Strange ATAN Results

Jerry notes that when he uses the ATAN function in Excel to calculate an arctangent, he gets a result that’s quite a bit different from the result provided when he uses a scientific calculator to derive the arctangent. This makes him wonder if there is something strange in how the ATAN function works.

There are two possibilities here. The most likely possibility is that your calculator defaults to using degrees in trigonometric functions such as calculating an arctangent. Excel uses radians exclusively. For example, let’s say you wanted to calculate the arctangent for 0.5. If you plug this into your calculator, and your calculator is working in degrees, you’ll get a rounded result of 26.565. However, using the ATAN function in Excel produces a rounded result of 0.464.

The result that Excel provides is in radians, and when you convert that result to degrees, you end up with 26.565-the same as your calculator’s result. Here’s how you can easily do the conversion:

=DEGREES(ATAN(0.5))

If the angle for which you want to find the arctangent is expressed in degrees instead of radians, then you’ll need to do the conversion on the input:

=ATAN(RADIANS(30))

Again, remember that the result of the ATAN function is always in radians, so you may also want to do a conversion on the output, as well.

The solution is to make sure that your calculator is working in radians mode, which should give you the same results as Excel. Either that or you need to convert Excel’s results (and, possibly, input) to degrees, as shown above.

The other possibility is much less likely, but it is worth mentioning: There are some values for which the ATAN function will break down, but for which your calculator may already compensate. The best explanation of the scenarios under which this could happen is provided in this Wikipedia article:

http://en.wikipedia.org/wiki/Atan2