@ATan2 (Formula Language)

Calculates the arc tangent using the tangent y/x of an angle.


@ATan2( x ; y )



Number or number list. The denominator of the tangent value y / x.


Number or number list. The numerator of the tangent value y / x.


If either parameter is a list, the function operates pair-wise on the list elements, and the return value is a list with the number of elements in the larger list.

Return value


Number. An angle, in radians, from -pi through pi. This represents an angle between -180 and 180 degrees, depending on the sign of x and y (see the list below).


Then angle is in the range

xis positive

yis positive

0 to pi/2 (Quadrant I)

x is negative

y is positive

pi/2 to pi (Quadrant II)

x is negative

y is negative

-pi to -pi/2 (Quadrant III)

x is positive

y is negative

-pi/2 to 0 (Quadrant IV)


  1. This example returns pi/4.
    @ATan2( 1; 1 )
  2. This example returns 3pi/4.
    @ATan2( -1; 1 )
  3. This example returns 1.10715 radians (63.4 degrees).
    @ATan2 ( 1; 2 )
  4. This example returns pi/4, 3pi/4, and 1.10715 radians in a list.
    @ATan2 ( 1 : : (-1) : 1; 1 : 1 : 2 )