atan2

float       atan2f( float y, float x );

double      atan2( double y, double x );

long double atan2l( long double y, long double x );

#define atan2( arg )

Parameters

Return value

If no errors occur, the arc tangent of y/x (arctan(

)) in the range [-π ; +π] radians, is returned.

Y argument

Return value

X argument

If a domain error occurs, an implementation-defined value 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.

Domain error may occur if x and y are both zero.

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

• If x and y are both zero, domain error does not occur
• If x and y are both zero, range error does not occur either
• If y is zero, pole error does not occur
• If y is ±0 and x is negative or -0, ±π is returned
• If y is ±0 and x is negative or +0, ±0 is returned
• If y is ±∞ and x is finite, ±π/2 is returned
• If y is ±∞ and x is -∞, ±3π/4 is returned
• If y is ±∞ and x is +∞, ±π/4 is returned
• If x is ±0 and y is negative, -π/2 is returned
• If x is ±0 and y is positive, +π/2 is returned
• If x is -∞ and y is finite and positive, +π is returned
• If x is -∞ and y is finite and negative, -π is returned
• If x is +∞ and y is finite and positive, +0 is returned
• If x is +∞ and y is finite and negative, -0 is returned
• If either x is NaN or y is NaN, NaN is returned

Notes

atan2(y, x) is equivalent to carg(x + I*y).

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

Example

#include <stdio.h>
#include <math.h>
 
int main(void)
{
    // normal usage: the signs of the two arguments determine the quadrant
    // atan2(1,1) = +pi/4, Quad I
    printf("(+1,+1) cartesian is (%f,%f) polar\n", hypot( 1, 1), atan2( 1, 1));
    // atan2(1, -1) = +3pi/4, Quad II
    printf("(+1,-1) cartesian is (%f,%f) polar\n", hypot( 1,-1), atan2( 1,-1));
    // atan2(-1,-1) = -3pi/4, Quad III
    printf("(-1,-1) cartesian is (%f,%f) polar\n", hypot(-1,-1), atan2(-1,-1));
    // atan2(-1,-1) = -pi/4, Quad IV
    printf("(-1,+1) cartesian is (%f,%f) polar\n", hypot(-1, 1), atan2(-1, 1));
 
    // special values
    printf("atan2(0, 0) = %f atan2(0, -0)=%f\n", atan2(0,0), atan2(0,-0.0));
    printf("atan2(7, 0) = %f atan2(7, -0)=%f\n", atan2(7,0), atan2(7,-0.0));
}

(+1,+1) cartesian is (1.414214,0.785398) polar
(+1,-1) cartesian is (1.414214,2.356194) polar
(-1,-1) cartesian is (1.414214,-2.356194) polar
(-1,+1) cartesian is (1.414214,-0.785398) polar
atan2(0, 0) = 0.000000 atan2(0, -0)=3.141593
atan2(7, 0) = 1.570796 atan2(7, -0)=1.570796

References

• C11 standard (ISO/IEC 9899:2011):
  • 7.12.4.4 The atan2 functions (p: 239)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.1.4 The atan2 functions (p: 519)
• C99 standard (ISO/IEC 9899:1999):
  • 7.12.4.4 The atan2 functions (p: 219)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.1.4 The atan2 functions (p: 456)
• C89/C90 standard (ISO/IEC 9899:1990):
  • 4.5.2.4 The atan2 function

See also