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#23 in Math

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Unit-safe computations with quantities.

What is a Quantity?

"The value of a quantity is generally expressed as the product of a number and a unit. The unit is simply a particular example of the quantity concerned which is used as a reference, and the number is the ratio of the value of the quantity to the unit." (Bureau International des Poids et Mesures: The International System of Units, 8th edition, 2006)

Basic types of quantities are defined "by convention", they do not depend on other types of quantities, for example Length, Mass or Duration.

Derived types of quantities, on the opposite, are defined as products of other types of quantities raised by some exponent.


  • Volume = Length ³

  • Speed = Length ¹ · Duration ⁻¹

  • Acceleration = Length ¹ · Duration ⁻²

  • Force = Mass ¹ · Acceleration ¹

Each type of quantity may have one special unit which is used as a reference for the definition of all other units, for example Meter, Kilogram and Second. The other units are then defined by their relation to the reference unit.

If a type of quantity is derived from types of quantities that all have a reference unit, then the reference unit of that type is defined by a formula that follows the formula defining the type of quantity.


  • Speed -> Meter per Second = Meter ¹ · Second ⁻¹

  • Acceleration -> Meter per Second squared = Meter ¹ · Second ⁻²

  • Force -> Newton = Kilogram ¹ · Meter ¹ · Second ⁻²

"Systems of Measure"

There may be different systems which define quantities, their units and the relations between these units in a different way.

This is not directly supported by this package. For each type of quantity there can be only no or exactly one reference unit. But, if you have units from different systems for the same type of quantity, you can define these units and provide mechanisms to convert between them.

The Basics: Quantity and Unit

The essential functionality of the package is provided by the traits Quantity, HasRefUnit, Unit and LinearScaledUnit and a macro generating the code for concrete types of quantities.

A basic type of quantity can easily be defined using the proc-macro attribute quantity, optionally followed by an attribute refunit and followed by at least one attribute unit.

The macro generates an enum with the given units (incl. the refunit, if given) as variants (together with an implemention of trait Unit and, if there's a reference unit, of trait LinearScaledUnit), a type named after the given struct, an implementation of trait Quantity for this type, an implementation of trait HasRefUnit in case there's a reference unit, as well as implementations of some std traits.

In addition, it creates a constant for each enum variant, thus providing a constant for each unit. This implies that the identifiers of all units over all defined quantitities have to be unique!


# use quantities::prelude::*;
#[ref_unit(Kilogram, "kg", KILO)]
#[unit(Milligram, "mg", MILLI, 0.000001)]
#[unit(Carat, "ct", 0.0002)]
#[unit(Gram, "g", NONE, 0.001)]
#[unit(Ounce, "oz", 0.028349523125)]
#[unit(Pound, "lb", 0.45359237)]
#[unit(Stone, "st", 6.35029318)]
#[unit(Tonne, "t", MEGA, 1000.)]
/// The quantity of matter in a physical body.
struct Mass {}

assert_eq!(MILLIGRAM.name(), "Milligram");
assert_eq!(POUND.symbol(), "lb");
assert_eq!(TONNE.si_prefix(), Some(SIPrefix::MEGA));
assert_eq!(CARAT.scale(), Amnt!(0.0002));

In order to create a derived type of quantity based on more basic types of quantities, an expression can be given as argument to the proc-macro attribute quantity, specifying the quantity as product or as quotient of two base quantities.

Instances of a derived quantity can then be build by multiplying or dividing instances of the base quantities. Instances of a quantity which is defined as a product can be divided by an instance of one of the base quantities, giving an instance of the other base quantity as result. Instances of a quantity which is defined as a quotient can be multiplied by an instance of the divisor quantity, resulting in an instance of the divident quantity.


# use quantities::prelude::*;
#[ref_unit(Meter, "m", NONE, "Reference unit of quantity `Length`")]
#[unit(Centimeter, "cm", CENTI, 0.01, "0.01·m")]
#[unit(Kilometer, "km", KILO, 1000, "1000·m")]
#[unit(Mile, "mi", 1609.344, "8·fur")]
pub struct Length {}

#[ref_unit(Second, "s", NONE, "Reference unit of quantity `Duration`")]
#[unit(Minute, "min", 60, "60·s")]
#[unit(Hour, "h", 3600, "60·min")]
pub struct Duration {}

