Convert degrees to radians instantly with our precise calculator. Includes the degrees-to-radians formula and a quick reference table for common angles.
Simple Degrees to Radians Conversion
Whether you are working on trigonometry homework, engineering calculations, or game development, converting angles from degrees to radians is a fundamental task. Our tool provides a real-time, high-precision conversion using the constant pi.
The Degrees to Radians Formula
To convert degrees to radians manually, you multiply the number of degrees by $\pi$ and then divide by 180. The mathematical formula is:
For example, to convert 90°:
- Multiply 90 by π (90π).
- Divide by 180.
- The result is π/2 or approximately 1.570796 radians.
3. Quick Conversion Reference Table
| Degrees (°) | Radians (rad) | Exact Value (in 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 |
| 270° | 4.712389 | 3π/2 |
| 360° | 6.283185 | 2π |
4. Frequently Asked Questions (FAQ)
A radian is the standard unit of angular measure. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. Since the circumference is $2\pi r$, a full circle contains $2\pi$ radians.
In calculus, the derivative of $\sin(x)$ is only $\cos(x)$ if $x$ is in radians. If you used degrees, the formula would become much more complex:
$$\frac{d}{dx}\sin(x^\circ) = \frac{\pi}{180}\cos(x^\circ)$$Yes. The relationship is defined as:
$$180^\circ = \pi \text{ radians}$$This is why the conversion factor is always a ratio of $\frac{\pi}{180}$.
To convert from radians to degrees, multiply by the inverse factor:
$$\text{degrees} = \text{radians} \times \frac{180}{\pi}$$