In this simple guide, we are going to run through how to use the Excel ATAN function to calculate the inverse tangent of a given number.
We will cover:
- What is an inverse tangent?
- The formula
- Converting to degrees
What is an inverse tangent?
An inverse tangent is a term used within trigonometry The inverse tangent is also known as the arctangent (hence the shortened ATAN name used in the formulas in Excel).
Without turning this guide into a full blown trigonometry lesson, essentially what this means is we take a number, either positive or negative, and we aim to return the angle of a right triangle, in radians, ranging from -Pi/2 up to Pi/2.
This can then be taken one step further and converted to degrees, which we will touch on later with a quick guide on another handy formula, and how to keep things nice and clean.
Returning the inverse tangent using the Excel ATAN function
Luckily, the method we need to take to return the inverse tangent (or arctangent) is far less complicated than the maths that sits behind it! This is one of the less complex Excel formulas available – and we mean really simple! The entire formula allows for a single value to be declared. The formula is as follows:
Let’s look at some examples. As we can see in the below table, the formula and corresponding outputs are quite easy to work with. We have 10 values listed in the initial value column, using a combination of both positive and negative figures:
So far nice and easy – the radian values have been returned in column D of our example workbook.
Converting the returned values to degrees
As we are working with radians, the next thing we can do here is convert these numbers to degrees.
There are two ways to go about doing this.
The first approach is a bit manual, and done via taking the existing result, multiplying by 180 and dividing by Pi. For example, if we were to take the top result above, sitting in cell D3, we would run with the following formula:
Pretty simple right? Generally there is nothing wrong with this approach, but given this guide is using a built in function for ATAN, let’s be consistent and use the built in function for degrees!
This simplified the formula even more to the below:
Some examples of this step are below, using our existing dataset:
If we didn’t care about the actual values returned from the ATAN formula and really just wanted to focus on the degrees, we can simplify this even more by wrapping them together in one easy formula! The syntax would be as follows:
Number in this case just being the original values over in column B of our examples. Nice and simple!
This just about covers off the basics of working with the Excel ATAN function in order to return inverse tangents of a value. The one area we have not touched on is working with the ATAN2 formula, which accepts two different values as part of the syntax. The use case for this one is slightly different so will be covered in it’s own separate guide down the line.
As we can see, the ATAN formula is a nice and simple one to help simplify what can be a challenging area of maths. There are a whole range of functions within Excel that can help with mathematical and statistical techniques.
This sums up our guide on working with ATAN in Excel – for more handy tips be sure to visit our Excel Tips page