Angle Converter

Convert between degrees, radians, gradians, and other angle units

Common Angle Conversions

Degree to Radian
1° = 0.0175 rad
Radian to Degree
1 rad = 57.3°
Right Angle
90° = π/2 rad
Straight Angle
180° = π rad
Full Circle
360° = 1 turn
Degree to Arcminute
1° = 60′

Angles in Real Life

Clock Hands

Each hour mark = 30° (π/6 rad)

Right Angle

Corner of square = 90° (π/2 rad)

Compass Bearing

North = 0°, East = 90°, South = 180°

Triangle Sum

All angles sum to 180° (π rad)

About Angle Measurement

An angle is the space between two intersecting lines or the amount of rotation between two directions. Angles are fundamental in mathematics, physics, engineering, and navigation. The most common units are degrees and radians, each with specific applications and advantages.

Common Applications

  • • Navigation and GPS systems
  • • Engineering and construction
  • • Astronomy and celestial mechanics
  • • Computer graphics and game development
  • • Trigonometry and mathematics
  • • Robotics and automation

Angle Types

  • • Acute: less than 90°
  • • Right: exactly 90°
  • • Obtuse: between 90° and 180°
  • • Straight: exactly 180°
  • • Reflex: greater than 180°
  • • Full turn: 360° (complete circle)

Degrees vs Radians

Degrees divide a circle into 360 equal parts and are intuitive for everyday use.Radians are based on the radius of a circle (2π radians = 360°) and are preferred in mathematics and physics because they simplify many formulas. 1 radian ≈ 57.3°.

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