#si-units #units #physics #measurement

no-std simple-si-units

A Rust library providing base SI Units and common conversions. SI Units are provided as templated types so that you can write APIs that enforce correct units

26 releases (4 stable)

1.1.1 May 4, 2023
0.9.1 Apr 25, 2023
0.7.4 Mar 23, 2023
0.3.1 Nov 7, 2022

#23 in Science

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This Rust library provides compiler-checked types for the standard set of SI units, as specified by the US National Institute of Standards and Technology (this project is not officially endorsed by NIST).

What's included?

  • Official standard SI Units
  • Common secondary units, such as velocity
  • Implements operators to automatically convert between units with basic arithmatic (eg distance / time = velocity)
  • Units are templated so that you can choose whether to use f32 or f64 or other number-like type as your concrete number type.
  • Compatible with uom


This crate provides types for the following units. Other kinds of quantities not listed below (eg jolt) are beyond the scope of this crate.

Base SI units (and standard unit of measure):

(import with use simple_si_units::base::*;)

  • Distance, aka Length (meters)
  • Mass (kilogram)
  • Time (seconds)
  • Temperature (kelvin)
  • Amount, aka Quantity (moles)
  • Current (amperes)
  • Luminosity (candela)

Derived units:

chemical electromagnetic geometry mechanical nuclear
Catalytic Activity (mol/s) Capacitance (C/V, aka F) Angle (rad) Acceleration (m/s^2) Absorbed Dose (J/kg, aka Gy)
Concentration (mol/m^3, aka mM) Charge, aka Coulomb (A.s, aka C) Area (m^2) Angular Acceleration (rad/s^2) Dose Equivalent (J/kg, aka Sv)
Molar Mass (kg/mol) Conductance (1/ohm, aka S) Solid Angle (sr) Angular Momentum (kg.m^2.rad/s) Radioactivity (1/s, aka Bq)
Molality (mol/kg) Illuminance (lm/m^2, aka lux) Volume (m^3) Angular Velocity (rad/s)
Specific Heat Capacity (J/kg.K) Inductance (Wb/A, aka H) Area Density (kg.m^2)
Luminous Flux (cd.sr, aka lm) Density (kg/L)
Magnetic Flux (V.s, aka Wb) Energy (kg.m^2/s^2, aka J)
Magnetic Flux Density (Wb/m^2, aka T) Force (kg.m/s^2, aka N)
Resistance (V/A, aka Ohm) Frequency (1/s, aka Hz)
Voltage (W/A, aka V) Moment of Inertia (kg.m^2)
Momentum (kg.m/s)
Power, aka Watt (J/s, aka W)
Pressure (N/m^2, aka Pa)
Torque (kg.m^2/s^2, aka N.m)
Velocity (m/s)

What's NOT included?

  • Not supporting dimensional analysis
  • Not providing an exhaustive list of all possible unit types (but you can use this library to implement your own)
  • Not supporting integer number types (use at your own risk)


The simple-si-units crate has the following optional features which can be enabled to provide additional compatibility:

  • serde - Adds serde serialization/deserialization compatibility
  • uom - If enabled, then unit structs will implement the Into and From traits to convert between simple-si-units and uom types
  • num-bigfloat - Adds core::ops::Mul and core::ops::Div implementations for multiplying and dividing unit structs by num-bigfloat scalar values
  • num-complex - Adds core::ops::Mul and core::ops::Div implementations for multiplying and dividing unit structs by num-complex scalar values

To enable these features in your project, add the following to your Cargo.toml file under [dependencies]:

simple-si-units = { version = "1.1", features = ["serde", "uom", "num-bigfloat", "num-complex"] }

Quickstart guide

Basic usage

To use simple-si-units, just add simple-si-units = "1.1" to the [dependencies] section of your Cargo.toml file, then import the units you need like this:

use simple_si_units::base::*;
use simple_si_units::geometry::*;
use simple_si_units::mechanical::*;

fn main() {
  let box_width = Distance::from_cm(33.5);
  let box_length = Distance::from_cm(45.0);
  let box_height = Distance::from_cm(23.5);
  let carboard_density = AreaDensity::from_grams_per_square_meter(300.);
  let box_volume = &box_width * &box_height * &box_length;
  println!("Your box holds a total volume of {:.2} liters", box_volume.to_L());
  let box_weight = (2. * &box_width * &box_length
    + 2. * &box_width * &box_height
    + 2. * &box_length * &box_height) * &carboard_density;
  println!("Your box has a weight of {}", box_weight);

Note that simple-si-units structs all implement core::ops::{Add,Sub,Mul,Div} for both values and references, which is useful for number type which do not implement the Copy trait.

Making APIs

simple-si-units was designed specifically to help people create safer APIs for libraries and functions that perform scientific calculations.

