jax.numpy.arctan2(x1, x2)

Element-wise arc tangent of x1/x2 choosing the quadrant correctly.

LAX-backend implementation of arctan2(). Original docstring below.

arctan2(x1, x2, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

The quadrant (i.e., branch) is chosen so that arctan2(x1, x2) is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “y-coordinate” is the first function parameter, the “x-coordinate” is the second.) By IEEE convention, this function is defined for x2 = +/-0 and for either or both of x1 and x2 = +/-inf (see Notes for specific values).

This function is not defined for complex-valued arguments; for the so-called argument of complex values, use angle.

  • x1 (array_like, real-valued) – y-coordinates.

  • x2 (array_like, real-valued) – x-coordinates. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output).


angle – Array of angles in radians, in the range [-pi, pi]. This is a scalar if both x1 and x2 are scalars.

Return type


See also

arctan(), tan(), angle()


arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: 1




+/- 0


+/- 0

+/- 0


+/- pi

> 0


+0 / +pi

< 0


-0 / -pi



+/- (pi/4)



+/- (3*pi/4)

Note that +0 and -0 are distinct floating point numbers, as are +inf and -inf.



ISO/IEC standard 9899:1999, “Programming language C.”


Consider four points in different quadrants:

>>> x = np.array([-1, +1, +1, -1])
>>> y = np.array([-1, -1, +1, +1])
>>> np.arctan2(y, x) * 180 / np.pi
array([-135.,  -45.,   45.,  135.])

Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range [-pi, pi]:

>>> np.arctan2([1., -1.], [0., 0.])
array([ 1.57079633, -1.57079633])
>>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
array([ 0.        ,  3.14159265,  0.78539816])