# ATAN2 function

## Description

Arc tangent of two numbers, or four-quadrant inverse tangent. ATAN2(y,x) returns the arc tangent of the two numbers x and y. It is similar to calculating the arc tangent of y / x, except that the signs of both arguments are used to determine the quadrant of the result.

The result is an angle expressed in radians. To convert from radians to degrees, use the DEGREES function.

In terms of the standard arc tangent function, atan2 can be expressed as follows:

$$ \operatorname{atan2}(y,x) = \begin{cases} \arctan(\frac y x) &\text{if } x > 0 \\ \arctan(\frac y x) + \pi &\text{if } x < 0 \text{ and } y \ge 0 \\ \arctan(\frac y x) - \pi &\text{if } x < 0 \text{ and } y < 0 \\ +\frac{\pi}{2} &\text{if } x = 0 \text{ and } y > 0 \\ -\frac{\pi}{2} &\text{if } x = 0 \text{ and } y < 0 \\ \text{undefined} &\text{if } x = 0 \text{ and } y = 0 \end{cases}$$

Note that in Excel the parameters y and x are reversed.

## Calculator

## Graph

## Related functions

## External links

## Recommended book

## Trigonometry: A Complete Introduction

Hugh Neill

Buy from Amazon

This book covers all areas of trigonometry including the theory and equations of tangent, sine and cosine, using trigonometry in three dimensions and for angles for any magnitude, related to triangles. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.