How to convert radians to degrees
Since 2π radians make a full 360° turn, deg = rad × 180 ÷ π. For example, π radians (≈ 3.14159265) = π × 180 ÷ π = 180°, and π ÷ 2 radians = 90°.
A radian is defined by the circle itself: it is the angle that sweeps out an arc as long as the radius. Since a full circumference is 2πr, exactly 2π radians fit around a circle, which pins the conversion factor at 180 ÷ π ≈ 57.2958 degrees per radian. That definition is why radians appear so often in calculus and physics — arc length is simply radius × angle when the angle is in radians. Radians are the natural unit for circular measure, which is why the arc length calculator insists on them.
How to use this calculator
Enter the angle in radians and read the equivalent in degrees, rounded to four decimals. To convert the other way, use the degrees to radians calculator.
- Enter a decimal, not a symbol. Type 3.14159265 rather than "π", and 1.5708 for π ÷ 2.
- Negative angles work and simply mean a clockwise rotation.
- Values above 2π are fine too — 7 radians converts to just over 401°, more than one full turn.
When you need degrees
Degrees are easier to read for everyday geometry, navigation and the law of cosines, while radians stay behind the scenes in the math. This converter bridges the two.
The most common reason to reach for this conversion is a mismatch between tools. Spreadsheet and programming functions such as sin, cos and atan almost always work in radians, while drawings, surveys, protractors and compass bearings are quoted in degrees. Converting an angle that was already in degrees is the classic error, and it shows up as an answer roughly 57 times too large — a useful signal that the units slipped somewhere.
Frequently asked questions
- What is π radians in degrees?
- π radians (about 3.14159265) equals 180°.
- What is the formula to convert radians to degrees?
- Multiply the radians by 180 and divide by π: deg = rad × 180 ÷ π.
- What is 1 radian in degrees?
- 1 radian is approximately 57.2958°.
- How many degrees are in 2π radians?
- 2π radians equal 360°, a full circle.
- How do I turn a decimal degree answer into degrees and minutes?
- Keep the whole number as degrees, then multiply the decimal part by 60 for minutes. So 57.2958° is 57° plus 0.2958 × 60 ≈ 17.7 minutes, or about 57° 17′ 45″.