# Radians to Turns (revolutions) (rad to turn)

> Convert radians to turns (revolutions): 1 rad = 0.159155 turn. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

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

## Formula

- `1 rad = 0.159155 turn`
- `turns (revolutions) = radians × 0.1591549431`
- Reverse: `radians = turns (revolutions) × 6.283185307`

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 rad = 0.795775 turn
- 12.5 rad = 1.98944 turn
- 100 rad = 15.9155 turn

## Conversion table

| Radians (rad) | Turns (revolutions) (turn) |
| --- | --- |
| 1 | 0.159155 |
| 2 | 0.31831 |
| 3 | 0.477465 |
| 4 | 0.63662 |
| 5 | 0.795775 |
| 6 | 0.95493 |
| 7 | 1.11408 |
| 8 | 1.27324 |
| 9 | 1.43239 |
| 10 | 1.59155 |
| 15 | 2.38732 |
| 20 | 3.1831 |
| 25 | 3.97887 |
| 30 | 4.77465 |
| 40 | 6.3662 |
| 50 | 7.95775 |
| 75 | 11.9366 |
| 100 | 15.9155 |
| 200 | 31.831 |
| 250 | 39.7887 |
| 500 | 79.5775 |
| 1000 | 159.155 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=rad&to_unit=turn` → 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":"rad","to_unit":"turn"}`
- 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 turns (revolutions) are in one radian?**

1 rad = 0.159155 turn. 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 radians to turns (revolutions)?**

Multiply the value in radians by 0.1591549431: turns (revolutions) = radians × 0.1591549431. For example, 5 rad = 0.795775 turn.

**How do I convert turns (revolutions) back to radians?**

Multiply by the inverse factor 6.283185307 (radians = turns (revolutions) × 6.283185307), or use the turns (revolutions)-to-radians page.

## Related conversions

- [Turns (revolutions) to radians](https://tttkmbb.com/conversion/turns-to-radians.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)