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Turns (revolutions) to Radians (turn to rad)
Convert turns (revolutions) to radians: 1 turn = 6.28319 rad. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.
Formula
1 turn = 6.28319 rad
radians = turns (revolutions) × 6.283185307 — reverse: turns (revolutions) = radians × 0.1591549431
The factor is derived from the SI definitions of both units (base unit: rad) as listed in NIST SP 811; results on this page are shown to 6 significant figures, the API returns up to 12.
Worked examples
- 5 turn = 31.4159 rad
- 12.5 turn = 78.5398 rad
- 100 turn = 628.319 rad
Turns (revolutions) to radians conversion table
| Turns (revolutions) (turn) | Radians (rad) |
|---|---|
| 1 | 6.28319 |
| 2 | 12.5664 |
| 3 | 18.8496 |
| 4 | 25.1327 |
| 5 | 31.4159 |
| 6 | 37.6991 |
| 7 | 43.9823 |
| 8 | 50.2655 |
| 9 | 56.5487 |
| 10 | 62.8319 |
| 15 | 94.2478 |
| 20 | 125.664 |
| 25 | 157.08 |
| 30 | 188.496 |
| 40 | 251.327 |
| 50 | 314.159 |
| 75 | 471.239 |
| 100 | 628.319 |
| 200 | 1256.64 |
| 250 | 1570.8 |
| 500 | 3141.59 |
| 1000 | 6283.19 |
FAQ
How many radians are in one turn?
1 turn = 6.28319 rad. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures.
What is the formula to convert turns (revolutions) to radians?
Multiply the value in turns (revolutions) by 6.283185307: radians = turns (revolutions) × 6.283185307. For example, 5 turn = 31.4159 rad.
How do I convert radians back to turns (revolutions)?
Multiply by the inverse factor 0.1591549431 (turns (revolutions) = radians × 0.1591549431), or use the radians-to-turns (revolutions) page.
Related conversions
Machine access
- API:
GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=turn&to_unit=rad - MCP: server
https://tttkmbb.com/mcp, toolconvert_unitswith{"value":5,"from_unit":"turn","to_unit":"rad"} - Markdown: https://tttkmbb.com/conversion/turns-to-radians.md · JSON: https://tttkmbb.com/conversion/turns-to-radians.json (add
?value=for a result) · Units: /api/v1/units?quantity=angle - OpenAPI operationId:
convert_units. Freshness:static. Authentication: none.