Radians to Degrees Converter Online — Free
Runs 100% in your browser — your files never leave your device.
π radians is 180°, but converting anything less tidy by hand invites rounding errors. Type a value in either field and the other converts live: degrees to radians or radians to degrees. Handy for physics homework, CAD exports, and graphics code that disagrees about angle units.
How it works
- 1
Type in either field
Degrees or radians — the field you focus becomes the source.
- 2
Read the other unit live
The conversion updates on every keystroke, in both directions.
- 3
Use it in your work
180° = π radians; everything else follows from that ratio.
About this tool
Why two angle units exist
Degrees divide the circle into 360 historical parts — intuitive for humans. Radians measure the arc length directly — one radian is the angle where the arc equals the radius — and are the natural unit for mathematics and every programming library. Both describe the same circle.
The conversion and the famous constant
π radians equal 180 degrees; the tool applies that exact relationship both directions. The numbers worth memorizing: 180° = π, 90° = π/2, 57.3° ≈ 1 radian, and a full circle is 360° = 2π.
The bug this tool prevents
Passing degrees to a function that expects radians produces answers wrong by a factor of 57.3 — the classic trigonometry bug in every language, because most math libraries silently assume radians. Convert first, compute second.
Frequently asked questions
What is a radian, physically?
The angle at which a circle's arc length equals its radius — about 57.3 degrees. It is the natural unit because arc length then equals radius times angle, with no conversion constant.
Why do programming libraries use radians?
Calculus and the underlying math simplify when angles are in radians — derivatives and series lose their conversion constants. Libraries follow the math.
Is the conversion exact?
The relationship is exactly π = 180°; the tool computes with full precision, so the conversion carries no rounding beyond the display.