Enter the standard angle into the reference angle calculator. The calculator will evaluate and display the reference angle. This calculator can also evaluate either of the angles in radians.

Reference Angle Formula

The reference angle for any angle can be calculated through the following formulas:

First Quadrant Formula: Reference Angle = Standard Angle

Second Quadrant Formula: Reference Angle = 180 - Standard Angle

Third Quadrant Formula: Reference Angle = Standard Angle - 180

Fourth Quadrant Formula: Reference Angle = 360 - Standard Angle

In these formulas, the reference angle is also known as the related acute angle or principal angle and the standard angle is sometime rereferred to as the original angle.

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Common Reference Angles

The following list outlines the most common reference angle conversions:

How to calculate a reference angle

The following is a step-by-step guide on how to calculate the reference angle of any angle.

First, the standard or original angle must be measured or calculated. For this example, we will assume the use of a protractor to measure an angle of 120 degrees.

Next, the quadrant that this angle lays in must be determined. The quadrant that an angle is in changes every 90 degrees. Therefore, this angle would be in the second quadrant.

Finally, the angle must be put into the formula above to calculate the reference angle. We find that the reference angle is 60 degrees.

Analyze these results and check using the graphic above to make sure it lies in the correct quadrant.


What is a reference angle?

A reference angle is defined as the absolute of the difference between 180 degrees and the original angle.

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