For most applications, you can simply specify both the SI unit type and data type for each variable, like this:

use simple_si_units::base::Distance;
use simple_si_units::geometry::Volume;
use std::f64::consts::PI;

pub fn sphere_volume(radius: Distance<f64>) -> Volume<f64> {
   &radius * &radius * &radius *  4. / 3. * PI

However, if you want to support more than one data type, then you should use a generic templated function. The simple-si-units crate provides the NumLike type to help simplify generic APIs, for example:

use simple_si_units::base::Distance;
use simple_si_units::geometry::Volume;
use std::f64::consts::PI;
use simple_si_units::NumLike;

pub fn sphere_volume<T>(radius: Distance<T>) -> Volume<T>
where T: NumLike + From<f64>
    &radius * &radius * &radius * T::from(4. / 3. * PI)

The above generic function will work for any number type which implements From<f64>, such as Complex64 or BigFloat (from the num-complex and num-bigfloat crates respectively).

Why not use uom?

You don't have to choose, you can use both! All simple-si-units types implement the Into and From traits to convert to and from their uom equivalent.

The uom and simple-si-units crates were both designed to provide compile-time type checking for scientific units of measure to help developers catch math errors and write cleaner calculation APIs. The difference is that uom also performs dimensional analysis but cannot handle custom data types, while simple-si-units handles any number-like data type but does not attempt to implement full compile-time dimensional analysis. simple-si-units also prioritizes developer ergonomics, adhering to a consistent Struct::from_...() and Struct.to_...() syntax for simple and intuitive number conversions. Whether uom or simple-si-units better suits your application depends on your needs.

Here's a table comparing simple-si-units v1.0 and uom v0.34 to help you decide which to use:

Feature simple-si-units uom
Zero-cost measurement unit type safety
All primary and secondary SI units as defined by NIST
Inverse (aka reciprical) of SI units partial
Support for standard decimal types (eg f64)
Support for standard integer types (eg i32) partial** partial**
Support for num-bigfloat
Support for num-complex
Support for num-rational partial**
Support for user-defined and other number types
Compile-time dimensional analysis

** integer types and int-based number types are not fully supported in simple-si-units

To further demonstrate the similarities and differences between simple-si-units and uom, here's two different versions of the same gravity calculation function, one using simple-si-units and the other using uom:

// simple-si-units version
mod simple_si_version {
  use simple_si_units::base::{Distance, Mass};
  use simple_si_units::mechanical::{Acceleration};

  pub fn calc_gravity(mass: Mass<f64>, dist: Distance<f64>) -> Acceleration<f64> {
    const G: f64 = 6.67408e-11; // m3 kg-1 s-2
    let d_squared = dist * dist;
    return Acceleration::from_mps2(G * mass.to_kg() / d_squared.to_m2())

  fn test_gravity1() {
    let radius = Distance::from_km(6378.1);
    let mass = Mass::from_earth_mass(1.0);
    println!("simple-si-units: Earth gravity at sea-level is {}", calc_gravity(mass, radius));

// uom version
mod uom_version {
  use uom::si::f64::{Length, Mass, Acceleration};
  use uom::si::length::*;
  use uom::si::mass::*;
  use uom::si::acceleration::*;
  use uom::fmt::DisplayStyle::Abbreviation;

  pub fn calc_gravity(mass: Mass, dist: Length) -> Acceleration {
    const G: f64 = 6.67408e-11; // m3 kg-1 s-2
    let d_squared = dist * dist;
    return Acceleration::new::<meter_per_second_squared>(G * mass.value / d_squared.value)

  fn test_gravity2() {
    let radius = Length::new::<kilometer>(6378.1);
    let mass = Mass::new::<kilogram>(5.972e24);
    println!("uom: Earth gravity at sea-level is {}",
             calc_gravity(mass, radius).into_format_args(meter_per_second_squared, Abbreviation));

How it works

For each type of unit (eg Distance), Simple SI Units provides a generic struct to represent the unit and which implements common type conversion. For example, dividing a Distance by a Time results in a Velocity:

use simple_si_units::base::{Distance, Mass};
use simple_si_units::mechanical::{Acceleration};
pub fn calc_gravity(mass: Mass<f64>, dist: Distance<f64>) -> Acceleration<f64>{
	const G: f64 = 6.67408e-11; // m3 kg-1 s-2
	let d_squared = dist * dist;
	return Acceleration::from_mps2(G * mass.to_kg() / d_squared.to_m2())

fn main(){
	let a = calc_gravity(Mass::from_solar_mass(1.0), Distance::from_au(1.0));
	println!("Solar gravity at Earth orbital distance: {}", a);

Since these structs use generic type templates for the internal data type, you can use any number-like data type with these structs, including num_complex::Complex and num_bigfloat::BigFloat (see limitations section below regarding types that do not implement From<f64>).

