Turns to Radians
Convert turns to radians instantly. 1 turn = 6.2831853072 rad. Includes the exact factor, a conversion table of common values and the definition of both units.
How to convert turns to radians
To convert turns to radians, multiply by 6.2831853072. The relationship is fixed, so the same factor works for any quantity — there is nothing to look up and nothing that changes with temperature, location or context.
rad = turn × 6.2831853072
Turns to Radians conversion table
The values people look up most often, rounded for reading. Use the calculator above for anything in between.
| Turns | Radians |
|---|---|
| 1 turn | 6.283185 rad |
| 2 turn | 12.566371 rad |
| 3 turn | 18.849556 rad |
| 5 turn | 31.415927 rad |
| 10 turn | 62.831853 rad |
| 20 turn | 125.663706 rad |
| 25 turn | 157.079633 rad |
| 50 turn | 314.159265 rad |
| 100 turn | 628.318531 rad |
| 500 turn | 3,141.59 rad |
| 1,000 turn | 6,283.19 rad |
What is a turn?
One full revolution, equal to 2π radians.
What is a radian?
The SI angle unit: the angle subtending an arc equal to the radius.
The formula
rad = turn × 6.2831853072
Every result on this page comes from this formula. Nothing is rounded until the final display, so figures match a spreadsheet to the cent.
How to use the Turns to Radians
- Type the number of turns you want to convert.
- Read the result in radians straight away — there is no button to press.
- Check the table below for the values that come up most often, or reverse the conversion with the linked radians to turns page.
Turns to Radians — frequently asked questions
How many radians are in a turn?
One turn equals 6.2831853072 rad. rad = turn × 6.2831853072
What is the formula to convert turns to radians?
The formula is rad = turn × 6.2831853072. It is an exact definition rather than an approximation, so the conversion never drifts no matter how large the number.
How do I convert radians back to turns?
Divide instead of multiplying: one radian is 0.1591549431 turn. The reverse converter is linked in the related tools list.
Is this conversion exact?
Yes. Both units are defined against the same base unit by international agreement, so the factor is exact — any rounding you see is only in the display, which you can widen by entering more decimal places.
Is this turns to radians free to use?
Yes. Every calculator on the site is free, needs no sign-up, and runs entirely in your browser, so your figures never leave your device.
What people search for
This page answers each of these searches. They are the exact phrases visitors use to find the turns to radians.
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About this calculator
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes.
Last reviewed August 19, 2026 · Calculation runs client-side · No data collected · Report an error