Angle Conversions

Angle conversions are used in geometry, navigation, astronomy, surveying, physics, and engineering. Degrees (°) are the most familiar unit for everyday use, while radians are required in mathematical formulas — particularly trigonometry, calculus, and physics. Gradians are used in some European surveying traditions. Arcseconds describe the extremely small angular separations measured in astronomy and precision geodesy.

  • ✓Converting degrees to radians for trigonometry, calculus, and physics formulas
  • ✓Converting radians to degrees for navigation headings and compass bearings
  • ✓Converting degrees to gradians for civil engineering and European surveying
  • ✓Converting degrees to arcminutes and arcseconds for GPS and astronomical coordinates

Most Popular Angle Conversions

Degrees → RadiansRadians → DegreesDegrees → GradiansGradians → DegreesDegrees → ArcminutesArcminutes → Arcseconds

All Angle Converters

Convert from Degrees (°)

Degrees → RadiansDegrees → GradiansDegrees → ArcminutesDegrees → ArcsecondsDegrees → Turns

Convert from Radians (rad)

Radians → DegreesRadians → GradiansRadians → ArcminutesRadians → ArcsecondsRadians → Turns

Convert from Gradians (grad)

Gradians → DegreesGradians → RadiansGradians → ArcminutesGradians → ArcsecondsGradians → Turns

Convert from Arcminutes (′)

Arcminutes → DegreesArcminutes → RadiansArcminutes → GradiansArcminutes → ArcsecondsArcminutes → Turns

Convert from Arcseconds (″)

Arcseconds → DegreesArcseconds → RadiansArcseconds → GradiansArcseconds → ArcminutesArcseconds → Turns

Convert from Turns (rev)

Turns → DegreesTurns → RadiansTurns → GradiansTurns → ArcminutesTurns → Arcseconds

Frequently Asked Questions — Angle

How do you convert degrees to radians?
Multiply degrees by π/180 (approximately 0.017453). Key values: 90° = π/2 ≈ 1.5708 rad, 180° = π ≈ 3.1416 rad, 360° = 2π ≈ 6.2832 rad. To convert radians to degrees, multiply by 180/π ≈ 57.296.
Why are radians used in mathematics instead of degrees?
Radians simplify calculus formulas — for example, the derivative of sin(x) is cos(x) only when x is in radians. Radians also arise naturally from the geometry of circles: an angle of 1 radian subtends an arc equal to the radius. In physics and engineering formulas, radians are almost always assumed.
What are arcminutes and arcseconds used for?
Arcminutes (1/60 of a degree) and arcseconds (1/3,600 of a degree) express very small angles. Geographic coordinates use them — 40° 42′ 46″ N means 40 degrees, 42 arcminutes, 46 arcseconds north latitude. In astronomy, arcseconds measure star positions and planet diameters.

Related Conversion Categories

Length Conversions

Convert between units of length and distance including metric and imperial measurements.

Speed Conversions

Convert between units of speed and velocity for travel, physics, and athletics.

Frequency Conversions

Convert between units of frequency for electronics, physics, and audio applications.

Want this converter on your website? Get the free embed code →