Angle calculator
Enter an angle in degrees or radians and see what type of angle it is, its complementary and supplementary angle, how much is missing to a full turn (360°) and the same angle in the other unit.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
Types of angle
- acute: between 0° and 90°
- right: exactly 90°
- obtuse: between 90° and 180°
- straight: exactly 180°
- reflex: between 180° and 360°
Complementary and supplementary
Two angles are complementary when they add up to 90° (30° and 60°) and supplementary when they add up to 180° (110° and 70°). An angle larger than 90° has no complementary angle, and one larger than 180° no supplementary angle.
Angles larger than 360° or negative angles are also brought back to between 0° and 360°: 450° is the same direction as 90°.
Worked examples
| Angle | Type | Complement | Supplement |
|---|---|---|---|
| 65° | acute | 25° | 115° |
| 90° | right | 0° | 90° |
| 135° | obtuse | none | 45° |
| 180° | straight | none | 0° |
| 250° | reflex | none | none |
Where you need them
- Triangles: the two acute angles of a right-angled triangle are complementary. Use the right triangle calculator to find them from two sides.
- Straight lines: two angles that sit side by side on a straight line are supplementary, so one is 180° minus the other.
- Turning: bearings, wheels and gears work with full turns, and the number missing to 360° tells you how much further to turn.
Degrees and radians side by side
| Degrees | Radians |
|---|---|
| 30° | π/6 ≈ 0.5236 |
| 45° | π/4 ≈ 0.7854 |
| 60° | π/3 ≈ 1.0472 |
| 90° | π/2 ≈ 1.5708 |
| 180° | π ≈ 3.1416 |
For the cosine or tangent of any of these, see the trigonometry calculator.
Frequently asked questions
What is the difference between complementary and supplementary angles?
Complementary angles add up to 90° and supplementary angles add up to 180°. The complement of 65° is 25° and its supplement is 115°.
Can an angle be negative or larger than 360°?
Yes. The calculator brings it back to between 0° and 360°, so 450° is treated as 90° and −30° as 330°.
What is a reflex angle?
An angle between 180° and 360°. A three-quarter turn of 270° is a reflex angle, and so is 200°.
How do I convert degrees to radians?
Multiply by π/180. 180° is π radians, 90° is π/2 and 60° is π/3. Choose *radians* above the field to enter or read angles in radians.