Finds angles that share the same terminal side as a given angle — angles differing by a whole number of full rotations.
How it works
The angle is normalized to a 0-360 degree range, and one full rotation is added and subtracted to show two more coterminal angles.
What this does not include
This shows only the normalized angle plus one rotation in each direction — infinitely many coterminal angles exist (any multiple of 360 degrees added or subtracted).
How to use this calculator
- Enter any angle, including negative values or values over 360 degrees.
A worked example
An angle of 400°: normalized to 40° (within 0–360°), one full turn forward gives 400° + 360° = 760°… actually stored as plus one turn: 400° from the normalized base, and minus one turn gives −320°.
An angle of −45°: normalizes to 315°, plus one turn gives 675°, minus one turn stays at −45°.
What the variables mean
| Variable | Meaning |
|---|---|
| Angle | Any angle, including values outside 0–360° |
| Normalized | The equivalent angle brought within the standard 0–360° range |
Edge cases worth knowing
Coterminal angles share the same terminal side but differ by a multiple of 360°. 400° and 40° point in the exact same direction — the extra 360° is simply a full unnecessary rotation.
Negative angles are just as valid as positive ones — they represent rotation in the opposite (clockwise) direction, and still have a full family of coterminal equivalents.
Frequently asked questions
Why do coterminal angles have the same trig function values?
Because they end at the exact same position on the unit circle, so sine, cosine, and tangent all evaluate identically for any coterminal pair.
What does “terminal side” mean?
The ray where an angle’s rotation ends, measured from the positive x-axis — angles that end at the same ray are coterminal.
Can a negative angle be coterminal with a positive one?
Yes — for example, −45 degrees and 315 degrees describe the exact same terminal position, just measured in opposite rotational directions.
