Degrees to Radians Converter
Convert degrees to radians and other angular measurements
Convert Degrees and Radians
Range: -3600° to 3600°
1 radian ≈ 57.2958°
Conversion Results
Conversion Formulas
Degrees to Radians: radians = degrees × (π/180°)
Radians to Degrees: degrees = radians × (180°/π)
*π ≈ 3.14159265359 | 1 radian ≈ 57.2958°
Example Calculations
Example 1: Right Angle
90° × (π/180°) = π/2 rad ≈ 1.5708 rad
This is a quarter of a full circle
Example 2: Straight Angle
180° × (π/180°) = π rad ≈ 3.1416 rad
This represents a half circle or straight line
Example 3: Full Circle
360° × (π/180°) = 2π rad ≈ 6.2832 rad
Complete rotation around a circle
Common Degrees to Radians Conversions
| Degrees | Radians (exact) | Radians (decimal) | Description |
|---|---|---|---|
| 0° | 0 rad | 0.000000 rad | No rotation |
| 30° | π/6 rad | 0.523599 rad | 30 degrees |
| 45° | π/4 rad | 0.785398 rad | 45 degrees |
| 60° | π/3 rad | 1.047198 rad | 60 degrees |
| 90° | π/2 rad | 1.570796 rad | Right angle |
| 120° | 2π/3 rad | 2.094395 rad | 120 degrees |
| 135° | 3π/4 rad | 2.356194 rad | 135 degrees |
| 150° | 5π/6 rad | 2.617994 rad | 150 degrees |
| 180° | π rad | 3.141593 rad | Straight angle |
| 270° | 3π/2 rad | 4.712389 rad | 3/4 circle |
| 360° | 2π rad | 6.283185 rad | Full circle |
Angular Units
Degree (°)
1/360 of a full circle
Radian (rad)
Arc length = radius
Gradian (gon)
1/400 of a full circle
Key Relationship
1 radian ≈ 57.2958°
Quick Facts
π ≈ 3.14159265359
360° = 2π radians
180° = π radians
90° = π/2 radians
Used in trigonometry and calculus
Understanding Degrees to Radians Conversion
What is a Radian?
A radian is a unit of angular measurement where the arc length equals the radius of the circle. One radian is approximately 57.2958 degrees. This natural unit makes many mathematical formulas simpler.
Conversion Formulas
- •Degrees to Radians: multiply by π/180°
- •Radians to Degrees: multiply by 180°/π
Example Calculation
Convert 90° to radians:
90° × (π/180°) = π/2 ≈ 1.5708 rad
Practical Applications
- 1Calculus: natural unit for trigonometric functions
- 2Physics: angular velocity and acceleration
- 3Engineering: rotational mechanics
- 4Computer graphics: rotation transformations
Why Use Radians?
Natural unit: Arc length = radius × angle
Simplified formulas: d/dx(sin x) = cos x
Mathematical elegance: No conversion factors
Universal standard: Used in scientific computing