Angle Converter (degrees, radians, gradians)
Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds — one value into every unit, with a common-angle reference table.
Common angles
| Degree | Radian | Gradian (gon) | Turn / revolution |
|---|---|---|---|
| 30 | 0.523599 | 33.3333 | 0.0833333 |
| 45 | 0.785398 | 50 | 0.125 |
| 60 | 1.0472 | 66.6667 | 0.166667 |
| 90 | 1.5708 | 100 | 0.25 |
| 180 | 3.14159 | 200 | 0.5 |
| 270 | 4.71239 | 300 | 0.75 |
| 360 | 6.28319 | 400 | 1 |
Converting angle units
An angle can be measured in several units, and unlike temperature they all share the same zero, so converting is a simple proportion. This tool works through radians internally and shows a value in every unit at once.
radians = degrees × π / 180 · degrees = radians × 180 / π
1 turn = 360° = 2π rad = 400 gon
The units, and where they're used
Degrees split a full circle into 360 parts and are the everyday unit. Radians are the mathematician's choice — a full circle is 2π — and are what trigonometry functions in most programming languages expect, so this converter is handy when your code returns the "wrong" number. Gradians (gon) split the circle into 400, making a right angle exactly 100, and appear in surveying.Arcminutes and arcseconds subdivide a degree into 60 and 3600 parts for astronomy and precise bearings.
Worked example
A right angle is 90°. In radians that's 90 × π/180 = π/2 ≈ 1.5708; in gradians it's exactly 100 gon; and it's a quarter turn, 0.25. This is the most common conversion in practice — remembering that 180° = π radians lets you do most of them in your head.
A note for programmers
Functions like Math.sin and Math.cos take radians, not degrees — feeding them degrees is a classic bug that produces plausible-looking but wrong results. Convert to radians first, or multiply your degrees by π/180 inline.