std::sqrt, std::sqrtf, std::sqrtl

Defined in header <cmath>
float       sqrt ( float arg );
float       sqrtf( float arg );
(since C++11)
double      sqrt ( double arg );
long double sqrt ( long double arg );
long double sqrtl( long double arg );
(since C++11)
double      sqrt ( IntegralType arg );
(4) (since C++11)
1-3) Computes the square root of arg.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) (the argument is cast to double).


arg - Value of a floating-point or integral type

Return value

If no errors occur, square root of arg (\({\small \sqrt{arg} }\)arg), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

Domain error occurs if arg is less than zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

  • If the argument is less than -0, FE_INVALID is raised and NaN is returned.
  • If the argument is +∞ or ±0, it is returned, unmodified.
  • If the argument is NaN, NaN is returned


std::sqrt is required by the IEEE standard to be exact. The only other operations required to be exact are the arithmetic operators and the function std::fma. After rounding to the return type (using default rounding mode), the result of std::sqrt is indistinguishable from the infinitely precise result. In other words, the error is less than 0.5 ulp. Other functions, including std::pow, are not so constrained.


#include <iostream>
#include <cmath>
#include <cerrno>
#include <cfenv>
#include <cstring>
int main()
    // normal use
    std::cout << "sqrt(100) = " << std::sqrt(100) << '\n'
              << "sqrt(2) = " << std::sqrt(2) << '\n'
              << "golden ratio = " << (1+std::sqrt(5))/2 << '\n';
    // special values
    std::cout << "sqrt(-0) = " << std::sqrt(-0.0) << '\n';
    // error handling
    errno = 0;
    std::cout << "sqrt(-1.0) = " << std::sqrt(-1) << '\n';
    if(errno == EDOM)
        std::cout << "    errno = EDOM " << std::strerror(errno) << '\n';
        std::cout << "    FE_INVALID raised\n";

Possible output:

sqrt(100) = 10
sqrt(2) = 1.41421
golden ratio = 1.61803
sqrt(-0) = -0
sqrt(-1.0) = -nan
    errno = EDOM Numerical argument out of domain
    FE_INVALID raised

See also

raises a number to the given power (\(\small{x^y}\)xy)
computes cubic root (\(\small{\sqrt[3]{x} }\)3x)
computes square root of the sum of the squares of two or three (C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)x2
), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)x2
complex square root in the range of the right half-plane
(function template)
applies the function std::sqrt to each element of valarray
(function template)
C documentation for sqrt

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