Use our free angle converter to quickly convert between degrees and radians. This simple angle calculator is perfect for students, teachers, engineers, and anyone who works with trigonometry, calculus, or geometry. Learn the degree to radian formula, see worked examples, and use our conversion tables for fast reference.
Degrees divide a full circle into 360 parts. Radians measure angles using arc length, where a full circle equals 2π radians. Both units are widely used, but radians are preferred in mathematics and physics because they simplify formulas.
| Degrees | Radians (fraction) | Radians (decimal) |
|---|---|---|
| 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 |
Converting between degrees and radians is essential because different fields use different units:
Most scientific calculators and computer functions use radians by default, so understanding the degree–radian conversion is critical.
Example 1: Convert 120° into radians.
rad = 120 × π / 180 = 2π/3 ≈ 2.094 rad.
Example 2: Convert π/4 radians into degrees.
deg = (π/4) × 180 / π = 45°.
The formula is: radians = degrees × π / 180.
Multiply by 180/π. For example, π/3 rad × 180/π = 60°.
Radians simplify trigonometric formulas and calculus because they directly relate angle and arc length.
180° equals π radians (≈ 3.1416).
π/2 radians = 90°.