acosh, acoshf, acoshl

Calculates the inverse hyperbolic cosine.


double acosh( double x );
float acoshf( float x );
long double acoshl( long double x );
#define acosh(X) // Requires C11 or higher

float acosh( float x );  // C++ only
long double acosh( long double x );  // C++ only


Floating-point value.

Return value

The acosh functions return the inverse hyperbolic cosine (arc hyperbolic cosine) of x. These functions are valid over the domain x ≥ 1. If x is less than 1, errno is set to EDOM, and the result is a quiet NaN. If x is a quiet NaN, indefinite, or infinity, the same value is returned.

Input SEH exception _matherr exception
± QNaN, IND, INF none none
x < 1 none none


When you use C++, you can call overloads of acosh that take and return float or long double values. In a C program, unless you're using the <tgmath.h> macro to call this function, acosh always takes and returns double.

If you use the <tgmath.h> acosh() macro, the type of the argument determines which version of the function is selected. See Type-generic math for details.

By default, this function's global state is scoped to the application. To change this behavior, see Global state in the CRT.


Function C header C++ header
acosh, acoshf, acoshl <math.h> <cmath>
acosh macro <tgmath.h>

For more compatibility information, see Compatibility.


// crt_acosh.c
// Compile by using: cl /W4 crt_acosh.c
// This program displays the hyperbolic cosine of pi / 4
// and the arc hyperbolic cosine of the result.

#include <math.h>
#include <stdio.h>

int main( void )
   double pi = 3.1415926535;
   double x, y;

   x = cosh( pi / 4 );
   y = acosh( x );
   printf( "cosh( %f ) = %f\n", pi/4, x );
   printf( "acosh( %f ) = %f\n", x, y );
cosh( 0.785398 ) = 1.324609
acosh( 1.324609 ) = 0.785398

See also

Math and floating-point support
asinh, asinhf, asinhl
atanh, atanhf, atanhl
cosh, coshf, coshl
sinh, sinhf, sinhl
tanh, tanhf, tanhl