Angle Converter
Convert plane angles among degrees, radians, gradians, and turns. The browser uses Math.PI. A percent grade is a slope ratio, not a unit on this list.
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How to convert degrees to radians
- Enter the angle. The default is 1 degree.
- Keep From as Degrees and To as Radians, or choose gradians or turns.
- Read the radian result. A full circle is 2π rad, 360 deg, 400 gon, or 1 turn.
- Swap units to go from radians back to degrees. The conversion stays in this tab.
Turn
Plane angle
| Turn | 1 turn = 2π rad |
|---|---|
| Degree | 360 deg = 1 turn |
| Radian | Canonical unit on this page (Math.PI) |
| Gradian | 400 gon = 1 turn |
| Degree to radian | 1 deg = π/180 rad |
| Gradian to radian | 1 gon = π/200 rad |
What this angle converter does
A plane angle measures how far a ray has rotated. This page converts degrees, radians, gradians (also called gon), and turns. One full rotation is 1 turn = 360 deg = 400 gon = 2π rad. The radian is the SI unit. The engine stores angles as radians using the browser value of Math.PI, so π is not a hand-typed 3.14.
Percent slope is rise over run times 100. That is not a degree or a radian. Convert a grade on the slope calculator. A dedicated grade page is the grade-slope job, not this converter. The unit converter lists other dimensions.
How degrees, radians, and gradians relate
To radians: degrees × π/180, gradians × π/200, turns × 2π. From radians, divide by those same factors. 180 deg equals π rad. 100 gon equals 90 deg, which is a right angle in the gradian system used on some surveying instruments. A turn is a full revolution, handy for rotary tables and winding counts.
Radians, gradians, and slope
Trigonometry in calculus almost always wants radians. CAD and navigation often want degrees. Gradians split a right angle into 100. Do not paste a roof pitch percent into Degrees and expect a correct radian. Use the slope calculator for m = rise/run, then convert that ratio to an angle only if you apply arctangent yourself. This page does not compute arctangent.
When to convert an angle here
Change a heading from degrees to radians for a formula, convert a mill turn into degrees, or move a gon reading into degrees. Keep map bearings, magnetic declination, and percent grade on their own tools.
What this page does not do
It does not wrap angles into 0-360 unless you do that after the result. It does not convert slope percent. It does not solve triangles. Math.PI is a floating-point approximation. Nothing is uploaded.