Angle Converter
Convert between degrees and radians.
How to use the Angle Converter
- Type the angle into the Value field. The page opens on degrees to radians.
- Choose Degrees or Radians in the From list, and the other one in the To list.
- The converted angle appears under the fields as you type, rounded to six decimal places.
The angles worth memorising
A full turn is 360 degrees or 2 pi radians, which makes a right angle pi over 2. Trigonometry reuses the same handful of angles, and the fractions of pi below are quicker to recognise than their decimals.
| Degrees | Radians | Decimal |
|---|---|---|
| 30 | pi/6 | 0.5236 |
| 45 | pi/4 | 0.7854 |
| 60 | pi/3 | 1.0472 |
| 90 | pi/2 | 1.5708 |
| 180 | pi | 3.1416 |
| 360 | 2 pi | 6.2832 |
Where the last decimal place comes from
The conversion uses 57.2958 degrees per radian, cut to four decimal places, while the exact figure runs 57.29577951 onwards. The gap is under one part in a million, so results hold to about six significant figures: fine for geometry and graphics, not for surveying.
Frequently asked questions
How many radians is 180 degrees?
Pi radians, about 3.14159.
Why do I need radians?
Trigonometric functions in most programming languages take radians, not degrees, which is a common source of bugs in graphics and animation code.
How many degrees is one radian?
About 57.2958 degrees, which is 180 divided by pi. It is the angle at which the arc along the circle matches the radius in length.
Can I enter a negative angle?
Yes. The sign carries through, so -90 degrees converts to -1.570796 radians, the same size as +90 with a minus in front.
Does it handle gradians or arcminutes?
No. The two lists hold degrees and radians only. Divide arcminutes by 60 for decimal degrees first, then convert that.