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Hertz to radian/sec conversion FullScreen

Easily convert frequencies from hertz (Hz) to radians per second (rad/s). This online tool simplifies the process of converting between these units, making it convenient for angular frequency calculations. Upgrade your conversions by effortlessly calculating the equivalent value in radians per second for a given frequency in hertz.

Result in radian per second: rad/s


What is Hertz to radian/sec conversion

Hertz (Hz) and radians per second (rad/s) are both units of angular frequency. The conversion between these two units depends on the type of angular motion being considered.

For simple harmonic motion, where the angular velocity is directly proportional to the frequency, the conversion factor is 2π. Therefore:

Angular frequency in rad/s = Frequency in Hz × 2π


Frequency in Hz = Angular frequency in rad/s / (2π)

For example, let's say we have a frequency of 10 Hz and want to convert it to radians per second:

Angular frequency in rad/s = 10 Hz × 2π ≈ 62.83 rad/s

Similarly, if we have an angular frequency of 100 rad/s and want to convert it to Hertz:

Frequency in Hz = 100 rad/s / (2π) ≈ 15.92 Hz

Remember, this conversion factor specifically applies to simple harmonic motion. For other types of angular motion or more complex systems, the relationship between Hertz and radians per second may differ.

How to calculate rad/sec from hertz

1 Hz = 2π rad/s = 6.2831853 rad/s


1 rad/s = 1/2π Hz = 0.1591549 Hz

Hertz to rad/s formula

The angular frequency or angular velocity ω in radian per second (rad/s) is equal to 2π times the frequency f in hertz (Hz):

ω(rad/s) = 2π×f(Hz)

Hertz to rad/s Example

Calculate angular velocity in rad/s from frequency of 300 hertz:

ω(rad/s) = 2π×300Hz = 1884.956 rad/s

Hertz to rad/sec conversion table

Radian per second
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