std::ratio(3)

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