Angular frequency converted by one revolution equals 2*pi radians.
Radians per second to Hertz Converter — rad/s to Hz
Convert Radians per second (rad/s) to Hertz (Hz) using the exact conversion factor (1 radians per second = 0.1591549431 hertz). See the formula, worked examples, conversion table, history, and common uses.
Radians per second to Hertz converter
Converter
Frequency Converter
Convert hertz, SI frequency prefixes, RPM, beats per minute, and angular frequency.
Context values
Some unit families need one extra value for a physically accurate result.
The hertz is one cycle per second.
Result = input x 0.1591549431 / 1.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians per second to Hertz
Radians per second and Hertz both describe how fast something cycles or rotates, and the conversion is a routine part of reading a car tachometer or motor spec sheet against a scientific frequency figure. Specifically: Angular frequency converted by one revolution equals 2*pi radians, and the hertz is one cycle per second.
Formula
hertz = radians per second × 0.159154943092
This factor comes from each unit's defined relationship to the category's base unit: 1 radians per second equals 0.159154943092 base units, and 1 hertz equals 1 base unit, so dividing one by the other gives the direct radians per second-to-hertz factor of 0.159154943092.
Simple example
1 rad/s × 0.1591549431 = 0.1591549431 Hz
1 radians per second = 0.1591549431 hertz.
Real-world example
1,000 rad/s × 0.1591549431 = 159.1549431 Hz
1,000 radians per second = 159.1549431 hertz.
Conversion table
| Radians per second (rad/s) | Hertz (Hz) |
|---|---|
| 60 rad/s | 9.549296586 Hz |
| 600 rad/s | 95.49296586 Hz |
| 1,000 rad/s | 159.1549431 Hz |
| 3,000 rad/s | 477.4648293 Hz |
| 6,000 rad/s | 954.9296586 Hz |
| 10,000 rad/s | 1,591.549431 Hz |
Reverse conversion: Hertz to Radians per second
0.1591549431 Hz × 6.283185307 = 1 rad/s
0.1591549431 hertz = 1 radians per second.
radians per second = hertz × 6.28318530718
For a page dedicated to this direction, see Hertz to Radians per second.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
Understanding the Hertz
Hertz (Hz) measures frequency. The hertz is the SI derived unit of frequency: one cycle per second. It is classified as a SI derived unit.
Where it's used: Standard scientific unit worldwide; also everyday (AC power frequency, radio, audio)
Uses of the Hertz today
- Electrical power frequency (50/60 Hz worldwide)
- Radio, audio, and signal processing
- Computer processor clock speeds (GHz)
History of the Hertz
The hertz is named after Heinrich Hertz, who in 1886-1889 was the first to conclusively demonstrate the existence of electromagnetic waves predicted by Maxwell's equations. The unit ('cycles per second') was renamed in his honor and adopted internationally in 1930, becoming the SI derived unit of frequency in 1960.
Historical origin. Hertz was not the invention of a single named person; it developed through the process described above.
Hertz — sources
- BIPM SI Brochure — Coherent derived units — Defines the hertz as the SI unit of frequency.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many hertz are in 1 radians per second?
1 radians per second equals 0.1591549431 hertz, using the exact defined conversion factor rather than an estimate.
How do I convert radians per second to hertz?
Multiply the radians per second value by 0.1591549431. The converter above does this instantly to whatever precision you set.
How do I convert hertz back to radians per second?
Use the reverse factor: 1 hertz equals 6.283185307 radians per second. You can also use the swap control in the converter above to flip the direction instantly.
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
What is a hertz?
Hertz (Hz) measures frequency. The hertz is the SI derived unit of frequency: one cycle per second. It is classified as a SI derived unit.
Is the radians per second to hertz conversion exact?
Yes. Both radians per second and hertz are defined by fixed standards rather than physical artifacts, so the factor of 0.1591549431 used above is exact to as many digits as you choose to display.