Angle converter
Type an angle and pick its unit: degrees, radians, and gradians update as you type, with the exact value in terms of pi whenever one exists.
| Degrees | Radians | Gradians |
|---|---|---|
| 0° | 0 | 0 gon |
| 30° | π/6 | 33.33 gon |
| 45° | π/4 | 50 gon |
| 60° | π/3 | 66.67 gon |
| 90° | π/2 | 100 gon |
| 120° | 2π/3 | 133.33 gon |
| 135° | 3π/4 | 150 gon |
| 180° | π | 200 gon |
| 270° | 3π/2 | 300 gon |
| 360° | 2π | 400 gon |
Degrees, radians, and gradians: when each is used
Degrees (a full turn = 360°) are the everyday unit — the one you see in school geometry, on protractors, and in weather reports about wind direction. Radians (a full turn = 2π) are the standard in math and programming: the trigonometric functions in almost every language, JavaScript included, only work in radians. Gradians, or "gon" (a full turn = 400), survive mainly in surveying and in the total stations used by land surveyors, because they turn a right angle into a convenient 100.
Why radians involve pi
One radian is the angle subtended by an arc exactly as long as the circle's radius: a full turn takes 2π radius-lengths of arc, so 360° = 2π rad. From there come the conversion formulas: radians = degrees × π ÷ 180 and gradians = degrees × 10 ÷ 9. When the angle in degrees is a whole number, the tool reduces the fraction and shows the exact value (for example 45° = π/4) — far more useful than the decimal 0.785398 when you're working by hand.