Formulas
- Radians = degrees × π ÷ 180
- Degrees = radians × 180 ÷ π
A full turn is 360° = 2π rad = 400 gradians.
Examples
- 45° = 0.7854 rad = π/4. Its sine and cosine are both 0.7071.
- 1 rad ≈ 57.2958°.
- 180° = π rad and 90° = π/2 rad.
Common angles
- 30° = π/6: sin 0.5, cos 0.866
- 60° = π/3: sin 0.866, cos 0.5
- 90° = π/2: sin 1, cos 0, tangent undefined
For triangles, use the triangle solver; for any expression, the scientific calculator.
Frequently asked questions
Why use radians?
In calculus and physics formulas the angle must be in radians. One radian is the angle whose arc is as long as the radius.
What is 30.5° in degrees, minutes and seconds?
30° 30′ 0″, because 0.5° × 60 = 30 minutes.
Why is the tangent of 90° undefined?
Because tan = sin ÷ cos and cos 90° = 0.
See also
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