Hertz to Radians per second Converter Hz → rad/s
1 hertz (Hz) = 6.283185307 radians per second (rad/s). Type a value below — the conversion happens instantly, entirely on your device.
1 Hz = 6.283185307 rad/s
1 hertz = 6.2831853 radians per second
1 × 6.28319 = 6.2831853
1 Hz equals 6.28319 rad/s, so multiplying by 6.28319 converts the value. The result describes the exact same quantity — only the measuring stick changes.
How to convert hertz to radians per second
radians per second = hertz × 6.283185307 — multiply the hertz value by 6.28319.
Example: 1 Hz = 6.28319 rad/s.
To convert the other way: hertz = radians per second ÷ 6.283185307
Hertz to radians per second multiplies by 2π (≈6.283), since one cycle is 2π radians of phase. So 1 Hz is 6.283 rad/s, and 50 Hz mains is about 314 rad/s — the ω that appears in AC and rotational-motion equations.
Hertz to Radians per second conversion table
| Hertz (Hz) | Radians per second (rad/s) |
|---|---|
| 0.1 | 0.62831853 |
| 0.25 | 1.5707963 |
| 0.5 | 3.1415927 |
| 1 | 6.2831853 |
| 2 | 12.566371 |
| 3 | 18.849556 |
| 4 | 25.132741 |
| 5 | 31.415927 |
| 6 | 37.699112 |
| 7 | 43.982297 |
| 8 | 50.265482 |
| 9 | 56.548668 |
| 10 | 62.831853 |
| 15 | 94.24778 |
| 20 | 125.66371 |
| 25 | 157.07963 |
| 30 | 188.49556 |
| 40 | 251.32741 |
| 50 | 314.15927 |
| 75 | 471.2389 |
| 100 | 628.31853 |
| 250 | 1570.7963 |
| 500 | 3141.5927 |
| 1000 | 6283.1853 |
About the units
What is a hertz?
One hertz is one cycle per second — the SI unit of frequency. Mains power is 50 or 60 Hz; audible sound spans roughly 20 Hz to 20 kHz.
What is a radian per second?
Angular frequency: one radian per second is 1/(2π) Hz. A full turn is 2π radians, so 1 Hz = 2π ≈ 6.283 rad/s.
Frequently asked questions
How many radians per second are in 1 hertz?
1 hertz (Hz) = 6.283185307 radians per second (rad/s).
What is the formula to convert hertz to radians per second?
radians per second = hertz × 6.283185307 — multiply the hertz value by 6.28319.
How do I convert Hz to rad/s without a calculator?
Multiply by 6.28 for a close estimate. Exact factor: 1 Hz = 6.283185307 rad/s.
Is this Hz-to-rad/s converter accurate and private?
Yes. It uses the exact internationally defined conversion factors and computes results locally in your browser — your input is never sent to a server, and the page keeps working offline.