Radian Converter
Convert an angle from degrees to radians with exact fractional-pi form when possible.
About Radian Converter
To convert degrees to radians, multiply by π/180. Common angles have exact fractional-pi forms: 90° = π/2, 60° = π/3, 45° = π/4, 30° = π/6.
Formula
Degree to Radian
radians = degrees × π / 180
- deg
- Angle in degrees
- rad
- Angle in radians
Worked example
With the default values below, Radian Converter returns Radians of 3.1415926536. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Angle in degrees
- 180
Results
- Radians
- 3.1415926536
- Exact form
- 1π
Step by step
- 1Multiply by π/180= 3.1415926536 rad
- 2Exact form= 1π
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why use radians instead of degrees?
Radians are the natural unit in calculus and physics. The derivative of sin(x) is cos(x) only when x is in radians. One radian is the angle subtended by an arc equal in length to the radius.
How many radians in a full circle?
2π radians = 360°. So π radians = 180°, and 1 radian ≈ 57.2958°.