Angle Converter

Convert angles between degrees, radians, turns, gradians, arcminutes and arcseconds.

Degree → Radian

0.017453 rad

1 degree = 0.017453 radians

1 degree = 0.0174532925 radians (exact definition; display rounded)

  • Radian (rad)0.017453
  • Degree (°)1
  • Gradian (gon)1.111111
  • Arcminute (′)60
  • Arcsecond (″)3600
  • Turn (tr)0.002778
  • Milliradian (mrad)17.453293

Understanding angle units

A complete turn is 360 degrees or 2π radians. An arcminute is 1/60 degree and an arcsecond 1/3600 degree. Negative angles remain signed; the converter does not wrap them into a single turn.

Conversion method

For linear units, multiply the input by its factor to the base unit, then divide by the target factor. The table lists definitions where exact and approximate constants where applicable.

Angle units in rad
Unit1 unit in base unitsDefinition
Radian (rad)1Exact definition; display may be rounded
Degree (°)0.0174532925Exact definition; display may be rounded
Gradian (gon)0.0157079633Exact definition; display may be rounded
Arcminute (′)0.0002908882Exact definition; display may be rounded
Arcsecond (″)0.0000048481Exact definition; display may be rounded
Turn (tr)6.2831853072Exact definition; display may be rounded
Milliradian (mrad)0.001Exact definition; display may be rounded

Worked example and common conversions

10 ° = 0.1745329252 rad. Keep full precision during conversion, then round the final result to the precision of your measurement.

Common angle conversions
FromTo
10 °0.1745329252 rad
10 rad572.9577951308 °
10 tr3,600 °
10 gon9 °

Frequently asked questions

Why might a angle conversion differ from another tool?

A complete turn is 360 degrees or 2π radians. An arcminute is 1/60 degree and an arcsecond 1/3600 degree. Negative angles remain signed; the converter does not wrap them into a single turn.

Last updated . Results are estimates for informational purposes only.