Angle conversion formulas
Degrees to radians: rad = deg × π / 180
Radians to degrees: deg = rad × 180 / π
Degrees to gradians: grad = deg × 10 / 9
Gradians to degrees: deg = grad × 0.9
Degrees to turns: turn = deg / 360
DMS to decimal degrees: deg = D + M/60 + S/3600
When to use each unit
- Degrees (°): human-friendly, geometry, navigation.
- Radians (rad): calculus, trigonometric functions in programming and math libraries.
- Gradians (gons): surveying and some European engineering contexts (right angle = 100 gons).
- Turns: animations, rotations in graphics, helpful when thinking in full revolutions.
- DMS: location, bearings, legacy measurements.
FAQ
1. Why does my calculator need radians?
Most math functions (sin, cos, tan) are defined in radians, so scientific calculators and programming languages expect radians by default.
2. Are gradians the same as gons?
Yes. “Grad”, “gon”, and “grade” are used interchangeably for the 400-based angle system.
3. How do I format negative angles in DMS?
Convert the absolute value to DMS, then apply the sign back. The tool above assumes positive angles for DMS, which is typical in surveying tables.
Full original guide (expanded)
Add here extra examples: converting bearings, comparing survey readings, converting robot joint rotations or CSS transforms to degrees.