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By Shailendra Singh
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Updated on 31 Mar 2025, 18:16 IST
Both “Hertz” and “radian per second” are units of frequency and angular velocity, respectively. Let’s delve into each:
Hertz is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second.
Usage: It is used to describe the number of cycles a periodic function completes in one second. This can apply to any periodic event, but it’s most commonly used with electrical signals and sound waves.
Radian per second is the unit of angular velocity in the SI system. It’s used to describe the rate of rotation. Specifically, it indicates how many radians a rotating object covers per unit of time.
1 Hz = 2π rad/s = 6.2831853 rad/s
or
1 rad/s = 1/2π Hz = 0.1591549 Hz
ω(rad/s) = 2π×f(Hz)
Example – Find angular velocity in rad/s from frequency of 300 hertz:
Ans. ω(rad/s) = 2π×300Hz = 1884.956 rad/s
| Hertz (Hz) | Radian per second (rad/s) |
| 0 Hz | 0 rad/s |
| 1 Hz | 6.28 rad/s |
| 2 Hz | 12.57 rad/s |
| 3 Hz | 18.85 rad/s |
| 4 Hz | 25.13 rad/s |
| 5 Hz | 31.42 rad/s |
| 6 Hz | 37.70 rad/s |
| 7 Hz | 43.98 rad/s |
| 8 Hz | 50.27 rad/s |
| 9 Hz | 56.55 rad/s |
| 10 Hz | 62.83 rad/s |
| 20 Hz | 125.66 rad/s |
| 30 Hz | 188.50 rad/s |
| 40 Hz | 251.33 rad/s |
| 50 Hz | 314.16 rad/s |
| 60 Hz | 376.99rad/s |
| 70 Hz | 439.82rad/s |
| 80 Hz | 502.65rad/s |
| 90 Hz | 565.49rad/s |
| 100 Hz | 628.32rad/s |
| 200 Hz | 1256.64rad/s |
| 300 Hz | 1884.96rad/s |
| 400 Hz | 2513.27rad/s |
| 500 Hz | 3141.59rad/s |
| 600 Hz | 3769.91rad/s |
| 700 Hz | 4398.23rad/s |
| 800 Hz | 5026.55rad/s |
| 900 Hz | 5654.87rad/s |
| 1000 Hz | 6283.19rad/s |
| 2000 Hz | 12566.37rad/s |
| 3000 Hz | 18849.56rad/s |
| 4000 Hz | 25132.74rad/s |
| 5000 Hz | 31415.93rad/s |
| 6000 Hz | 37699.11rad/s |
| 7000 Hz | 43982.30rad/s |
| 8000 Hz | 50265.48rad/s |
| 9000 Hz | 56548.67rad/s |
| 10000 Hz | 62831.85rad/s |
To convert Hz to radians per second, you multiply the frequency in Hz by 2π. The formula is: radian/second = Hz x 2π
1 Hz, when converted to radians per second, is 2π rad/s.
No, radians per second and Hz are not equivalent. However, they are related by a factor of 2π.
The term 1 hz per second is redundant or incorrect. Hertz (Hz) already means cycles per second. So, 1 Hz is simply 1 cycle per second.
No, 1 Hz represents a frequency of 1 cycle per second. It's a measure of frequency, not time.
1 radian per second (rad/s) is an angular velocity indicating that an object completes 1 radian of rotation in one second.