The ATAN function is used to return the arctangent of a number.
Contents:
Syntax
= ATAN(number)number - The tangent value for which you want to calculate the arctangent
Note: the results will be returned as radians. To return a degree, use the DEGREES function like so:
= DEGREES(ATAN(number))Explanation
The ATAN function is part of the "Math and Trigonometry" group of functions within Excel.
This function calculates an arctangent, which is the inverse of the tangent function, and returns the angle in radians.
What is an Arctangent
To understand arctangent, consider the relationship between angles and the ratios of sides in right-angled triangles.
The tangent of an angle (a) is the ratio of the length of the opposite side (y) to the length of the adjacent side (x).
Conversely, arctangent (arctan or ATAN) finds the inverse angle. The inverse of arctangent is useful when the tangent is known but the angle itself is not.
For example, if the tangent of an angle is calculated as a = opposite / adjacent = y / x = 35 / 41 ≈ 0.707, then a = arctan(0.707) ≈ 40°.
In trigonometry, every function has an inverse that works in reverse. These inverses are prefixed with 'arc', making the inverse of tan the arctan.
Examples
How to Calculate Arctangent Using the Opposite and Adjacent Sides of a Triangle
Let's say we have table representing triangles with two know sides, the side opposite and adjacent to the angle that we want to calculate the arctangent of, in degrees.
The formula to calculate the arctangent in degrees would be:
= DEGREES(ATAN(opposite/adjacent))If we plug this formula into the table, we get the correct arctangent angles (rounded here to the nearest degree.
This table uses the ATAN function to calculate the angle from the given sides of a right-angled triangle, and converts that result into degrees.
If you don't want to use the DEGREES function, you can also multiply the result by 180/pi.