# Radians per second to Revolutions per minute (rpm) (rad/s to rpm)

> Convert radians per second to revolutions per minute (rpm): 1 rad/s = 9.5493 rpm. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

- Page id: `rad-per-second-to-rpm` · Quantity: Frequency (`frequency`, base unit Hz) · Tool: `convert_units`
- Canonical page: https://tttkmbb.com/conversion/rad-per-second-to-rpm · This document: https://tttkmbb.com/conversion/rad-per-second-to-rpm.md · JSON: https://tttkmbb.com/conversion/rad-per-second-to-rpm.json (add `?value=` for a result)

## Formula

- `1 rad/s = 9.5493 rpm`
- `revolutions per minute (rpm) = radians per second × 9.549296586`
- Reverse: `radians per second = revolutions per minute (rpm) × 0.1047197551`

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/s = 47.7465 rpm
- 12.5 rad/s = 119.366 rpm
- 100 rad/s = 954.93 rpm

## Conversion table

| Radians per second (rad/s) | Revolutions per minute (rpm) (rpm) |
| --- | --- |
| 1 | 9.5493 |
| 2 | 19.0986 |
| 3 | 28.6479 |
| 4 | 38.1972 |
| 5 | 47.7465 |
| 6 | 57.2958 |
| 7 | 66.8451 |
| 8 | 76.3944 |
| 9 | 85.9437 |
| 10 | 95.493 |
| 15 | 143.239 |
| 20 | 190.986 |
| 25 | 238.732 |
| 30 | 286.479 |
| 40 | 381.972 |
| 50 | 477.465 |
| 75 | 716.197 |
| 100 | 954.93 |
| 200 | 1909.86 |
| 250 | 2387.32 |
| 500 | 4774.65 |
| 1000 | 9549.3 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=rad%2Fs&to_unit=rpm` → 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/s","to_unit":"rpm"}`
- All frequency units: https://tttkmbb.com/api/v1/units?quantity=frequency · full converter: [Frequency Converter](https://tttkmbb.com/conversion/frequency.md)
- Authentication: none. Freshness: `static` (fixed conversion factors).

## FAQ

**How many revolutions per minute (rpm) are in one radian per second?**

1 rad/s = 9.5493 rpm. 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 per second to revolutions per minute (rpm)?**

Multiply the value in radians per second by 9.549296586: revolutions per minute (rpm) = radians per second × 9.549296586. For example, 5 rad/s = 47.7465 rpm.

**How do I convert revolutions per minute (rpm) back to radians per second?**

Multiply by the inverse factor 0.1047197551 (radians per second = revolutions per minute (rpm) × 0.1047197551), or use the revolutions per minute (rpm)-to-radians per second page.

## Related conversions

- [Revolutions per minute (rpm) to radians per second](https://tttkmbb.com/conversion/rpm-to-rad-per-second.md) (reverse)
- [Hertz to Revolutions per minute (rpm)](https://tttkmbb.com/conversion/hz-to-rpm.md)
- [Revolutions per minute (rpm) to Hertz](https://tttkmbb.com/conversion/rpm-to-hz.md)
- [Gigahertz to Megahertz](https://tttkmbb.com/conversion/ghz-to-mhz.md)
- [Megahertz to Gigahertz](https://tttkmbb.com/conversion/mhz-to-ghz.md)
- [Megahertz to Kilohertz](https://tttkmbb.com/conversion/mhz-to-khz.md)
- [Kilohertz to Megahertz](https://tttkmbb.com/conversion/khz-to-mhz.md)
- [Kilohertz to Hertz](https://tttkmbb.com/conversion/khz-to-hz.md)
- [Hertz to Kilohertz](https://tttkmbb.com/conversion/hz-to-khz.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)