Degrees to Radians Converter
Convert degrees (°) to radians instantly and accurately
Common Angle Conversions
About Degrees to Radians Conversion
Converting from degrees to radians is essential in many mathematical and scientific calculations. Degrees are commonly used in everyday contexts, while radians are the standard unit in calculus, physics, and engineering.
Conversion Formula
To convert from degrees to radians, multiply the angle value by π/180. The formula is:
radians = degrees × (π/180)
Common Degrees to Radians Conversions
Degrees to Radians Conversion Table
| Degrees (°) | Radians (rad) |
|---|---|
| 30° | π/6 ≈ 0.5236 rad |
| 45° | π/4 ≈ 0.7854 rad |
| 60° | π/3 ≈ 1.0472 rad |
| 90° | π/2 ≈ 1.5708 rad |
| 120° | 2π/3 ≈ 2.0944 rad |
| 180° | π ≈ 3.1416 rad |
| 270° | 3π/2 ≈ 4.7124 rad |
| 360° | 2π ≈ 6.2832 rad |
Practical Examples
Here are some practical examples of degrees to radians conversions:
- In trigonometry, sin(30°) = sin(π/6) = 0.5, where 30° is converted to π/6 radians for the calculation.
- When calculating the arc length of a circle, the formula s = r × θ requires the angle θ to be in radians. For example, a 90° arc on a circle with radius 5 units has length s = 5 × (90 × π/180) = 5 × (π/2) = 7.85 units.
- In physics, angular velocity is often measured in radians per second. A rotation of 360° per second is equivalent to 2π radians per second.
Why Use Radians?
Radians are the natural unit for measuring angles in mathematics and physics for several reasons:
- The derivatives and integrals of trigonometric functions take their simplest form when angles are measured in radians.
- The small-angle approximation (sin θ ≈ θ for small angles) is only valid when θ is measured in radians.
- In a circle, the radian measure of an angle is equal to the ratio of the arc length to the radius, making it a natural geometric measure.