tanh, tanhf, tanhl

Defined in header <math.h>
float       tanhf( float arg );
(1) (since C99)
double      tanh( double arg );
long double tanhl( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define tanh( arg )
(4) (since C99)
1-3) Computes the hyperbolic tangent of arg.
4) Type-generic macro: If the argument has type long double, tanhl is called. Otherwise, if the argument has integer type or the type double, tanh is called. Otherwise, tanhf is called. If the argument is complex, then the macro invokes the corresponding complex function (ctanhf, ctanh, ctanhl).


arg - floating point value representing a hyperbolic angle

Return value

If no errors occur, the hyperbolic tangent of arg (tanh(arg), or earg-e-arg/earg+e-arg) 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, ±0 is returned
  • If the argument is ±∞, ±1 is returned
  • if the argument is NaN, NaN is returned


POSIX specifies that in case of underflow, arg is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.


#include <stdio.h>
#include <math.h>
int main(void)
    printf("tanh(1) = %f\ntanh(-1) = %f\n", tanh(1), tanh(-1));
    printf("tanh(0.1)*sinh(0.2)-cosh(0.2) = %f\n", tanh(0.1) * sinh(0.2) - cosh(0.2));
    // special values
    printf("tanh(+0) = %f\ntanh(-0) = %f\n", tanh(0.0), tanh(-0.0));


tanh(1) = 0.761594
tanh(-1) = -0.761594
tanh(0.1)*sinh(0.2)-cosh(0.2) = -1.000000
tanh(+0) = 0.000000
tanh(-0) = -0.000000


  • C11 standard (ISO/IEC 9899:2011):
    • The tanh functions (p: 242)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.2.6 The tanh functions (p: 520)
  • C99 standard (ISO/IEC 9899:1999):
    • The tanh functions (p: 222-223)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.2.6 The tanh functions (p: 457)
  • C89/C90 standard (ISO/IEC 9899:1990):
    • The tanh function

See also

computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x))
computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x))
computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x))
computes the complex hyperbolic tangent
C++ documentation for tanh

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