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)