Unit Conversion

Convert numbers between two units quickly and precisely

Angle Converter

Unit Conversion

Convert angle units: degrees, radians, and gon

Angles are usually stated in degrees (°) in everyday life, but in radians (rad) – the SI unit for plane angles – in mathematics and physics. In surveying and geodesy, gon (grad) is sometimes used, and for very precise astronomical and geographic figures, arcminutes and arcseconds.

Key conversion factors:

  • 1 full turn = 360° = 2π rad ≈ 6.2832 radian
  • 1 radian (rad) ≈ 57.296°
  • 1 gon (gon) = 0.9° – a full turn has 400 gon
  • 1° = 60 arcminutes (') = 3,600 arcseconds (")

Applications:

  • Math & physics: converting between degrees and radians for trigonometric functions
  • Surveying & geodesy: angle figures in gon for theodolite measurements
  • Astronomy & navigation: precise position data in degrees, arcminutes, and arcseconds

The angle converter supports mathematical calculations, surveying tasks, and navigation figures.

Frequently asked questions about converting angles

To convert degrees to radians, multiply the degree value by π/180 (≈ 0.01745). Conversely, multiply radians by 180/π (≈ 57.296) to get degrees. A full turn equals 360° or 2π radians.

The gon (also called grad) divides a full turn into 400 instead of 360 parts. 1 gon equals 0.9°. It's mainly used in surveying and geodesy, because it makes right angles (100 gon) easier to handle.

1 degree (°) equals 60 arcminutes ('), and 1 arcminute equals 60 arcseconds ("). This fine subdivision is mainly used in astronomy and navigation for precise position data.