SI  2.5.4
A header only c++ library that provides type safety and user defined literals for handling physical values defined in the International System of Units.
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SI - Type safety for physical units

A header only c++ library that provides type safety and user defined literals for handling physical values defined in the International System of Units regulated by the International Bureau of Weights and Measures (BIPM) and published in the SI brochure. For a quick start see the installation guide. Contributions and comments are welcome, please check the contribution guidelines for further information.

An illustrative example:

#include <SI/mass.h>
using namespace SI::literals;
constexpr auto one_kilogram = 1.0_kg;
constexpr auto ten_coulomb = 5.0_A * 2.0_s;
constexpr auto half_an_ampere = ten_coulomb / 20.0_s;
constexpr auto thousand_grams =<SI::gram_t>();
void calculate_mass(const SI::kilo_gram_t<long double> &kg) {
// do something meaningful here
int main(int, char **) {
return 0;
Definition: absorbed_dose.h:51
base template class for holding values of type _type to be multiplied with a ratio _ratio
Definition: unit.h:51

SI provides conversions and arithmetic operations with values of any of the International System of Units with strong type safety at compile time. All units are special typedefs of the template struct SI::unit_t. Only the value of the unit is stored internally, the ratio (i.e. milli, micro, kilo...) is determined as a type trait to allow all units to have the same resolution across the whole implemented ratios. SI handles operations of units of the same ratios as well as when the ratios are different. See the documentation implementation details for further information. Operations between units of the same ratio are overhead-free, else there is an additional computation cost to adjust the values to the units. Passing the flag SI_DISABLE_IMPLICIT_RATIO_CONVERSION to the compiler implicit ratio conversion is not done and fails with a compiler error. See the continuous benchmark results for a comparison between the reference measurements and the implementation in SI.

It is possible to supply custom ratios to the built-in types and they are fully compatible for calculation with other units. However, the necessary literals or typedefs have to be supplied by the user. For instance SI::velocity_t<double, std::ratio<1000, 36>> would be "kilometre per one-hundredth-of-an-hour".

Converting between units is either done with the as<unit_t>() member function of unit_ or the free function SI::unit_cast<unit_t>(unit_t u). This will convert a value of the same type but a different ratio.

SI Base units

For each unit the available literals are the implemented ratios prefixed with an underscore. i.e. _mm. _km. Generally the ratios follow metric prefixes of the international system of units The typedefs are prefixed (or in rare cases interfixed) with the standard metric prefixes. i.e. metre_t, milli_metre_t, kilo_metre_t. The prefix or interfix is marked with an * in the tables below. Units that have defined typedefs and literals can be converted to strings using stream operators or the SI::to_string function. To use the stream operators, include the header file SI/stream.h

Unit Dimension Symbol Unit Symbol implemented ratios unit typedefs
Length L m 10-18 to 1018 *_metre_t
Time T s 10-18 to 100 and 60/1, 3600/1 *_seconds_t, minutes_t, hours_t
Mass* M kg 10-15 to 1018 *_gram_t, *_ton_t
Electric current I A 10-18 to 1018 *_ampere_t
Thermodynamic temperature** t K 10-18 to 1018 *_kelvin_t
Amount of substance N mol 10-18 to 1018 *_mol_t
Luminosity J cd 10-18 to 1018 *_candela_t
  • for mass the base ratio is kg (not g) as defined in the SI unit table. So there is a mismatch between the literal prefix and the internal representation.

** The dimension symbol for thermodynamic temperature should be Θ (Theta), but the current implementation does not allow for non-ASCII symbols or multi-char symbols

Special Units

Unit Dimension Symbol Exponent Unit Symbol implemented ratios unit typedefs
Area L 2 m2 10-18 to 1018 square_*_metre_t
Volume L 3 m3 10-18 to 1018 cubic_*_metre_t
Frequency T -1 Hz 10-18 to 1018 *_hertz_t
Angle* r 1 rad 10-18 to 1 *_radian_t
Angle (Degrees)* r 1 deg micro, milli, 1 *_radian_t
Solid Angle* R 1 sr 10-18 to 1 *_steradian_t
  • Angle, Angle (degree) and solid angle are simple containers, not containing any functionality to do angle/solid-angle computation such as an overflow after 2*pi. Converting between radians and degree might lose precision, especially if working with long doubles because the ratios not precise enough, as they have to be represented as long ints

