What is being measured?
Frequency is the number of cycles per time. Hertz is inverse seconds, but a cycle frequency is distinct from angular frequency.
A revolution or beat is one cycle. Angular frequency in rad/s divides by 2π to obtain cycles per second.
Meaning of rad/s
radians per second uses the symbol rad/s in this library and measures frequency. Under the stated reference convention, 1 rad/s = approximately 0.159154943092 Hz. This equivalence changes how a known value is written. It does not increase measurement accuracy or establish whether a measurement is appropriate to a real application.
Conversion method
Multiply the value by the source factor (0.15915494309189535), then divide by the target factor (1). The factor ratio expresses the same frequency measurement in the other unit.
Worked example
For a known value of 10 rad/s, the reference conversion gives 1.59154943092 Hz. Converting that result back gives approximately 10 rad/s. This reverse check helps catch a reversed factor, but matching round-trip arithmetic alone does not independently verify a source definition.
Common reference values
| Input (rad/s) | Reference equivalent (Hz) |
|---|---|
| 1 | 0.159154943092 |
| 5 | 0.795774715459 |
| 10 | 1.59154943092 |
| 25 | 3.9788735773 |
| 50 | 7.95774715459 |
| 100 | 15.9154943092 |
Compare one rad/s with other units
| Target unit | Equivalent of 1 rad/s | Definition guide |
|---|---|---|
| hz (Hz) | 0.159154943092 | Read definition |
| khz (kHz) | 0.000159154943092 | Read definition |
| mhz (MHz) | 1.59154943092e-7 | Read definition |
| ghz (GHz) | 1.59154943092e-10 | Read definition |
| rpm (rpm) | 9.54929658551 | Read definition |
| Terahertz (THz) | 1.59154943092e-13 | Read definition |
Precision and common mistakes
- Keep the source and target quantity consistent. A matching symbol is not enough to establish a compatible definition.
- Record the original measurement precision. Showing twelve significant digits in a table does not make a rounded input more precise.
- Check symbol capitalization, prefixes and any regional convention in the source. Use the displayed unit definition rather than a similarly named unit.
- Factors involving repeating fractions or π use finite numerical precision. Round the final answer to the precision justified by your input.
Use a working converter
- Frequency converter
- Radians per second to hz converter
- Radians per second to khz converter
- Radians per second to mhz converter
- Radians per second to ghz converter
- Radians per second to rpm converter
Source and verification scope
Examples and tables are computed from the versioned unit definitions used by the linked converters. The source access dates appear below. Computandum is independent of the cited organizations; a citation does not mean that a publisher endorses this page or an actual project.
Sources
- NIST / BIPM: NIST: unit conversion factors ↗ · 2026-10-08