The hertz
The hertz (Hz) is the SI derived unit of frequency, equal to one cycle per second. It is the universal unit for sound pitch, electrical AC frequency, processor clock speed (in multiples), and radio and wireless signal frequencies.
Hertz to Radians per second Converter
1 Hz = 6.28319 rad/s (hertz → radian per second)
1 Hz = 6.28319 rad/s
1 hertz equals 6.28319 radians per second. To convert hertz to radians per second, multiply the hertz value by 6.28319. For quick reference: 1 Hz = 6.28319 rad/s, 5 Hz = 31.4159 rad/s, 10 Hz = 62.8319 rad/s, 100 Hz = 628.319 rad/s.
Formula
Radians per second = Hertz × 6.28319Quick
How to convert hertz to radians per second
Take your value
Start with your value in hertz.
Multiply by 6.28319
Multiply the hertz value by 6.28319. This is the exact conversion factor from hertz to radians per second.
Read the result
The product is your value in radians per second. For example, 5 Hz × 6.28319 = 31.4159 rad/s.
Conversion formula
The exact factor from hertz to radians per second is 6.28319.
Radians per second = Hertz × 6.28319
Hertz to Radians per second conversion table
Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.
| Hertz (Hz) | Radians per second (rad/s) |
|---|---|
| 0.1 Hz | 0.62832 rad/s |
| 0.25 Hz | 1.5708 rad/s |
| 0.5 Hz | 3.1416 rad/s |
| 1 Hz | 6.2832 rad/s |
| 2 Hz | 12.566 rad/s |
| 3 Hz | 18.85 rad/s |
| 4 Hz | 25.133 rad/s |
| 5 Hz | 31.416 rad/s |
| 6 Hz | 37.699 rad/s |
| 7 Hz | 43.982 rad/s |
| 8 Hz | 50.265 rad/s |
| 9 Hz | 56.549 rad/s |
| 10 Hz | 62.832 rad/s |
| 11 Hz | 69.115 rad/s |
| 12 Hz | 75.398 rad/s |
| 13 Hz | 81.681 rad/s |
| 14 Hz | 87.965 rad/s |
| 15 Hz | 94.248 rad/s |
| 16 Hz | 100.53 rad/s |
| 18 Hz | 113.1 rad/s |
| 20 Hz | 125.66 rad/s |
| 22 Hz | 138.23 rad/s |
| 24 Hz | 150.8 rad/s |
| 25 Hz | 157.08 rad/s |
| 28 Hz | 175.93 rad/s |
| 30 Hz | 188.5 rad/s |
| 32 Hz | 201.06 rad/s |
| 36 Hz | 226.19 rad/s |
| 40 Hz | 251.33 rad/s |
| 45 Hz | 282.74 rad/s |
| 48 Hz | 301.59 rad/s |
| 50 Hz | 314.16 rad/s |
| 60 Hz | 376.99 rad/s |
| 70 Hz | 439.82 rad/s |
| 75 Hz | 471.24 rad/s |
| 80 Hz | 502.65 rad/s |
| 90 Hz | 565.49 rad/s |
| 100 Hz | 628.32 rad/s |
| 125 Hz | 785.4 rad/s |
| 150 Hz | 942.48 rad/s |
| 200 Hz | 1256.6 rad/s |
| 250 Hz | 1570.8 rad/s |
| 300 Hz | 1885 rad/s |
| 400 Hz | 2513.3 rad/s |
| 500 Hz | 3141.6 rad/s |
| 600 Hz | 3769.9 rad/s |
| 750 Hz | 4712.4 rad/s |
| 800 Hz | 5026.5 rad/s |
| 900 Hz | 5654.9 rad/s |
| 1000 Hz | 6283.2 rad/s |
Real-world reference
Standard mains electricity in most of the world is 50 or 60 Hz. Human hearing spans roughly 20 Hz to 20,000 Hz. In radians per second, that gives you: 1 Hz = 6.28319 rad/s, 10 Hz = 62.8319 rad/s, 100 Hz = 628.319 rad/s.
Frequently asked questions
- How many radians per second are in 1 hertz?
- 1 hertz equals 6.28319 radians per second.
- How do I convert hertz to radians per second?
- Multiply the hertz value by 6.28319. So x Hz × 6.28319 = the equivalent in rad/s.
- What is 5 hertz in radians per second?
- 5 hertz equals 31.4159 radians per second.
- What is 10 hertz in radians per second?
- 10 hertz equals 62.8319 radians per second.
- What is 100 hertz in radians per second?
- 100 hertz equals 628.319 radians per second.
- How do I convert back from radians per second to hertz?
- Multiply the radian per second value by 0.159155. For example, 1 rad/s = 0.159155 Hz.
- Is the hertz bigger than the radian per second?
- Yes. 1 hertz is larger than 1 radian per second — specifically 6.28319 times larger.
- Are these conversion factors exact?
- The factor is derived directly from the SI definitions of hertz and radian per second; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.
About the hertz and the radian per second
The radian per second
The radian per second (rad/s) equals 1/(2π) Hz, since one full cycle sweeps out 2π radians. It is the standard unit for angular velocity in physics and control-systems engineering, distinct from RPM's mechanical-engineering convention.