The hertz is one cycle per second.
Hertz to Radians per second Converter — Hz to rad/s
Convert Hertz (Hz) to Radians per second (rad/s) using the exact conversion factor (1 hertz = 6.283185307 radians per second). See the formula, worked examples, conversion table, history, and common uses.
Hertz to Radians per second 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.
Angular frequency converted by one revolution equals 2*pi radians.
Result = input x 1 / 0.1591549431.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Hertz to Radians per second
Hertz and Radians per second 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. Hertz is most often used for electrical power frequency (50/60 hz worldwide).
Formula
radians per second = hertz × 6.28318530718
This factor comes from each unit's defined relationship to the category's base unit: 1 hertz equals 1 base unit, and 1 radians per second equals 0.159154943092 base units, so dividing one by the other gives the direct hertz-to-radians per second factor of 6.28318530718.
Simple example
1 Hz × 6.283185307 = 6.283185307 rad/s
1 hertz = 6.283185307 radians per second.
Real-world example
1,000 Hz × 6.283185307 = 6,283.185307 rad/s
1,000 hertz = 6,283.185307 radians per second.
Conversion table
| Hertz (Hz) | Radians per second (rad/s) |
|---|---|
| 60 Hz | 376.9911184 rad/s |
| 600 Hz | 3,769.911184 rad/s |
| 1,000 Hz | 6,283.185307 rad/s |
| 3,000 Hz | 18,849.55592 rad/s |
| 6,000 Hz | 37,699.11184 rad/s |
| 10,000 Hz | 62,831.85307 rad/s |
Reverse conversion: Radians per second to Hertz
6.283185307 rad/s × 0.1591549431 = 1 Hz
6.283185307 radians per second = 1 hertz.
hertz = radians per second × 0.159154943092
For a page dedicated to this direction, see Radians per second to Hertz.
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.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
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 radians per second are in 1 hertz?
1 hertz equals 6.283185307 radians per second, using the exact defined conversion factor rather than an estimate.
How do I convert hertz to radians per second?
Multiply the hertz value by 6.283185307. The converter above does this instantly to whatever precision you set.
How do I convert radians per second back to hertz?
Use the reverse factor: 1 radians per second equals 0.1591549431 hertz. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
Is the hertz to radians per second conversion exact?
Yes. Both hertz and radians per second are defined by fixed standards rather than physical artifacts, so the factor of 6.283185307 used above is exact to as many digits as you choose to display.
Where is the hertz still used today?
Standard scientific unit worldwide; also everyday (AC power frequency, radio, audio)