Radians to Degrees Converter
Convert radians to degrees in one step. Enter a value such as 1.5708, or type π/2, and get degrees with the formula, examples and a table of common angles below.
Degrees = Radians × 180 ÷ π
Radians to Degrees Formula
A half turn is π radians or 180 degrees, so to convert radians to degrees you multiply by 180 and divide by π. To convert degrees to radians, multiply by π and divide by 180. You can type the radians as a decimal or as a multiple of π, such as π/2, 3π/4 or 2pi.
About Radians and Degrees
A degree divides a full circle into 360 equal parts, a convention that goes back to ancient Babylon. A radian is defined by the circle itself: one radian is the angle at the center of a circle that cuts off an arc equal in length to the radius. That makes the full circle exactly 2π radians, about 6.283185. Degrees are common in everyday use and navigation, while radians are the natural unit in mathematics, physics and programming.
How to Convert Radians to Degrees
- Enter the angle in radians. Decimals such as 0.7854 work, and so do negative angles. You can also type π forms like π/4 or pi/6.
- The answer in degrees appears instantly, or press Convert Now. Gradians and full turns are shown as side values.
- Use Swap Units to convert degrees to radians, Copy Result to copy the answer, or Clear to start again.
By hand: multiply the radians by 57.29578 (which is 180 ÷ π). To check, π/2 radians × 57.29578 gives 90 degrees.
Practical Examples
- One radian: 1 rad × 180 ÷ π = 57.29578°.
- Right angle: π/2 ≈ 1.570796 rad = 90°.
- Full turn: 6.283185 rad = 359.999982°, essentially 360°.
- Small angle: 0.1 rad = 5.729578°.
- Negative angle (clockwise): −π/4 rad = -45°.
Radians to Degrees – Common Values
Quick reference for frequently used conversions
| Radians | Degrees | Gradians |
|---|---|---|
| 0 (0 rad) | 0° | 0 grad |
| π/12 (0.261799 rad) | 15° | 16.666667 grad |
| π/6 (0.523599 rad) | 30° | 33.333333 grad |
| π/4 (0.785398 rad) | 45° | 50 grad |
| π/3 (1.047198 rad) | 60° | 66.666667 grad |
| π/2 (1.570796 rad) | 90° | 100 grad |
| 2π/3 (2.094395 rad) | 120° | 133.333333 grad |
| 3π/4 (2.356194 rad) | 135° | 150 grad |
| 5π/6 (2.617994 rad) | 150° | 166.666667 grad |
| π (3.141593 rad) | 180° | 200 grad |
| 3π/2 (4.712389 rad) | 270° | 300 grad |
| 2π (6.283185 rad) | 360° | 400 grad |
| 0.5 rad | 28.64789° | 31.830989 grad |
| 1 rad | 57.29578° | 63.661977 grad |
| 2 rad | 114.591559° | 127.323954 grad |
| 3 rad | 171.887339° | 190.985932 grad |
| 5 rad | 286.478898° | 318.309886 grad |
| 10 rad | 572.957795° | 636.619772 grad |
Where and Why This Conversion Is Used
Most calculators, programming languages and physics formulas work in radians, while drawings, maps and everyday descriptions use degrees. Converting between them keeps results consistent.
- Mathematics and trigonometry: sine, cosine and tangent functions on many calculators and in code expect radians.
- Physics and engineering: angular velocity, oscillations and rotation are expressed in radians.
- Programming and graphics: game engines, animation and CSS rotate transforms use a mix of radians and degrees.
- Navigation and surveying: bearings and slopes are read in degrees.
- Robotics and CAD: joint angles and tolerances move between the two units.
For other everyday conversions see the CM to Inches Converter and the Meters to Yards Converter.