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)
  • = 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°