About Angle Converter

Angles are fundamental measurements in mathematics, engineering, and navigation. The degree (°) is the most common unit of angle measurement, equal to 1/360 of a full circle.

Common Angle Units

  • Degree (°): The most common unit of angle measurement, equal to 1/360 of a full circle. Used in everyday applications and most engineering contexts.
  • Radian (rad): The SI unit of angle, defined as the angle subtended by an arc equal in length to the radius. Essential in calculus and advanced mathematics.
  • Gradian (grad): A unit of angle equal to 1/400 of a full circle, used in surveying and some engineering applications.
  • Minute of arc (arcmin): One sixtieth of a degree, commonly used in astronomy and navigation for precise measurements.
  • Second of arc (arcsec): One sixtieth of a minute of arc, used for very precise angular measurements.

Applications

Angle conversions are essential in:

  • Navigation: Compass bearings, GPS coordinates, and marine navigation
  • Astronomy: Celestial observations and telescope positioning
  • Engineering: Mechanical design, structural analysis, and rotation calculations
  • Mathematics: Trigonometry, calculus, and geometric calculations
  • Surveying: Land measurement and mapping applications

Conversion Examples

  • 90° = π/2 radians (Right angle conversion)
  • 180° = π radians (Straight angle conversion)
  • 360° = 2π radians (Full circle conversion)
  • 1° = 60 arcmin (Degree to minute of arc)

Use our angle converter to quickly convert between these and other angle units for your calculations and applications.

Common Conversions

90 Degrees
→
1.5708 Radians
Common right angle conversion
180 Degrees
→
3.14159 Radians
Straight angle to radians
360 Degrees
→
6.28319 Radians
Full circle conversion

Unit Definitions

Degree (°)

The most common unit of angle measurement, equal to 1/360 of a full circle.

Formula: 1° = π/180 radians

Radian (rad)

The SI unit of angle, defined as the angle subtended by an arc equal in length to the radius.

Formula: 1 rad = 180°/π

Gradian (grad)

A unit of angle equal to 1/400 of a full circle, used in surveying and some engineering applications.

Formula: 1 grad = 0.9°

Minute of arc (arcmin)

One sixtieth of a degree, commonly used in astronomy and navigation.

Formula: 1 arcmin = 1/60°

Second of arc (arcsec)

One sixtieth of a minute of arc, used for precise angular measurements.

Formula: 1 arcsec = 1/3600°