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

> Convert hertz to radians per second: 1 Hz = 6.28319 rad/s. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

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

## Formula

- `1 Hz = 6.28319 rad/s`
- `radians per second = hertz × 6.283185307`
- Reverse: `hertz = radians per second × 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 Hz = 31.4159 rad/s
- 12.5 Hz = 78.5398 rad/s
- 100 Hz = 628.319 rad/s

## Conversion table

| Hertz (Hz) | Radians per second (rad/s) |
| --- | --- |
| 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=Hz&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":"Hz","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 hertz?**

1 Hz = 6.28319 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 hertz to radians per second?**

Multiply the value in hertz by 6.283185307: radians per second = hertz × 6.283185307. For example, 5 Hz = 31.4159 rad/s.

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

Multiply by the inverse factor 0.1591549431 (hertz = radians per second × 0.1591549431), or use the radians per second-to-hertz page.

## Related conversions

- [Radians per second to hertz](https://tttkmbb.com/conversion/rad-per-second-to-hz.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)