Last updated October 7, 2026 · Report an error
Coterminal angles are angles that, when drawn in standard position on the unit circle (starting from the positive x-axis), end up pointing in exactly the same direction — sharing the same terminal side — even though their measured values are different. They differ only by a whole number of full rotations, 360° or 2π radians, so 30°, 390°, 750°, and -330° are all coterminal with each other, since each pair differs by an exact multiple of 360°. Recognizing coterminal angles matters because every trig function treats them identically: sin(30°) = sin(390°) = sin(-330°), since all three angles land on the same point of the unit circle. This comes up whenever a real-world rotation exceeds a single turn — tracking the total rotation of a wheel, motor shaft, or drone propeller (which can rack up thousands of degrees), simplifying a large or negative angle in a physics or engineering problem before evaluating its sine or cosine, and standardizing angles in navigation or surveying where a compass bearing needs to be expressed within a single 0°-360° range.
How it works
Enter an angle in degrees or radians, including large angles beyond 360° or negative angles. The calculator repeatedly adds or subtracts 360° (or 2π radians) until the result lands within the standard [0°, 360°) or [0, 2π) range — equivalent to taking the angle modulo 360°. It also reports a negative coterminal angle (the standard-range value minus 360°) and the general formula θ + 360°n, which describes every coterminal angle at once as n ranges over all integers.
- Enter angle (θ).
- Enter angle unit.
- Click Calculate to see your results.
Examples
400°
400° − 360° = 40°, so 40° is the coterminal angle in the standard [0°, 360°) range — a single subtraction was enough since 400° is only slightly more than one full rotation.
-100°
-100° + 360° = 260°, so 260° is the standard-range coterminal angle. The original -100° is a perfectly valid angle, just outside the conventional [0°, 360°) window.
1000°
1000° − 360° = 640°, still too large, so subtract 360° again: 640° − 360° = 280°. Two full rotations (720°) had to be removed before landing in the standard range.
Common mistakes to avoid
- Forgetting that negative angles also have a standard-range positive coterminal equivalent, and treating them as somehow invalid.
- Confusing coterminal angles with reference angles — coterminal angles share a full terminal side, while reference angles are always acute and measure distance to the x-axis.
- Only subtracting 360° once for very large angles, instead of continuing to subtract full rotations until the result actually lands within [0°, 360°).
- Assuming coterminal angles must be positive multiples apart — subtracting 360° (a negative multiple) is just as valid as adding it.