How to convert hertz to radians per second
rad/s = Hz × 6.283185307Multiply the value in hertz by 6.283185307. To go the other way, multiply by 0.1591549431 (or divide by 6.283185307).
A hertz is larger than a radian per second: one hertz contains 6.283185307 radians per second.
Worked examples
- 1 hertz1 Hz × 6.283185307 = 6.283185307 rad/s
- 5 hertz5 Hz × 6.283185307 = 31.41592654 rad/s
- 10 hertz10 Hz × 6.283185307 = 62.83185307 rad/s
- 20 hertz20 Hz × 6.283185307 = 125.6637061 rad/s
- 100 hertz100 Hz × 6.283185307 = 628.3185307 rad/s
Hertz to radians per second conversion table
Values are calculated by the conversion engine and rounded to 8 significant figures.
| Hertz (Hz) | Radians per second (rad/s) |
|---|---|
| 0.1 Hz | 0.62831853 rad/s |
| 0.25 Hz | 1.5707963 rad/s |
| 0.5 Hz | 3.1415927 rad/s |
| 1 Hz | 6.2831853 rad/s |
| 2 Hz | 12.566371 rad/s |
| 3 Hz | 18.849556 rad/s |
| 4 Hz | 25.132741 rad/s |
| 5 Hz | 31.415927 rad/s |
| 6 Hz | 37.699112 rad/s |
| 7 Hz | 43.982297 rad/s |
| 8 Hz | 50.265482 rad/s |
| 9 Hz | 56.548668 rad/s |
| 10 Hz | 62.831853 rad/s |
| Hertz (Hz) | Radians per second (rad/s) |
|---|---|
| 12 Hz | 75.398224 rad/s |
| 15 Hz | 94.24778 rad/s |
| 20 Hz | 125.66371 rad/s |
| 25 Hz | 157.07963 rad/s |
| 30 Hz | 188.49556 rad/s |
| 40 Hz | 251.32741 rad/s |
| 50 Hz | 314.15927 rad/s |
| 75 Hz | 471.2389 rad/s |
| 100 Hz | 628.31853 rad/s |
| 250 Hz | 1,570.7963 rad/s |
| 500 Hz | 3,141.5927 rad/s |
| 1,000 Hz | 6,283.1853 rad/s |
About the units
Hertz (Hz)
One cycle per second.
Radian per second (rad/s)
The radian per second (rad/s) is a unit of frequency in the International System of Units (SI). One radian per second equals 0.1591549431 hertz (Hz).
Frequently asked questions
How many radians per second are in one hertz?
There are 6.283185307 radians per second in one hertz, and this value is exact by definition.
How do I convert hertz to radians per second?
Multiply the number of hertz by 6.283185307. For example, 10 Hz × 6.283185307 = 62.83185307 rad/s.
How many hertz are in one radian per second?
One radian per second equals 0.1591549431 hertz. That is the reverse factor, 1 ÷ 6.283185307.
What is 10 hertz in radians per second?
10 Hz = 62.83185307 rad/s.
Is this Hz to rad/s converter accurate?
Yes. Both units are defined exactly in terms of SI units, so the conversion factor is exact; results are shown to 12 significant figures by default and you can change precision in the converter. Calculations run in your browser using the same tested engine that generated this page.