Derived units with special names

All units that can be built from other units decay to the respective units by inverting the mathematical operation. I.e if Q = I * T then Q / I = T and Q / T = I

Unit Dimension Symbol Unit Symbol buildable from implemented literals unit typedefs
Velocity v m/s L / T m_p_s, km_p_h, _c metre_per_second_t, kilometre_per_second_t, speed_of_light_t
Acceleration a m/s^2 v / T, v^2 / L none none
Electric charge Q C I * T aC to EC *_coulomb_t
Electric potential U V P / I, E/Q aV to EV *_volt_t
Electric resistance O* Ohm (Ω) U / I, 1/G aOhm to EOhm *_ohm_t
Electric conductance G S I / U, 1/R aS to ES *_siemens_t
Electric capacity C F Q / U aF to EF *_farad_t
Force F N M * a aN to EN *_newton_t
Pressure p pa F / L^2 apa to Epa *_pascal_t
Energy E J F * L, p * L^3 aJ to EJ *_joule_t
Power P W E/T aW to EW *_watt_t
Magnetic Flux f* Wb U * T aWb to EWb *_weber_t
Magnetic Field B T f/L^2 aT to ET *_tesla_t
Momentum o* kg⋅m/s M * v none none
Inductance l H f / I aH to EH *_henry_t
Luminous flux m* lm J * R alm to Elm *_lumen_t
Luminance i* lx m / a alx to Elx *_lux_t
Radioactivity A Bq aBq to EBq *_becquerel_t
Absorbed Dose D Gy aGy to EGy *_gray_t
Equivalent Dose H Sv aSv to ESv *_sievert_t
Catalytic activity K kat N / T akat to Ekat *_katal_t
Surface flow s m^2/s L^2 / T none
Volumetric flow V m^3/s L^3 / T none
Angular frequency w* rad/s r / T none
  • These dimensions do not yet have the correct symbols, because the current implementation does not allow for non-ASCII symbols or multi-char symbols. The dimension symbol for electric resistance should be Ω (Ohm) and for magnetic flux Φ (Phi). Luminance should be Eb. Angular velocity should be ω (omega). Luminous flux should be Φv which is even less supported than Φ (Phi) itself.

Non-Standard Units

Non standard units are not regulated by the BIPM but are accepted for use with the SI standard.

Unit Dimension Symbol literals implemented ratios unit typedefs
Astronomic Units of length L AU, ly, pc 149597870691:1 (AU), 9460730777119564:1 (ly), 30856775814913700:1 (pc) astronomic_unit_t (_AU), lightyear_t (_ly), parsec_t (_pc)

Building & compatibility

SI is a header-only library that uses C++17 features. Building is tested using cmake > 3.23 and verified for g++7, g++8, clang5, clang6, clang7, msvc 19, and AppleClang 10.0. I recommend using conan 2.0 to download any dependencies for testing, but can be used without it, if the tests are not built.

SI uses CMakeDeps generator of conan to find dependencies. To install the dependencies use

conan install . --output-folder=build --build=missing --settings=build_type=Debug

substitute --settings=build_type=Debug with --settings=build_type=Release to switch between debug and release builds.

By using the CMAkeDeps generator, you can either build manually or use the CMake presets provided.

cmake --preset=ci-ninja-debug
cmake --build build


The default installation location for SI is /usr/local/lib/SI. SI can be installed using raw cmake, cpack (cmakes package mechanism), or as a package provided from conan center

See the installation guide for detailed instructions

Including with FetchContent

Note: Getting SI as a conan package is preferred.

To install with CMake's FetchContent, add the following to your CMakeLists.txt

# This will get the latest version
# To pin to a specific version or hash, add the version/hash here instead
# (e.g. 2.5.1 or 63b267211a6f256f7ba8d5a26e17138bbcf95ba8)
GIT_TAG main
# ...
# Link the library to your target. Change this as needed!
target_link_libraries(${PROJECT_NAME} PUBLIC SI::SI)


SI is available as 'raw' download from this repository but also as conan package. Getting SI from conan-center is the preferred way.

Implementation details

For further information and deeper technical details refer to the implementation details document

Breaking changes between versions 1.x.x and versions 2.x.x

Versions above 2.0.0 will not be fully compatible with older versions because of the breaking changes mentioned in the changelog. From version 2.0.0 on the conan package is named lower case si to conform to the conan naming convention.