Coterminal Angle Calculator

Calculate Coterminal Angles

Formulas

The formulas to calculate coterminal angles are:

Positive Coterminal Angle = Angle + 360

Negative Coterminal Angle = Angle - 360

What is a Coterminal Angle?

A coterminal angle is an angle that ends at the same geometric point on the coordinate plane as another angle. Since the coordinate circle has a total rotation of 360 degrees, adding or subtracting 360 degrees to the angle yields a coterminal angle.

Example Calculation

Let's assume the following value:

Using the formulas:

Positive Coterminal Angle = 45 + 360 = 405°

Negative Coterminal Angle = 45 - 360 = -315°

The Positive Coterminal Angle is 405° and the Negative Coterminal Angle is -315°.