Radians to Turns
Convert radians to turns instantly. 1 rad = 0.1591549431 turn. Includes the exact factor, a conversion table of common values and the definition of both units.
How to convert radians to turns
To convert radians to turns, divide by 6.2831853072 (multiply by 0.1591549431). 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.
turn = rad × 0.1591549431
Radians to Turns conversion table
The values people look up most often, rounded for reading. Use the calculator above for anything in between.
| Radians | Turns |
|---|---|
| 1 rad | 0.159155 turn |
| 2 rad | 0.31831 turn |
| 3 rad | 0.477465 turn |
| 5 rad | 0.795775 turn |
| 10 rad | 1.591549 turn |
| 20 rad | 3.183099 turn |
| 25 rad | 3.978874 turn |
| 50 rad | 7.957747 turn |
| 100 rad | 15.915494 turn |
| 500 rad | 79.577472 turn |
| 1,000 rad | 159.154943 turn |
What is a radian?
The SI angle unit: the angle subtending an arc equal to the radius.
What is a turn?
One full revolution, equal to 2π radians.
The formula
turn = rad × 0.1591549431
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 Radians to Turns
- Type the number of radians you want to convert.
- Read the result in turns 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 turns to radians page.
Radians to Turns — frequently asked questions
How many turns are in a radian?
One radian equals 0.1591549431 turn. turn = rad × 0.1591549431
What is the formula to convert radians to turns?
The formula is turn = rad × 0.1591549431. It is an exact definition rather than an approximation, so the conversion never drifts no matter how large the number.
How do I convert turns back to radians?
Divide instead of multiplying: one turn is 6.2831853072 rad. 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 radians to turns 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 radians to turns.
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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