Calculate Arctan of An Angle in Degrees Excel

The arctangent function (arctan) is the inverse of the tangent function. In Excel, you can calculate the arctangent of an angle in degrees using the ATAN2 function combined with degree conversion. This guide explains how to do it accurately and provides practical examples.

What is Arctan?

The arctangent function, often written as arctan or tan⁻¹, returns the angle whose tangent is the specified number. The result is always in the range of -90 to 90 degrees.

In Excel, the ATAN function returns the arctangent of a number in radians. To get the result in degrees, you need to multiply by 180/π (or use the DEGREES function).

Note: The arctangent function is periodic with a period of 180 degrees, meaning arctan(x) = arctan(-x) + 180 degrees.

Excel Formula for Arctan

To calculate the arctangent of an angle in degrees in Excel, use the following formula:

=DEGREES(ATAN(opposite/adjacent))

Where:

opposite is the length of the side opposite the angle
adjacent is the length of the side adjacent to the angle

For example, if you have a right triangle with opposite side = 3 and adjacent side = 4, the angle would be calculated as:

=DEGREES(ATAN(3/4))

This returns approximately 36.87 degrees.

For angles outside the -90 to 90 degree range, use the ATAN2 function which takes both x and y coordinates: =DEGREES(ATAN2(opposite, adjacent))

How to Use the Calculator

Our interactive calculator makes it easy to compute the arctangent of an angle in degrees. Simply enter the values for the opposite and adjacent sides, then click "Calculate".

The calculator will:

Validate your inputs
Compute the arctangent in degrees
Display the result in a clear format
Show a visualization of the angle

You can also reset the calculator to start over.

Examples

Here are some practical examples of calculating arctangent in degrees:

Opposite Side	Adjacent Side	Arctan (Degrees)
1	1	45.00
3	4	36.87
5	12	22.62
-2	2	-26.57

These examples show how the arctangent function works with different input values.

FAQ

What is the difference between ATAN and ATAN2 in Excel?: The ATAN function takes a single argument and returns an angle in the range of -90 to 90 degrees. The ATAN2 function takes two arguments (y and x) and returns an angle in the range of -180 to 180 degrees, which is more useful for full-circle calculations.
How do I convert radians to degrees in Excel?: Use the DEGREES function: =DEGREES(radian_value). This converts radians to degrees by multiplying by 180/π.
What if I get a #NUM! error in Excel?: This error occurs when you try to calculate the arctangent of a non-numeric value. Make sure your inputs are numbers, not text or empty cells.
Can I use arctangent for angles greater than 90 degrees?: Yes, but you need to use the ATAN2 function which can handle all angles. The formula would be =DEGREES(ATAN2(opposite, adjacent)).