Calculating the difference between two angles

Context

Given a target angle \(A_t\) and a reference angle \(A_r\), we want to calculate the "smallest difference" between them. In other words:

• The difference between target angle 180° and reference angle -180° is 0°
• The difference between target angle 359° and reference angle 0° is 1°

Problem

How to calculate the "smallest difference" between the two angles?

Solution

Use the following formula to calculate the signed difference:

\[ d = (A_t - A_r + 180) \% 360 -180 \]

Then take the absolute value of \(d\) to get the unsigned difference.

Reference

• https://stackoverflow.com/questions/1878907/how-can-i-find-the-difference-between-two-angles

Note

If the modulo operation returns a value with the same sign as the dividend (i.e., \(-1 \% 360 = -1\)), then the formula should be changed to

\[ d = ( (A_t - A_r)\%360 + 180) \% 360 -180 \]