Angle Calculator

Convert between angle units and calculate angle relationships

About Angle Measurements

Angles can be measured in different units, each with specific applications in mathematics, physics, and engineering.

Angle Units

1 full rotation = 360° = 2π rad = 400 gon = 1 turn
  • Degrees (°): 1/360 of a full rotation
  • Radians (rad): Arc length equal to radius
  • Gradians (gon): 1/400 of a full rotation
  • Turns: Complete rotations

Conversion Formulas

Degrees to Radians: rad = deg × π/180
Radians to Degrees: deg = rad × 180/π
Degrees to Gradians: gon = deg × 10/9
Gradians to Degrees: deg = gon × 9/10

Angle Types

Acute
0° < θ < 90°
Right
θ = 90°
Obtuse
90° < θ < 180°
Straight
θ = 180°
Reflex
180° < θ < 360°
Full
θ = 360°

Angle Relationships

  • Complementary: Two angles that sum to 90°
  • Supplementary: Two angles that sum to 180°
  • Vertical: Opposite angles formed by intersecting lines
  • Adjacent: Angles that share a common vertex and side

Common Angles

Degrees Radians Description
30°π/6One-twelfth turn
45°π/4Eighth turn
60°π/3Sixth turn
90°π/2Quarter turn
180°πHalf turn

Applications

  • Navigation: Compass bearings and headings
  • Engineering: Mechanical design and rotations
  • Astronomy: Celestial coordinates
  • Computer Graphics: Rotations and transformations
  • Physics: Pendulum motion and waves