Degrees to Radians Converter
Instantly convert between degrees and radians. Visualize angles on a unit circle, explore common angles, and understand the π relationship.
Degrees → Radians
45°
Formula: radians = degrees × π/180
Multiply degrees by π (≈3.14159) and divide by 180 to get radians.
Radians → Degrees
0.785 rad
Formula: degrees = radians × 180/π
Multiply radians by 180 and divide by π. Common angles: π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°.
Angle conversion & visualization
Converter
Common Angles
Formula
Current conversion
45° = π/4 rad
0.785 rad
Degrees
45°
Radians (decimal)
0.785
Radians (π‑fraction)
π/4
sin(θ)
0.707
Common Angles (degrees & radians)
| Degrees | Radians (exact) | Radians (decimal) |
|---|
Radian values of common angles
Conversion formulas
Degrees → Radians
rad = deg × (π / 180)
Radians → Degrees
deg = rad × (180 / π)
Why π?
A full circle = 360° = 2π radians. Therefore 180° = π rad, 90° = π/2, 60° = π/3, 45° = π/4, 30° = π/6.
Use the slider or input any angle (positive or negative) to see its equivalent in both units.
Quick reference
180° = π rad
90° = π/2 rad
60° = π/3 rad
45° = π/4 rad
30° = π/6 rad
360° = 2π rad
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