Measurements and Units in Foundation

New in Foundation in iOS 10 and macOS 10.12 is a family of types for modeling units of measurement as well as actual measurements in those units, such as 1 kilometer or 21 degrees Celsius. If you haven’t looked at it yet, WWDC session 238 gives a good overview.


Here is an example of what you can do with this. Let’s start by creating a value for the distance I covered on my latest bike tour:

let distance = Measurement(value: 106.4, unit: UnitLength.kilometers)
// → 106.4 km

A Measurement (which is a value type in Swift) combines a quantity (106.4) with a unit of measure (kilometers). We could define our own units, but Foundation already includes a bunch of the most common physical quantities. There are currently 21 predefined unit types. These are all subclasses of the abstract Dimension class, and their names all begin with Unit…, such as UnitAcceleration, UnitMass, or UnitTemperature. Here, we use UnitLength.

Each unit class provides class properties for the various specific units that can represent measurements of that type, such as .meters, .kilometers, .miles, or .lightyears. To convert our original measurement in kilometers to other units, we can write:

let distanceInMeters = distance.converted(to: .meters)
// → 106400 m
let distanceInMiles = distance.converted(to: .miles)
// → 66.1140591795394 mi
let distanceInFurlongs = distance.converted(to: .furlongs)
// → 528.911158832419 fur

UnitLength comes with 22 predefined units from picometers to lightyears, but if your preferred unit is not among them, it is easy to add your own. Simply extend the type with another static property that describes the new unit’s symbol and its conversion factor to the type’s base unit. This last part is done through a UnitConverter. The base unit is the unit in terms of which all other units of the same type are defined. It must be documented and is usually (but not necessarily) identical to the corresponding base unit in the SI system. For UnitLength, the base unit is .meters.

extension UnitLength {
    static var leagues: UnitLength {
        // 1 league = 5556 meters
        return UnitLength(symbol: "leagues", 
            converter: UnitConverterLinear(coefficient: 5556))

let distanceInLeagues = distance.converted(to: .leagues)
// → 19.150467962563 leagues

(I’d like leagues to be a static stored constant rather than a computed property, but stored type properties don’t seem to be supported in extensions of NSObject subclasses. See SR-993 for more information.)

We can also multiply measurements by scalar values, as well as add and subtract measurements. Unit conversions are handled automatically if necessary:

let doubleDistance = distance * 2
// → 212.8 km
let distance2 = distance + Measurement(value: 5, unit: UnitLength.kilometers)
// → 111.4 km
let distance3 = distance + Measurement(value: 10, unit: UnitLength.miles)
// → 122493.4 m

Note what happens in the last example. When we add one measurement in kilometers and one in miles, the framework converts both to meters (the base unit of UnitLength) before adding them together. The original unit information gets lost. This does not happen in the previous example, where we add two measurements that have the same unit (kilometers).



This works great so far, and is vastly better than what most of us usually do, which is to use plain floating-point numbers for all measurements and encode the units in variable names, such as distanceInKilometers or temperatureInCelsius. Not only does it prevent conversion errors, the stricter typing also enables the compiler to check our logic: it is impossible to accidentally add a Measurement<UnitLength> to a Measurement<UnitTemperature> because that code wouldn’t compile.

More expressive APIs

APIs (from Apple or third parties) that adopt the new types in the future will become more expressive and self-documenting, too.

Imagine a method to rotate an image. Right now it probably takes a Double for the angle parameter. The author of the method must document whether the angle should be passed in degrees or radians, and the developer using the API must take care not to violate this assumption. In the new world of units, the angle parameter’s type would be Measurement<UnitAngle>, giving both the API client and the author the freedom to work in the unit that is most convenient for them, and eliminating bugs due to conversion errors.

Similarly, an animation API would no longer need to document that the duration parameter must be passed in seconds. It would simply be a Measurement<UnitDuration>.


Finally, the new MeasurementFormatter is another plus. It formats measurements in a locale-specific way, taking regional unit preferences (miles over kilometers), number formats, and symbols into account.

let formatter = MeasurementFormatter()
let 🇩🇪 = Locale(identifier: "de_DE")
formatter.locale = 🇩🇪
formatter.string(from: distance) // "106,4 km"

let 🇺🇸 = Locale(identifier: "en_US")
formatter.locale = 🇺🇸
formatter.string(from: distance) // "66.114 mi"

let 🇨🇳 = Locale(identifier: "zh_Hans_CN")
formatter.locale = 🇨🇳
formatter.string(from: distance) // "106.4公里"

What I don’t like

One thing I do not like about the new API is its verbosity. Measurement(value: 5, unit: UnitLength.kilometers) is tedious to write and hard to read. It’s always hard to find the right balance between conciseness and clarity, but I think this initializer errs on the side of verbosity.

An extreme alternative would be something like let d = 5.kilometers, which reads extremely well, but has the drawback of polluting the common integer and floating-point namespaces. Maybe something like 5.measure.kilometers?

I think it would already be a big improvement to lose the argument labels for the initializer. let d = Measurement(5, UnitLength.kilometers) reads much nicer. Now add one typealias per unit class to get rid of the UnitLength prefix and I really start to like it:

typealias Length = Measurement<UnitLength>
let d = Length(5, .kilometers)

typealias Duration = Measurement<UnitDuration>
let t = Duration(10, .seconds)

These things are easy to add in your own projects, but only Apple can introduce a better standard syntax.

Relationships between unit classes

We have seen that we can add measurements of the same class, but what if I wanted to calculate my average speed during the bike tour? Velocity is distance divided by time, so let’s create a measurement for the tour’s duration and then do the calculation:

// 8h 6m 17s
let time = Measurement(value: 8, unit: UnitDuration.hours)
    + Measurement(value: 6, unit: UnitDuration.minutes)
    + Measurement(value: 17, unit: UnitDuration.seconds)
let speed = distance / time
// error: binary operator '/' cannot be applied to operands of type 'Measurement<UnitLength>' and 'Measurement<UnitDuration>'

The division operation causes a compiler error. It turns out Apple (probably wisely for a first version) stopped short of creating a fully coherent system of interrelated units. So we cannot express a division of UnitLength by UnitDuration in terms of UnitSpeed. However, we can easily add this manually. All we need to do is provide a matching overload for the division operator /:

func / (lhs: Measurement<UnitLength>, rhs: Measurement<UnitDuration>) -> Measurement<UnitSpeed> {
    let quantity = lhs.converted(to: .meters).value / rhs.converted(to: .seconds).value
    let resultUnit = UnitSpeed.metersPerSecond
    return Measurement(value: quantity, unit: resultUnit)

We convert the length value to meters and the duration value to seconds, perform the division, and return the result as a measurement in meters per second. Now the compiler is happy:

let speed = distance / time
// → 3.64670802344312 m/s
speed.converted(to: .kilometersPerHour)
// → 13.1281383818845 km/h

Can we do better?

This is nice, but also a bit limited. We would need to provide additional overloads for the reverse operations (length = speed × time, or time = length / speed), and if we wanted to express other relations (e.g. resistance = voltage / current), we would have to do the same thing all over again. Wouldn’t it be cool if we could somehow declaratively express these relations once and then it would all work automatically? And that’s what I’m going to show you in the next article.