Coterminal Angle Calculator
Enter any angle to find its coterminal angles and the equivalent within 0-360 degrees.
Coterminal Angles
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Request a ToolHow to Use the Coterminal Angle Calculator
This calculator finds coterminal angles for any angle you enter.
- Enter an angle. Type any angle value, positive or negative, in any magnitude.
- Choose degrees or radians. The calculator works with both and converts between them.
- Read the results. You will see the normalized angle (within 0-360 degrees), three positive coterminal angles, and three negative coterminal angles, all shown in both degrees and radians.
About Coterminal Angles
Coterminal angles share the same terminal side when drawn in standard position on the coordinate plane. Two angles are coterminal if they differ by a multiple of 360 degrees (or 2 pi radians). For example, 30 degrees, 390 degrees, and -330 degrees are all coterminal because they point in the same direction. Every angle has infinitely many coterminal angles. To find them, simply add or subtract 360 degrees repeatedly. To find the coterminal angle within 0-360, take the angle modulo 360.
Frequently Asked Questions
What are coterminal angles?
Coterminal angles are angles that end at the same position when drawn from the positive x-axis. They differ by full rotations (multiples of 360 degrees or 2 pi radians). For instance, 45 degrees and 405 degrees are coterminal because 405 - 360 = 45.
How do I find a coterminal angle within 0 to 360 degrees?
Add or subtract 360 degrees until the result is between 0 and 360. Mathematically, compute angle mod 360. If the result is negative, add 360. For example, -45 mod 360 = -45, then -45 + 360 = 315 degrees.
Do coterminal angles have the same trig values?
Yes. Since coterminal angles point in the same direction, they produce identical values for all trigonometric functions. sin(30) = sin(390) = sin(-330) = 0.5. This is why normalizing angles to 0-360 is a common first step in trig calculations.