atan, atanf, atanl, atan2, atan2f, atan2l

Calculates the arctangent of x (atan, atanf, and atanl) or the arctangent of y/x (atan2, atan2f, and atan2l).


double atan( double x );
float atanf( float x );
long double atanl( long double x );
#define atan(X) // Requires C11 or higher

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

double atan2( double y, double x );
float atan2f( float y, float x );
long double atan2l( long double y, long double x );
#define atan2(Y, X) // Requires C11 or higher

float atan2( float y, float x );  // C++ only
long double atan2( long double y, long double x );  // C++ only


x, y
Any numbers.

Return value

atan returns the arctangent of x in the range -π/2 to π/2 radians. atan2 returns the arctangent of y/x in the range -π to π radians. If x is 0, atan returns 0. If both parameters of atan2 are 0, the function returns 0. All results are in radians.

atan2 uses the signs of both parameters to determine the quadrant of the return value.

Input SEH exception _matherr exception
± QNaN, IND none _DOMAIN


The atan function calculates the arctangent (the inverse tangent function) of x. atan2 calculates the arctangent of y/x (if x equals 0, atan2 returns π/2 if y is positive, -π/2 if y is negative, or 0 if y is 0.)

If you use the atan or atan2 macro from <tgmath.h>, the type of the argument determines which version of the function is selected. See Type-generic math for details.

atan has an implementation that uses Streaming SIMD Extensions 2 (SSE2). For information and restrictions about using the SSE2 implementation, see _set_SSE2_enable.

Because C++ allows overloading, you can call overloads of atan and atan2 that take float or long double arguments. In a C program, unless you're using the <tgmath.h> macro to call this function, atan and atan2 always take double arguments and return a double.

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


Routine Required header (C) Required header (C++)
atan, atan2, atanf, atan2f, atanl, atan2l <math.h> <cmath> or <math.h>
atan, atan2 macros <tgmath.h>


// crt_atan.c
// arguments: 5 0.5
#include <math.h>
#include <stdio.h>
#include <errno.h>

int main( int ac, char* av[] )
   double x, y, theta;
   if( ac != 3 ){
      fprintf( stderr, "Usage: %s <x> <y>\n", av[0] );
      return 1;
   x = atof( av[1] );
   theta = atan( x );
   printf( "Arctangent of %f: %f\n", x, theta );
   y = atof( av[2] );
   theta = atan2( y, x );
   printf( "Arctangent of %f / %f: %f\n", y, x, theta );
   return 0;
Arctangent of 5.000000: 1.373401
Arctangent of 0.500000 / 5.000000: 0.099669

See also

Math and floating-point support
acos, acosf, acosl
asin, asinf, asinl
cos, cosf, cosl
sin, sinf, sinl
tan, tanf, tanl