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.

Graph

Function:	ATAN2(,)
	X-axis	Y-axis
Minimum:	Minimum X	Minimum Y
Maximum:	Maximum X	Maximum Y

Enter the argument(s) for the function, including the symbol x.
Enter the minimum and maximum for the X-axis and for the Y-axis.
To let the software define the Y-axis automatically, leave both input fields for the Y-axis empty.

Related functions

• ATAN function: returns the arc tangent of a number.
• DEGREES function: converts radians to degrees.
• Trigonometric functions

External links

• atan2 function on Wikipedia.