Formula. degrees = radians × 180 ÷ π.
Relationship. π radians = 180°.
Worked example. 3.141593 rad = 180 °.
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Radians to Degrees Converter.
Convert radians to degrees instantly with this free calculator. π radians = 180°.
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Copied ✓ Reference Table
| ° | rad | grad | ' | " | turn | mrad |
|---|---|---|---|---|---|---|
| 0.1799999998 | 0.0031415927 | 0.1999999998 | 10.8 | 647.999999 | 0.0005 | 3.141593 |
| 1.8 | 0.0314159265 | 2 | 108 | 6480 | 0.005 | 31.415927 |
| 18 | 0.314159265 | 20 | 1080 | 64799.9999 | 0.0499999999 | 314.159265 |
| 180 | 3.141593 | 200 | 10800 | 647999.9993 | 0.4999999994 | 3141.5927 |
| 1800 | 31.415927 | 2000 | 107999.9999 | 6479999.9926 | 5 | 31415.9265 |
| 18000 | 314.159265 | 20000 | 1079999.9988 | 64799999.926 | 50 | 314159.265 |
| 179999.9998 | 3141.5927 | 199999.9998 | 10799999.9877 | 647999999.2596 | 499.999999 | 3141592.65 |
How to convert radians to degrees
radians to degrees conversion table
| rad | ° |
|---|---|
| 0.1 | 5.729578 |
| 0.25 | 14.323945 |
| 0.5 | 28.64789 |
| 0.7853982 | 45.000002 |
| 1 | 57.29578 |
| 1.2 | 68.754935 |
| 1.5 | 85.943669 |
| 1.570796 | 89.999998 |
| 2 | 114.591559 |
| 2.356194 | 135.000001 |
| 2.5 | 143.239449 |
| 3 | 171.887339 |
| 3.141593 | 180.000003 |
| 3.5 | 200.535228 |
| 4 | 229.183118 |
| 4.18879 | 240 |
| 4.5 | 257.831008 |
| 4.712389 | 270.000001 |
| 5 | 286.478898 |
| 5.5 | 315.126787 |
| 6 | 343.774677 |
| 6.283185 | 360 |
| 7 | 401.070457 |
| 8 | 458.366236 |
| 10 | 572.957795 |
FAQ
Frequently Asked Questions
How do I convert radians to degrees?
Multiply by 180/π (about 57.29578). For example, π/2 ≈ 1.5708 rad × 57.29578 ≈ 90°.
How many degrees is 1 radian?
About 57.29578°. One radian is the angle at which the arc length equals the radius, which is why it is not a round number of degrees.
How many degrees is 2π radians?
Exactly 360° — a full circle. Half that, π radians, is 180°, and π/4 ≈ 0.7854 rad is 45°.
Why are radians the "natural" unit for angles?
Because the mathematics comes out cleaner: the derivative of sin(x) is cos(x) only when x is in radians, and series expansions like sin(x) ≈ x for small x hold only in radians. Degrees are a human convention; radians fall out of the geometry itself.
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