Convert degrees to radians instantly with our free calculator. Includes the degrees to radians formula, a conversion table, and an explanation of circular measure.
Degrees to Radians
How to Convert Degrees to Radians
In geometry and trigonometry, angles are measured in two primary units: degrees and radians. While degrees are common in everyday life (like a 360° circle), radians are the standard unit used in calculus, physics, and higher-level mathematics because they simplify many formulas.
The Conversion Formula
To convert from degrees to radians, you multiply the angle by π divided by 180. The formula is written as:
Radians = Degrees × (π / 180)
Degrees to Radians Conversion Table
Use this reference table for the most common angles used in trigonometry:
| Degrees (°) | Radians (Decimal) | Radians (in terms of π) |
|---|---|---|
| 30° | 0.523599 | π/6 |
| 45° | 0.785398 | π/4 |
| 60° | 1.047198 | π/3 |
| 90° | 1.570796 | π/2 |
| 180° | 3.141593 | π |
| 360° | 6.283185 | 2π |
Context: Why Use Radians?
A radian is defined as the angle created when the arc length is equal to the radius of the circle. Because radians are based on the intrinsic properties of a circle (its radius and circumference), they are considered a “natural” unit of measurement.
- Calculus: Derivatives of trigonometric functions like sin(x) only work simply if x is in radians.
- Angular Velocity: In physics, rotations per second are easier to calculate using radians.
- Arc Length: The formula for the length of an arc is simply s = rθ, where θ must be in radians.
Why Use Our Converter?
While manual calculation is possible, angles in radians often result in long irrational numbers. Our converter uses high-precision values for Pi (π) to ensure that your conversions for engineering, schoolwork, or computer graphics are as accurate as possible.