Degrees to radians converter
Convert positive, negative, and decimal degree measures into exact radians or a rounded decimal result.
Degrees to radians
radians = degrees × π / 180
Because a half turn is 180° and π radians, multiplying by π/180 converts the degree measure into radians.
Examples
Common angle conversions
30°→π/6
45°→π/4
90°→π/2
180°→π
360°→2π
Reference
Quick conversion table
| Degrees | Radians |
|---|---|
| 30° | π/6 |
| 45° | π/4 |
| 60° | π/3 |
| 90° | π/2 |
| 180° | π |
| 360° | 2π |
Why convert degrees to radians?
Radians are the natural unit for calculus, trigonometric functions, angular velocity, and many scientific formulas. A full turn is 360 degrees or 2π radians, so one degree equals π/180 radians.
Questions
Frequently asked questions
What is the degrees to radians formula?
Multiply degrees by π and divide by 180: radians = degrees × π/180.
What is 180 degrees in radians?
180 degrees equals exactly π radians.
Should I use exact or decimal radians?
Use the exact π fraction for symbolic work and a decimal when entering the value into numerical software.
Continue learning