Angle Converter
Convert degrees, radians, gradians, arcminutes and more.
About Angle Units
Degrees (°) divide a full circle into 360 parts — a convention from ancient Babylonian astronomy. Radians (rad) are the SI unit; a full circle = 2π rad ≈ 6.2832 rad. Radians are preferred in mathematics and physics because they simplify calculus. Gradians (grad) divide a right angle into 100 parts, used in surveying.
Conversion Formulas
- Degrees → Radians:
° × π/180 - Radians → Degrees:
rad × 180/π - Degrees → Gradians:
° × 10/9 - 1 turn = 360° = 2π rad = 400 grad
Key Reference Angles
- Right angle: 90° = π/2 rad = 100 grad
- Straight angle: 180° = π rad
- Full circle: 360° = 2π rad
- 30° = π/6 rad (sin = 0.5)
- 45° = π/4 rad (sin = cos = 1/√2)
- 60° = π/3 rad (sin = √3/2)