Angle Converter
Convert angles between degrees, radians, gradians, arcminutes, arcseconds, full turns, and NATO mils. Trigonometry functions in almost every programming language take radians while designers and CAD tools work in degrees, and that mismatch is the usual reason to be here.
Converters
Private by default
This tool runs entirely in your browser. Your data is never uploaded to a server.
How it works
How the angle units divide a circle
1 turn = 360° = 2π rad = 400 gon = 6,400 mils
Every angle unit is just a different number of slices per full turn. Degrees give 360, radians give 2π (an arc as long as the radius), gradians give 400, and NATO mils give 6,400 for artillery arithmetic.
- Arcminutes and arcseconds subdivide the degree by 60 and 3,600 — the same sexagesimal split as hours and minutes, used for coordinates and telescopes.
- CSS accepts deg, rad, grad, and turn directly, so `transform: rotate(0.25turn)` and `rotate(90deg)` are identical.
- The radian is dimensionless by definition: it is arc length divided by radius, which is why it has no conversion factor in physics formulas.
- NATO mils approximate a milliradian: 6,400 per turn rather than the exact 6,283.19, chosen because it divides evenly.
For reference
The angles you look up most
| Degrees | Radians | Exact | Gradians |
|---|---|---|---|
| 30° | 0.5236 | π/6 | 33.33 |
| 45° | 0.7854 | π/4 | 50 |
| 60° | 1.0472 | π/3 | 66.67 |
| 90° | 1.5708 | π/2 | 100 |
| 180° | 3.1416 | π | 200 |
| 360° | 6.2832 | 2π | 400 |
CSS gradients measure from the top and run clockwise, so `180deg` points down the element, not left.
How to use
4 clear steps.
Enter the angle value.
Select the unit it is in (degrees, radians, gradians…).
Select the unit you need and read the converted angle.
Use the table of common angles to check your result at a glance.
Good to know
Frequently asked questions
- How do I convert degrees to radians?
- Multiply by π/180. So 180° is π radians, 90° is π/2 ≈ 1.5708, and 1° is about 0.01745 radians. To go the other way, multiply radians by 180/π.
- Why do programming languages use radians?
- Math.sin, cos, and tan take radians in JavaScript, Python, C, and most others, because the calculus behind them is only clean in radians. Convert your degrees first or the result will be silently wrong.
- What is a gradian?
- A gradian (or gon) divides a right angle into 100 parts instead of 90, so a full turn is 400 gon. It survives in surveying and on some calculators, marked GRAD.