Find positive and negative coterminal angles by adding or subtracting full rotations in degrees or radians.
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Trigonometry
The coterminal angle calculator finds angles that share the same terminal side by adding or subtracting 360° (or 2pi radians). Enter any angle to see its positive and negative coterminal equivalents.
Two angles are coterminal if they share the same initial and terminal sides when drawn in standard position. For example, 30° and 390° are coterminal because 390° - 360° = 30°.
Every angle has infinitely many coterminal angles, found by adding or subtracting any multiple of 360° (or 2pi radians).
To find a positive coterminal angle, add 360° until the result is between 0° and 360°. To find a negative coterminal angle, subtract 360° until the result is negative. The same logic applies with 2pi for radians.
Trigonometric functions have the same value for all coterminal angles, so simplifying to a reference angle between 0° and 360° makes evaluation easier. Coterminal angles also appear in physics when describing rotational motion.
Frequently asked questions
Yes. They share the same terminal side along the positive x-axis. In fact, any multiple of 360° is coterminal with 0°.
Yes. For example, -30° and 330° are coterminal because -30° + 360° = 330°. They represent the same position on the unit circle.
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