#[quantity(Length * Length)]
#[ref_unit(Square_Meter, "", NONE, "Reference unit of quantity `Area`")]
#[unit(Square_Centimeter, "cm²", 0.00001, "cm²")]
#[unit(Square_Kilometer, "km²", MEGA, 1000000., "km²")]
pub struct Area {}

let a = Amnt!(3.) * METER;
let b = Amnt!(0.5) * KILOMETER;
let ab = a * b;
assert_eq!(ab, Amnt!(1500.) * SQUARE_METER);
let c = ab / (Amnt!(2.) * KILOMETER);
assert_eq!(c, Amnt!(0.75) * METER);

#[quantity(Length / Duration)]
#[ref_unit(Meter_per_Second, "m/s", NONE, "Reference unit of quantity `Speed`")]
#[unit(Miles_per_Hour, "mph", 0.44704, "mi/h")]
pub struct Speed {}

let l = Amnt!(150.) * MILE;
let t = Amnt!(1.2) * HOUR;
let v = l / t;
assert_eq!(v, Amnt!(125.) * MILES_PER_HOUR);
let d = v * Duration::new(Amnt!(3.), HOUR);
assert_eq!(d, Amnt!(375.) * MILE);

Type of the numerical part

The package allows to use either float or fixed-point decimal values for the numerical part of a Quantity value.

Internally the type alias AmountT is used. This alias can be controlled by the optional feature fpdec (see features).

When feature fpdec is off (= default), AmountT is defined as f64 on a 64-bit system or as f32 on a 32-bit system.

When feature fpdec is activated, AmountT is defined as Decimal (imported from crate fpdec).

The macro Amnt! can be used to convert float literals correctly to AmountT depending on the configuration. This is done automatically for the scale values of units by the proc-macro quantity described above.

Instantiating quantities

An instance of a quantity type can be created by calling the function new, giving an amount and a unit. Alternatively, an amount and a unit can be multiplied.


# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let m = Mass::new(Amnt!(17.4), GRAM);
assert_eq!(m.to_string(), "17.4 g");
let m = Amnt!(17.4) * GRAM;
assert_eq!(m.to_string(), "17.4 g");

Unit-safe computations

If the quantity type has a refernce unit, a quantity instance can be converted to a quantity instance with a different unit of the same type by calling the method convert.


# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Carat, "ct", 0.0002)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Mass::new(Amnt!(13.5), GRAM);
let y = x.convert(CARAT);
assert_eq!(y.to_string(), "67.5 ct");

Quantity values with the same unit can always be added or subtracted. Adding or subtracting values with different units requires the values to be convertable.


# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Amnt!(17.4) * GRAM;
let y = Amnt!(1.407) * KILOGRAM;
let z = x + y;
assert_eq!(z.amount(), Amnt!(1424.4));
assert_eq!(z.unit(), GRAM);
let z = y + x;
assert_eq!(z.to_string(), "1.4244 kg");

Quantity values can always be multiplied or divided by numerical values, preserving the unit.


# use quantities::prelude::*;
# #[quantity]
# #[ref_unit(Kilogram, "kg", KILO)]
# #[unit(Gram, "g", NONE, 0.001)]
# struct Mass {}
let x = Amnt!(7.4);
let y = Amnt!(1.7) * KILOGRAM;
let z = x * y;
assert_eq!(z.to_string(), "12.58 kg");

Commonly Used Quantities

The package provides optional modules with definitions of commonly used quantities; each can be activated by a feature with a corresponding name (see below).

Crate features

By default, only the feature std is enabled.


  • std - When enabled, this will cause quantities to use the standard library, so that conversion to string, formatting and printing are available. When disabled, the use of crate alloc together with a system-specific allocator is needed to use that functionality.

Optional dependencies

  • fpdec - When enabled, instead of f64 or f32 fpdec::Decimal is used as AmountT (see above).

Predefined quantities

With the following features additional modules can be enabled, each providing a predefined quantity.

  • mass - module [mass] - quantity Mass
  • length - module [length] - quantity Length
  • duration - module [duration] - quantity Duration
  • area - module [area] - quantity Area
  • volume - module [volume] - quantity Volume
  • speed - module [speed] - quantity Speed
  • acceleration - module [acceleration] - quantity Acceleration
  • force - module [force] - quantity Force
  • energy - module [energy] - quantity Energy
  • power - module [power] - quantity Power
  • frequency - module [frequency] - quantity Frequency
  • datavolume - module [datavolume] - quantity DataVolume
  • datathroughput - module [datathroughput] - quantity DataThroughput
  • temperature - module [temperature] - quantity Temperature


~18K SLoC