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Four-quadrant inverse tangent



P = atan2(Y,X) returns an array P the same size as X and Y containing the element-by-element, four-quadrant inverse tangent (arctangent) of the real parts of Y and X. The elements of P are in the interval . Any imaginary parts of the inputs are ignored.

Elements of P lie in the closed interval [-pi,pi], where pi is the MATLAB floating-point representation of . atan uses sign(Y) and sign(X) to determine the specific quadrant.

atan2(Y,X) contrasts with atan(Y/X), whose results are limited to the interval , or the right side of this diagram.


Any complex number is converted to polar coordinates with

For example,

This is a common operation, so MATLAB provides a function, angle(z), that computes theta = atan2(imag(z),real(z)).

To convert back to the original complex number


atan2 uses FDLIBM, which was developed at SunSoft, a Sun Microsystems, Inc. business, by Kwok C. Ng, and others. For information about FDLIBM, see

See Also

angle, atan, atanh

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