Real Online Protractor
Mathematical Angle Converter

Angle Unit Converter

Real-time conversion between Degrees (°), Radians (rad), Gradians (gon), DMS, and Turns.

Interactive Angle Converter

Convert instantly between Degrees, Radians, Gradians, DMS, and Turns with dynamic ray visualizer.

Live Two-Way Sync
°
rad
gon
rev
DMS:45° 0' 0"
Acute Angle (45.0°)
Quadrant I (0° - 90°)

Degrees to Radians Formula

To convert degrees (d) to radians (r), multiply degrees by π and divide by 180:

radians = degrees × (π / 180)

Radians to Degrees Formula

To convert radians (r) to degrees (d), multiply radians by 180 and divide by π:

degrees = radians × (180 / π)

Degrees to Gradians Formula

Gradians (or gon) divide a full circle into 400 parts. 90° right angle equals 100 gon:

gradians = degrees × (400 / 360) = degrees × (10 / 9)

Degrees, Minutes, Seconds (DMS)

Each degree has 60 minutes ('), and each minute has 60 seconds (''):

decimal degrees = D + (M / 60) + (S / 3600)