For example, the above function could be rewritten as follows to allow almost any number-like data type:

use simple_si_units::base::{Distance, Mass};
use simple_si_units::mechanical::{Acceleration};
use simple_si_units::NumLike;

pub fn calc_gravity_generic<T>(mass: Mass<T>, dist: Distance<T>) -> Acceleration<T> 
  where T: NumLike+From<f64> 
  const G: f64 = 6.67408e-11; // m3 kg-1 s-2
  let d_squared = &dist * &dist;
  return Acceleration::from_mps2(T::from(G) * mass.to_kg() / d_squared.to_m2())

Adding Your Own Units

Simple SI Units does not provide an exhaustive list of possible units of measure. To create your own units, use the UnitStruct procedural macro and NumLike trait bundle (NumLike is just shorthand for core::ops::*<Output=Self>+Clone+Debug+Display, you could instead use the Num trait from the num-traits crate if you prefer):

use simple_si_units::{UnitStruct, NumLike};

#[derive(UnitStruct, Debug, Clone)]
struct HyperVelocity<T: NumLike>{
  square_meters_per_second: T

fn weighted_hypervel_sum<T: NumLike>(a: HyperVelocity<T>, b: HyperVelocity<T>, weight: f64) -> HyperVelocity<T>
  where T:NumLike + From<f64>
  return weight*a + (1.-weight)*b;

Note that the UnitStruct derive macro only works on structs that contain only a single member variable. Otherwise it will generate a compiler error.


Due to the Rust compiler's lack of type specialization in stable Rust, some of the unit constructor functions (eg Mass::from_g(...)) only work with number types that implement From<f64>. This means that those functions will not work for Rust's built-in f32 or integer types. You can still construct unit structs with their SI reference measurement using any number type (eg Mass::from_kg(1f32) will work).

Custom number types

simple-si-units works with any "number-like" data type, including libraries such as num-bigfloat, num-complex, and even number types you define yourself. A data type is "number-like" if it implements the following traits: Clone, Debug, Display, Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg

For example, here's a snippet of code that defines and uses a number type that is like f32 but also implements From<f64>:

use std::ops::*;
use std::fmt::{Display, Formatter, Result};
use simple_si_units::base::Mass;
use simple_si_units::geometry::Volume;
use simple_si_units::mechanical::Density;

#[derive(Debug, Copy, Clone)]
struct MyNumber(f32);

impl Display for MyNumber {
  fn fmt(&self, f: &mut Formatter<'_>) -> Result {std::fmt::Display::fmt(&self.0, f)}
impl Add for MyNumber {
  type Output = MyNumber;
  fn add(self, rhs: Self) -> Self::Output {MyNumber(self.0 + rhs.0)}
impl AddAssign for MyNumber {
  fn add_assign(&mut self, rhs: Self) {self.0 += rhs.0;}
impl Sub for MyNumber {
  type Output = MyNumber;
  fn sub(self, rhs: Self) -> Self::Output {MyNumber(self.0 - rhs.0)}
impl SubAssign for MyNumber {
  fn sub_assign(&mut self, rhs: Self) {self.0 -= rhs.0;}
impl Mul for MyNumber {
  type Output = MyNumber;
  fn mul(self, rhs: Self) -> Self::Output {MyNumber(self.0 * rhs.0)}
impl MulAssign for MyNumber {
  fn mul_assign(&mut self, rhs: Self) {self.0 *= rhs.0;}
impl Div for MyNumber {
  type Output = MyNumber;
  fn div(self, rhs: Self) -> Self::Output {MyNumber(self.0 / rhs.0)}
impl DivAssign for MyNumber {
  fn div_assign(&mut self, rhs: Self) {self.0 /= rhs.0;}
impl Neg for MyNumber {
  type Output = MyNumber;
  fn neg(self) -> Self::Output {MyNumber(-self.0)}
impl From<f64> for MyNumber{
  fn from(value: f64) -> Self {MyNumber(value as f32)}

fn my_fn() -> Density<MyNumber>{
  let m = Mass::from_g(MyNumber(1222.5_f32));
  let v = Volume::from_L(MyNumber(11.3_f32));
  return m / v;

It's highly recommended that you also implement the std::ops::* operators for all combinations of values and reference types (eg X + X, X + &X, &X + X, and &X + &X), as this will make your number type much easier to use and integrate with simple-si-units.


This library is open source, licensed under the Mozilla Public License version 2.0. In summary, you may include this source code as-is in both open-source and proprietary projects without requesting permission from me, but if you modify the source code from this library then you must make your modified version of this library available under an open-source license.

Developer notes

Note that the unit struct source files (excluding lib.rs), were all generated by a Python program which performs dimensional analysis and other code generation activities, found in the code-generator folder of the GitHub repository.

If you wish to contribute, please start by adding the unit tests for your new feature and then modify the Python project to generate the Rust implementation of the new feature. Thanks!


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