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

Formula

1 Hz = 6.28319 rad/s

radians per second = hertz × 6.283185307 — reverse: hertz = radians per second × 0.1591549431

The factor is derived from the SI definitions of both units (base unit: Hz) as listed in NIST SP 811; results on this page are shown 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

Hertz to radians per second conversion table

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 (reverse)
• Frequency Converter — all frequency units in one tool
• Hertz to Revolutions per minute (rpm)
• Revolutions per minute (rpm) to Hertz
• Radians per second to Revolutions per minute (rpm)
• Revolutions per minute (rpm) to Radians per second
• Gigahertz to Megahertz
• Megahertz to Gigahertz
• Megahertz to Kilohertz
• Kilohertz to Megahertz

Machine access

• API: GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=Hz&to_unit=rad%2Fs
• MCP: server https://tttkmbb.com/mcp, tool convert_units with {"value":5,"from_unit":"Hz","to_unit":"rad/s"}
• Markdown: 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) · Units: /api/v1/units?quantity=frequency
• OpenAPI operationId: convert_units. Freshness: static. Authentication: none.

Sources

• NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors (standard)
• BIPM – The International System of Units (SI Brochure, 9th edition) (standard)
• Wikipedia – Conversion of units (reference)