NAME¶

std::ratio - std::ratio

Synopsis¶

Defined in header <ratio>
template<

std::intmax_t Num, (since C++11)
std::intmax_t Denom = 1

> class ratio;

The class template std::ratio provides compile-time rational arithmetic support.
Each instantiation of this template exactly represents any finite rational number as
long as its numerator Num and denominator Denom are representable as compile-time
constants of type std::intmax_t. In addition, Denom may not be zero and both Num and
Denom may not be equal to the most negative value.

The static data members num and den representing the numerator and denominator are
calculated by dividing Num and Denom by their greatest common divisor. However, two
std::ratio with different Num or Denom are distinct types even if they represent the
same rational number (after reduction). A std::ratio type can be reduced to the
lowest terms via its type member: std::ratio<3, 6>::type is std::ratio<1, 2>.

The following convenience typedefs that correspond to the SI ratios are provided by
the standard library:

Defined in header <ratio>
Type Definition
quecto (since C++26) std::ratio<1, 1000000000000000000000000000000> (10^-30)^[1]
ronto (since C++26) std::ratio<1, 1000000000000000000000000000> (10^-27)^[1]
yocto std::ratio<1, 1000000000000000000000000> (10^-24)^[1]
zepto std::ratio<1, 1000000000000000000000> (10^-21)^[1]
atto std::ratio<1, 1000000000000000000> (10^-18)
femto std::ratio<1, 1000000000000000> (10^-15)
pico std::ratio<1, 1000000000000> (10^-12)
nano std::ratio<1, 1000000000> (10^-9)
micro std::ratio<1, 1000000> (10^-6)
milli std::ratio<1, 1000> (10^-3)
centi std::ratio<1, 100> (10^-2)
deci std::ratio<1, 10> (10^-1)
deca std::ratio<10, 1> (10^1)
hecto std::ratio<100, 1> (10^2)
kilo std::ratio<1000, 1> (10^3)
mega std::ratio<1000000, 1> (10^6)
giga std::ratio<1000000000, 1> (10^9)
tera std::ratio<1000000000000, 1> (10^12)
peta std::ratio<1000000000000000, 1> (10^15)
exa std::ratio<1000000000000000000, 1> (10^18)
zetta std::ratio<1000000000000000000000, 1> (10^21)^[2]
yotta std::ratio<1000000000000000000000000, 1> (10^24)^[2]
ronna (since C++26) std::ratio<1000000000000000000000000000, 1> (10^27)^[2]
quetta (since C++26) std::ratio<1000000000000000000000000000000, 1> (10^30)^[2]

1. ↑ ^1.0 ^1.1 ^1.2 ^1.3 These typedefs are only defined if std::intmax_t can
represent the denominator.
2. ↑ ^2.0 ^2.1 ^2.2 ^2.3 These typedefs are only defined if std::intmax_t can
represent the numerator.

Notes¶

Feature-test macro Value Std Feature
__cpp_lib_ratio 202306L (C++26) Adding the new 2022 SI prefixes: quecto, quetta,
ronto, ronna

Example¶

// Run this code

#include <ratio>

static_assert
(
std::ratio_equal_v<std::ratio_multiply<std::femto, std::exa>, std::kilo>
);

int main() {}

See also¶

Mathematical constants (C++20) provides several mathematical constants, such as
std::numbers::e for e