Degrees to Radians Converter
A bidirectional converter for angles. Enter a value in any field to instantly convert between degrees and radians (as a decimal or in terms of π).
Calculation Steps:
Enter a value to see the step-by-step conversion.
How to Convert Degrees to Radians
The conversion from degrees to radians is fundamental in trigonometry, calculus, and physics. The key is the relationship that **180 degrees is equal to π (pi) radians**.
The Formula (Degrees to Radians)
To convert from degrees to radians, you multiply the angle in degrees by the conversion factor `π / 180°`.
For example, to convert 60°:
60° × (π / 180°) = 60π / 180 = π/3 radians
Our calculator shows this step-by-step simplification for any degree you enter.
The Formula (Radians to Degrees)
To convert from radians back to degrees, you multiply the angle in radians by the inverse factor `180° / π`.
For example, to convert 3.14159 radians (which is π):
π rad × (180° / π) = 180°
Common Conversions (Unit Circle)
This table shows the most common angles used in trigonometry.
| Degrees | Radians (in terms of π) | Radians (Decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.524 |
| 45° | π/4 | 0.785 |
| 60° | π/3 | 1.047 |
| 90° | π/2 | 1.571 |
| 180° | π | 3.142 |
| 270° | 3π/2 | 4.712 |
| 360° | 2π | 6.283 |
Frequently Asked Questions (FAQ)
What is a radian?
A radian is a unit for measuring angles. It is defined as the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. One full circle (360°) is equal to 2π radians.
Why use radians instead of degrees?
Radians are the "natural" unit for angles in mathematics and physics. Using radians simplifies many important formulas in calculus (like the derivatives of `sin(x)` or `cos(x)`) and physics (like the formulas for angular velocity and centripetal acceleration).
What is 1 radian in degrees?
1 radian is equal to `180° / π`, which is approximately **57.296 degrees**.