# Radians per second to Hertz (rad/s to Hz)

> Convert radians per second to hertz: 1 rad/s = 0.159155 Hz. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

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

## Formula

- `1 rad/s = 0.159155 Hz`
- `hertz = radians per second × 0.1591549431`
- Reverse: `radians per second = hertz × 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/s = 0.795775 Hz
- 12.5 rad/s = 1.98944 Hz
- 100 rad/s = 15.9155 Hz

## Conversion table

| Radians per second (rad/s) | Hertz (Hz) |
| --- | --- |
| 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%2Fs&to_unit=Hz` → 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":"Hz"}`
- 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 hertz are in one radian per second?**

1 rad/s = 0.159155 Hz. 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 hertz?**

Multiply the value in radians per second by 0.1591549431: hertz = radians per second × 0.1591549431. For example, 5 rad/s = 0.795775 Hz.

**How do I convert hertz back to radians per second?**

Multiply by the inverse factor 6.283185307 (radians per second = hertz × 6.283185307), or use the hertz-to-radians per second page.

## Related conversions

- [Hertz to radians per second](https://tttkmbb.com/conversion/hz-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)
- [Radians per second to Revolutions per minute (rpm)](https://tttkmbb.com/conversion/rad-per-second-to-rpm.md)
- [Revolutions per minute (rpm) to Radians per second](https://tttkmbb.com/conversion/rpm-to-rad-per-second.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)

## 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)