Reference Angle Calculator

How do you Calculate Reference Angle?

How you calculate for reference angle will depend on the degree of the angle. There are four different formulas, one if the angle is less than 90 degrees, another if the angle is greater than 90 but less than 180 degrees, another one if the angle is greater than 180 but less than 270 degrees, and a final if the angle is greater than 270 degrees. Here is the formula if the angle is greater than 180 degrees but less than 270:

• RA = Reference Angle


• NA = Normalized Angle

Understanding Your Results

The reference angle is always a positive acute angle (less than 90 degrees). It represents the smallest angle between the terminal side of your given angle and the x-axis. This helps in trigonometric calculations by simplifying the analysis of angles in different quadrants.

How to Use the Reference Angle Calculator

To use our tool, follow these simple steps:

1. Enter the given angle value into the input field.


2. Select the unit of measurement for the angle: degrees, radians, or n radians.


3. Click calculate and get your answer instantly!

Example Calculations

If we are trying to find the reference angle for an angle that is 50 degrees, the result will be 50 degrees. Now if we evaluate a degree 91-degree angle, we will see the reference angle is 89 degrees. If we inspect a 185-degree angle the reference angle will be 5 degrees. Finally, if we evaluate a 320-degree angle, the reference angle is 40 degrees.