Degrees to Radians Converter
Convert degrees to radians instantly. Free angle converter for mathematics and physics.
Formula
radians = degrees Γ PI / 180
Common Conversions
How to Convert Degrees to Radians
Multiply degrees by Ο/180. So 90Β° Γ Ο/180 = Ο/2 β 1.571 radians. Radians are the SI unit for angles, mathematically natural because the radian definition makes calculus and trigonometry cleaner. Full circle = 360Β° = 2Ο radians = 6.283 radians.
Used in mathematics, physics, computer graphics, and game programming. Trigonometric functions (sin, cos, tan) in most programming languages require radians, not degrees. So if your input is in degrees, multiply by Ο/180 first. Common conversion in graphics programming: rotating a sprite '45Β°' means rotating it Ο/4 β 0.785 radians.
Common Degrees to Radians
| Degrees | Radians |
|---|---|
| 0Β° | 0 |
| 30Β° | Ο/6 β 0.524 |
| 45Β° | Ο/4 β 0.785 |
| 60Β° | Ο/3 β 1.047 |
| 90Β° | Ο/2 β 1.571 |
| 180Β° | Ο β 3.142 |
| 270Β° | 3Ο/2 β 4.712 |
| 360Β° | 2Ο β 6.283 |
Frequently Asked Questions
Why use radians instead of degrees?
Mathematical elegance. The derivative of sin(x) is cos(x) only when x is in radians (in degrees, you get extra factors of Ο/180 cluttering the math). Calculus, physics, and engineering use radians for cleaner equations. Geometry textbooks often use degrees for accessibility.
How do I convert in code?
Most languages: radians = degrees Γ Math.PI / 180. So 90 degrees in JavaScript: 90 * Math.PI / 180 = 1.5708. The reverse: degrees = radians Γ 180 / Math.PI.
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