MATLAB Function Reference |

**Syntax**

**Description**

```
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.

**Examples**

Any complex number is converted to polar coordinates with

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

**Algorithm**

`atan2`

uses FDLIBM, which was developed at SunSoft, a Sun Microsystems, Inc. business, by Kwok C. Ng, and others. For information about FDLIBM, see http://www.netlib.org.

**See Also**

atan | atand |

© 1994-2005 The MathWorks, Inc.