# atan2, atan2f, atan2l

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float atan2f( float y, float x ); | (1) | (since C99)
double atan2( double y, double x ); | (2) |
long double atan2l( long double y, long double x ); | (3) | (since C99)
_Decimal32 atan2d32( _Decimal32 y, _Decimal32 x ); | (4) | (since C23)
_Decimal64 atan2d64( _Decimal64 y, _Decimal64 x ); | (5) | (since C23)
_Decimal128 atan2d128( _Decimal128 y, _Decimal128 x ); | (6) | (since C23)
Defined in header `<tgmath.h>` |  |
#define atan2( y, x ) | (7) | (since C99)

1-6) Computes the arc tangent of y / x using the signs of arguments to determine the correct quadrant.
7) Type-generic macro: If any argument has type long double, (3) (`atan2l`) is called. Otherwise, if any argument has integer type or has type double, (2) (`atan2`) is called. Otherwise, (1) (`atan2f`) is called.

The functions (4-6) are declared if and only if the implementation predefines `__STDC_IEC_60559_DFP__` (i.e. the implementation supports decimal floating-point numbers). | (since C23)

### Parameters

x, y | - | floating-point value

### Return value

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

y
x

)) 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 positive 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

Run this code

    #include <math.h>
    #include <stdio.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));
    }

Output:

    (+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

- C23 standard (ISO/IEC 9899:2023):

  - 7.12.4.4 The atan2 functions (p: TBD)

  - 7.25 Type-generic math <tgmath.h> (p: TBD)

  - F.10.1.4 The atan2 functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.4.4 The atan2 functions (p: 174)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - F.10.1.4 The atan2 functions (p: 378)

- 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

asin asinf asinl (C99)(C99) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
acos acosf acosl (C99)(C99) | computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
atan atanf atanl (C99)(C99) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
carg cargf cargl (C99)(C99)(C99) | computes the phase angle of a complex number (function)

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