Coterminal Angle Calculator
Find an equivalent angle from 0° up to but excluding 360°, plus a negative representative, for an input in degrees.
Formula
α = θ − 360° floor(θ/360°); β = α − 360°. All coterminal angles are θ + 360°k, k integer.
Principal angle α ≈ (800)-360×floor((800)÷360) · Negative coterminal angle β ≈ (80)-360
How to use
- Enter a signed angle in degrees.
- Read α in the interval [0°, 360°).
- Read β in [−360°, 0°) or add any whole turns.
Examples
- 800° gives 80° and −280°; −45° gives 315° and −45°.
Frequently asked questions
What does coterminal mean?
The angles have the same terminal side and differ by a whole number of turns.
Is 0° allowed as the principal result?
Yes. Complete turns map to 0°, not 360°; the negative representative is −360°.
Can the input be negative or decimal?
Yes, within ±360,000°. This form uses degrees only.
Sources
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