Coterminal Angles Calculator
Coterminal angles share the same terminal side and differ by whole multiples of 360°.
°
Smallest negative coterminal angle: -300°
- 1
Reduce modulo 360°
420 mod 360 = 60JavaScript % preserves the sign of the dividend. - 2
Shift into positive range
(60 + 360) mod 360 = 60 - 3
Smallest positive coterminal angle
60° = 60
How does this calculator work?
Coterminal angles end at the same terminal side and differ by multiples of 360°. The smallest positive one equals ((angle mod 360) + 360) mod 360, and subtracting 360° gives the smallest negative. Add or subtract 360° × n for any whole number n to generate the full family of coterminal angles.
Formula
How this is calculated
Enter any angle in degrees. Two angles are coterminal when they end at the same terminal side on the unit circle, which happens whenever they differ by a whole number of full revolutions (360°). The calculator reduces your angle to the smallest positive coterminal value using ((θ mod 360) + 360) mod 360, which works for both positive and negative inputs. Subtracting 360° from that value gives the smallest negative coterminal angle (in the range −360° to 0°).
The "pairs (k)" input controls how many additional coterminal angles are listed in each direction. For each i from 1 to k, the family includes the smallest positive angle plus and minus 360° × i, so you get k positive and k negative members beyond the base value. The list is sorted from most negative to most positive.
All values are in degrees. If you need radians, divide by 180 and multiply by π. The formula assumes a full revolution of 360°; k is clamped between 1 and 10. Non-numeric inputs produce no result.
Frequently asked questions
An angle that shares the same initial and terminal sides as another angle, differing only by a whole number of full 360° rotations.
Yes. Subtracting 360° (or any multiple) from an angle gives a negative coterminal angle that lands on the same terminal side.
Compute ((θ mod 360) + 360) mod 360. This always returns a value between 0° and 360° regardless of the sign of θ.
Also known as
TG we-Calculate Editorial Team. (2026). Coterminal Angles Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/coterminal-angles-calculator
TG we-Calculate Editorial Team. "Coterminal Angles Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/coterminal-angles-calculator.
TG we-Calculate Editorial Team, "Coterminal Angles Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/coterminal-angles-calculator
@misc{wecalculate_coterminal_angles_calculator, title = {Coterminal Angles Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/coterminal-angles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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