# 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.

- Page id: `turns-to-radians` · Quantity: Angle (`angle`, base unit rad) · Tool: `convert_units`
- Canonical page: https://tttkmbb.com/conversion/turns-to-radians · This document: https://tttkmbb.com/conversion/turns-to-radians.md · JSON: https://tttkmbb.com/conversion/turns-to-radians.json (add `?value=` for a result)

## Formula

- `1 turn = 6.28319 rad`
- `radians = turns (revolutions) × 6.283185307`
- Reverse: `turns (revolutions) = radians × 0.1591549431`

The factor follows from the SI definitions of both units (NIST SP 811); values below are rounded 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

## 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 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=turn&to_unit=rad` → unified JSON envelope with `result.values.result`, `formula`, `factor`, `sources`, `freshness`
- MCP: server `https://tttkmbb.com/mcp`, tool `convert_units` with `{"value":5,"from_unit":"turn","to_unit":"rad"}`
- All angle units: https://tttkmbb.com/api/v1/units?quantity=angle · full converter: [Angle Converter](https://tttkmbb.com/conversion/angle.md)
- Authentication: none. Freshness: `static` (fixed conversion factors).

## 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

- [Radians to turns (revolutions)](https://tttkmbb.com/conversion/radians-to-turns.md) (reverse)
- [Degrees to Radians](https://tttkmbb.com/conversion/degrees-to-radians.md)
- [Radians to Degrees](https://tttkmbb.com/conversion/radians-to-degrees.md)
- [Gradians to Degrees](https://tttkmbb.com/conversion/gradians-to-degrees.md)
- [Degrees to Gradians](https://tttkmbb.com/conversion/degrees-to-gradians.md)
- [Turns (revolutions) to Degrees](https://tttkmbb.com/conversion/turns-to-degrees.md)
- [Degrees to Turns (revolutions)](https://tttkmbb.com/conversion/degrees-to-turns.md)
- [Arcminutes to Degrees](https://tttkmbb.com/conversion/arcminutes-to-degrees.md)
- [Degrees to Arcminutes](https://tttkmbb.com/conversion/degrees-to-arcminutes.md)

## Data Sources

- NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-24)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-24)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, retrieved 2026-09-24)