## How to use the ATAN2 function

**What is the ATAN2 function?**

The ATAN2 function calculates the arctangent of an angle using specific x- and y-coordinates. The returned angle is in radians between -pi to pi, including pi. The angle is between the x-axis and the line from (0,0) and point (x_num, y_num)

Atan2 is more useful when converting cartesian (x,y) to polar (r,Î¸)

**What is the difference between atan2 and atan?**

Atan handles only angles in the first quadrant while atan2 covers all quadrants.

**When to use the atan2 function?**

The atan2 function is more useful than atan for converting from cartesian (x,y) coordinates to polar (r,Î¸) form because it correctly handles all quadrants and signs to determine the full angular direction Î¸.

**What is cartesian (x,y)?**

The Cartesian coordinate grid has an x-axis running left-to-right and a y-axis running up-and-down meaning it has two axis or dimensions (2D). Cartesian coordinates are just a way to capture any point on a 2D grid using an x and y value.

**What is a quadrant?**

The Cartesian coordinate grid has 4 quadrants formed by the x-axis and the y-axis.

Each quadrant has a combination of positive or negative x and y values:

- Quadrant 1 is the upper right with positive x and positive y.

- Quadrant 2 is the upper left with negative x but positive y.

- Quadrant 3 is the lower left with negative x and negative y.

- Quadrant 4 is the lower right with positive x but negative y.

The signs of the (x,y) coordinates tell you which quadrant a given point is located in.

**What is a sign?**

The sign tells you if a numeral value is positive or negative. For example, if x is -5 and y is -10 then the coordinate is in the third quadrant.

**What is polar (r,Î¸)?**

Polar coordinates identify points using a distance r and angle Î¸. r is the distance of the point from the center origin. Î¸ (theta) is the angle between the point and the positive x-axis.

For example, (5, 100Â°) in polar coordinates represents r=5 units from the origin or intersection of the x and y axis. The angle Î¸=100 degrees is related to the x-axis counterclockwise.

### Excel Function Syntax

ATAN2(*x_num*, *y_num*)

### Arguments

x_num |
Required. The x-coordinate. |

y_num |
Required. The y-coordinate. |

### Comments

If x_num is 1 and y_num is 1 then the angle between theÂ x-axis and the line from (0,0) to (1,1) is 45 degrees or 1/4 pi radians. 1/4 pi isÂ 0.785398163.

### Functions in 'Math and trigonometry' category

The ATAN2 function function is one of many functions in the 'Math and trigonometry' category.

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