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

> Convert revolutions per minute (rpm) to radians per second: 1 rpm = 0.10472 rad/s. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

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

## Formula

- `1 rpm = 0.10472 rad/s`
- `radians per second = revolutions per minute (rpm) × 0.1047197551`
- Reverse: `revolutions per minute (rpm) = radians per second × 9.549296586`

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 rpm = 0.523599 rad/s
- 12.5 rpm = 1.309 rad/s
- 100 rpm = 10.472 rad/s

## Conversion table

| Revolutions per minute (rpm) (rpm) | Radians per second (rad/s) |
| --- | --- |
| 1 | 0.10472 |
| 2 | 0.20944 |
| 3 | 0.314159 |
| 4 | 0.418879 |
| 5 | 0.523599 |
| 6 | 0.628319 |
| 7 | 0.733038 |
| 8 | 0.837758 |
| 9 | 0.942478 |
| 10 | 1.0472 |
| 15 | 1.5708 |
| 20 | 2.0944 |
| 25 | 2.61799 |
| 30 | 3.14159 |
| 40 | 4.18879 |
| 50 | 5.23599 |
| 75 | 7.85398 |
| 100 | 10.472 |
| 200 | 20.944 |
| 250 | 26.1799 |
| 500 | 52.3599 |
| 1000 | 104.72 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=rpm&to_unit=rad%2Fs` → 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":"rpm","to_unit":"rad/s"}`
- 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 radians per second are in one rpm?**

1 rpm = 0.10472 rad/s. 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 revolutions per minute (rpm) to radians per second?**

Multiply the value in revolutions per minute (rpm) by 0.1047197551: radians per second = revolutions per minute (rpm) × 0.1047197551. For example, 5 rpm = 0.523599 rad/s.

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

Multiply by the inverse factor 9.549296586 (revolutions per minute (rpm) = radians per second × 9.549296586), or use the radians per second-to-revolutions per minute (rpm) page.

## Related conversions

- [Radians per second to revolutions per minute (rpm)](https://tttkmbb.com/conversion/rad-per-second-to-rpm.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)