Coterminal Angle Calculator
Find coterminal angles for any angle in degrees or radians, the equivalent angle between 0° and 360°, its quadrant and its reference angle.
What are coterminal angles?
Coterminal angles share the same starting and ending sides. You find them by adding or subtracting full turns.
Degrees: θ ± 360° × k Radians: θ ± 2π × k
Worked examples
765° − 2 × 360° = 45°, so 765° and 45° are coterminal. For −100°, add 360° to get 260°.
Reference angles
| Quadrant | Reference angle |
|---|---|
| I (0°–90°) | θ |
| II (90°–180°) | 180° − θ |
| III (180°–270°) | θ − 180° |
| IV (270°–360°) | 360° − θ |
Frequently asked questions
How do I find a coterminal angle?
Add or subtract 360° (or 2π radians) as many times as you like.
Are coterminal angles equal?
They are different angles, but they point in the same direction and have the same trig values.
How many coterminal angles does an angle have?
Infinitely many, one for every whole number of full turns.
What is a reference angle?
The acute angle between the terminal side and the x-axis.
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