Convert degrees to radians (and back)
Angles show up in degrees, radians, gradians, and turns depending on the field — here is how to move between them and read DMS.
Tools used in this guide
The job
Math libraries take radians, protractors read degrees, surveying sometimes uses gradians, and revolutions per minute count in turns. One value, four spellings.
Convert
Type the value, pick the unit it is written in, and read the same angle in all four units plus degrees-minutes-seconds. The conversion is exact — 180° is π, a full circle is one turn.
- 360° = 2π rad = 400 gon = 1 turn; 90° = π/2 ≈ 1.5708 rad.
- DMS reads the degrees field: 45.5° is 45°30′0″.
Worked example
A shader takes radians and you measured 30° — the tool reports 0.5236 rad. Setting latitude 35.6812° reads as 35°40′52″ in DMS.
Where it stops
Inputs up to ±1e15 are accepted — larger values lose meaning as floats anyway. Radians in the output are not wrapped to a 0–2π range, and there is no symbol input like "π/4"; enter the decimal.