Coterminal angle calculator
Coterminal angles differ by whole turns and end in the same place, so they share every trig value.
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How to use it
- Enter angle and angle unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
θ + 360° × k for any whole number k, or θ + 2π × k in radians. The smallest non-negative one is θ mod 360°.
Example
Inputs: Angle = 400, Angle unit = Degrees. Result: Smallest non-negative coterminal angle: 40 °; Nearest negative coterminal angle: -320 °.
Limits and caveats
- The table shows three turns each way. Any other number of turns works the same way.
Questions about this tool
What are coterminal angles?
Angles with the same initial and terminal sides. They differ from each other by multiples of 360°.
How do I get a positive coterminal angle for a negative one?
Add 360° until it is positive, for example -30° + 360° = 330°.
Do they have the same sine?
Yes. Coterminal angles share every trig value because they end at the same point on the unit circle.