Radians to Degrees Converter
Convert radians to degrees easily. Free angle converter for maths and engineering.
Formula
degrees = radians Γ 180 / PI
Common Conversions
How to Convert Radians to Degrees
Multiply radians by 180/Ο. So Ο/2 radians Γ 180/Ο = 90Β°. Ο radians = 180Β°. 2Ο radians = 360Β° (full circle). The conversion factor is approximately 57.296 - so 1 radian β 57.296Β°.
Used in: programming (when input is radians but display needs degrees), physics, engineering. A scientific calculator typically has both modes; check which one is active. Common conversions: Ο/6 = 30Β°, Ο/4 = 45Β°, Ο/3 = 60Β°, Ο/2 = 90Β°, Ο = 180Β°, 2Ο = 360Β°.
Common Radians to Degrees
| Radians | Degrees |
|---|---|
| 0 | 0Β° |
| Ο/6 β 0.524 | 30Β° |
| Ο/4 β 0.785 | 45Β° |
| Ο/3 β 1.047 | 60Β° |
| Ο/2 β 1.571 | 90Β° |
| Ο β 3.142 | 180Β° |
| 3Ο/2 β 4.712 | 270Β° |
| 2Ο β 6.283 | 360Β° |
Frequently Asked Questions
Should I memorise these conversions?
Useful values: Ο/6 = 30Β°, Ο/4 = 45Β°, Ο/3 = 60Β°, Ο/2 = 90Β°, Ο = 180Β°. These come up constantly in trigonometry. The exact decimal values aren't important to memorise - the multiples of Ο are.
Why use radians at all?
Mathematical naturalness. Calculus formulas are simpler in radians. Trigonometric identities are cleaner. Engineering and scientific applications use radians by default. Geometry textbooks often use degrees for accessibility, but advanced math/science uses radians.
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