed.

A basic unit is implemented as a thin wrapper around a type-level string. That string is an identifier that is used for type equality comparison, and is also used for implicit name generation.

The main type for units (MUnit) is a linked list of pairs of basic units and non-zero integers, used to represent a type-level map.