Coterminal angles share the same terminal side because they differ by full rotations. Adding or subtracting 360 degrees keeps the angle position unchanged on the coordinate plane.
⚠This calculator uses degrees. For radians, the equivalent full-turn adjustment is 2πk.
How Coterminal Angles Work
A full rotation returns to the same terminal side. Therefore any angle plus or minus one or more full turns is coterminal with the original angle.
Full Rotation
One full turn is 360°.
Same Terminal Side
Coterminal angles end in the same place.
Positive Angle
Add or reduce into 0°-360°.
Negative Angle
Subtract 360° for a clockwise version.
💡 Example: For 725°, a positive coterminal angle is 5° and a negative one is -355°.
Applications of Coterminal Angles
Unit CircleTrig GraphsExact ValuesAngle Simplification
Frequently Asked Questions
What is a coterminal angle calculator?▼
It finds angles that end at the same terminal side as the original angle.
What is the coterminal angle formula?▼
Coterminal angles are found by adding or subtracting 360°k, where k is an integer.
How do I use this calculator?▼
Enter an angle in degrees and click Calculate.
Can coterminal angles be negative?▼
Yes. Negative coterminal angles rotate clockwise but end at the same terminal side.
Where are coterminal angles used?▼
They are used in unit circle work, trig graphs, angle simplification, and exact value problems.
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