Radians Converter
Convert angles between degrees, radians, gradians, and turns — plus milliradians, arcminutes, and arcseconds — for mathematics, physics, and engineering. Negative and very small angles are fully supported.
Conversion reference
| From | To | Result |
|---|---|---|
| 180 ° | Radian (rad) | 3.14159265359 rad |
| 180 ° | Gradian (gon) (gon) | 200 gon |
| 180 ° | Turn (revolution) (turn) | 0.5 turn |
| 90 ° | Radian (rad) | 1.57079632679 rad |
| 90 ° | Gradian (gon) (gon) | 100 gon |
| 360 ° | Radian (rad) | 6.28318530718 rad |
| 360 ° | Turn (revolution) (turn) | 1 turn |
| 1 rad | Degree (°) | 57.2957795131 ° |
Values are generated by the converter engine, at Auto precision.
About this converter
An angle can be measured as a fraction of a full turn. The radian is the SI unit: the angle subtended when the arc length equals the radius, so a full circle is 2π radians. A degree is 1/360 of a full turn, a gradian 1/400, and a turn the whole circle.
The converter expresses your value in radians and then in the target unit. Because degrees and radians are related by π, results are irrational and are shown with as many digits as are meaningful (change Precision for a shorter display).
How to use it
- Type the angle in the Value field — a minus sign, decimals, and exponent notation are all allowed.
- Choose the unit to convert from (for example Degree) and the unit for the answer (for example Radian).
- Read the result, press Copy result, or press Swap to reverse the direction.
The result updates as you type — there is no Calculate button. Use Swap to reverse the two units, and Reset to return to the defaults.
Formula and common values
radians = degrees × π / 180 · degrees = radians × 180 / π
- 180° = π radians ≈ 3.14159265358979
- 90° = π/2 radians ≈ 1.57079632679490
- 360° = 2π radians ≈ 6.28318530717959
- 1 radian ≈ 57.2957795130823°
- 1 turn = 360° = 400 gradians = 2π radians
FAQ
How do I convert degrees to radians?
Multiply the number of degrees by π / 180. So 180° = π radians ≈ 3.14159265, 90° = π/2 ≈ 1.57079633, and 360° = 2π ≈ 6.28318531.
How do I convert radians to degrees?
Multiply the number of radians by 180 / π. One radian ≈ 57.29577951°.
What is a gradian?
A gradian (also gon or grad) divides a right angle into 100 parts, so a full turn is 400 gradians. It is used in surveying. 1 gradian = π/200 radians = 0.9°.
Can I enter negative or very small angles?
Yes. Negative angles, decimals, exponent notation like 1e-6, and very small values are all accepted — a mathematically valid angle is never blocked.
Don't see the tool you need?
Goeroe Digital builds custom calculators, generators, and business tools on request.
Request a Custom ToolThis is a free tool provided by Goeroe Digital. All results, generated files, and figures are estimates or drafts for general informational use only. Goeroe Digital accepts no responsibility or liability for any output, outcome, loss, or decision arising from the use of these free tools — always review the results yourself before relying on them.