cbrt, cbrtf, cbrtl

Defined in header <math.h>
float       cbrtf( float arg );
(1) (since C99)
double      cbrt( double arg );
(2) (since C99)
long double cbrtl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define cbrt( arg )
(4) (since C99)
1-3) Computes the cube root of arg.
4) Type-generic macro: If arg has type long double, cbrtl is called. Otherwise, if arg has integer type or the type double, cbrt is called. Otherwise, cbrtf is called.


arg - floating point value

Return value

If no errors occur, the cube root of arg (\(\small{\sqrt[3]{arg} }\)3arg), is returned.

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.

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

  • if the argument is ±0 or ±∞, it is returned, unchanged
  • if the argument is NaN, NaN is returned.


cbrt(arg) is not equivalent to pow(arg, 1.0/3) because the rational number \(\small{\frac1{3} }\)1/3 is typically not equal to 1.0/3 and std::pow cannot raise a negative base to a fractional exponent. Moreover, cbrt(arg) usually gives more accurate results than pow(arg, 1.0/3) (see example).


#include <stdio.h>
#include <float.h>
#include <math.h>
int main(void)
    printf("Normal use:\n"
           "cbrt(729)      = %f\n", cbrt(729));
    printf("cbrt(-0.125)   = %f\n", cbrt(-0.125));
    printf("Special values:\n"
           "cbrt(-0)       = %f\n", cbrt(-0.0));
    printf("cbrt(+inf)     = %f\n", cbrt(INFINITY));
           "cbrt(343)      = %.*f\n", DBL_DECIMAL_DIG, cbrt(343));
    printf("pow(343,1.0/3) = %.*f\n", DBL_DECIMAL_DIG, pow(343, 1.0/3));

Possible output:

Normal use:
cbrt(729)      = 9.000000
cbrt(-0.125)   = -0.500000
Special values:
cbrt(-0)       = -0.000000
cbrt(+inf)     = inf
cbrt(343)      = 7.00000000000000000
pow(343,1.0/3) = 6.99999999999999911


  • C17 standard (ISO/IEC 9899:2018):
    • The cbrt functions (p: 180-181)
    • 7.25 Type-generic math <tgmath.h> (p: 272-273)
    • F.10.4.1 The cbrt functions (p: 381-)
  • C11 standard (ISO/IEC 9899:2011):
    • The cbrt functions (p: 247)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.4.1 The cbrt functions (p: 524)
  • C99 standard (ISO/IEC 9899:1999):
    • The cbrt functions (p: 228)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.4.1 The cbrt functions (p: 460)

See also

computes a number raised to the given power (\(\small{x^y}\)xy)
computes square root (\(\small{\sqrt{x} }\)x)
computes square root of the sum of the squares of two given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)x2
C++ documentation for cbrt

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