Degrees and Radians Converter
Convert any angle between degrees and radians instantly. The calculator shows both the decimal value and the exact form (in terms of π) where applicable — handy for trigonometry, calculus and programming.
Convert an angle
Enter a value and direction, then press Convert.
Conversion formulas
Degrees → Radians: rad = deg × π / 180
Radians → Degrees: deg = rad × 180 / π
Common conversions
| Degrees | Radians (exact) | Radians (approx) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
| 270° | 3π/2 | 4.7124 |
| 360° | 2π | 6.2832 |
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Frequently asked questions
A radian is the angle subtended at the centre of a circle by an arc whose length equals the circle's radius. A full circle is 2π radians, so 1 radian = 180/π ≈ 57.2958°.
Radians are the natural unit for angles in calculus and higher mathematics. Derivatives and series such as d/dx sin(x) = cos(x) and the Taylor series for sin and cos only hold cleanly when x is measured in radians. Using degrees requires extra conversion factors in every formula.