Radians Per Second to Hertz Conversion

Enter the frequency in radians per second below to get the value converted to hertz.

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Results in Hertz:
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1 rad/s = 0.159155 Hz
Do you want to convert hertz to radians per second?

How to Convert Radians Per Second to Hertz

To convert a radian per second measurement to a hertz measurement, multiply the frequency by the conversion ratio.

Since one radian per second is equal to 0.159155 hertz, you can use this simple formula to convert:

hertz = radians per second × 0.159155

The frequency in hertz is equal to the radians per second multiplied by 0.159155.

For example, here's how to convert 5 radians per second to hertz using the formula above.
5 rad/s = (5 × 0.159155) = 0.795775 Hz
conversion scale showing radians per second and equivalent hertz frequency values

The following formula can also be used to convert the angular frequency in radians per second to frequency in hertz:

ƒ = ω2π

In other words, the frequency ƒ in hertz is equal to the angular frequency ω in radians per second divided by 2 times pi.

Radians per second and hertz are both units used to measure frequency. Keep reading to learn more about each unit of measure.

Radians Per Second

Radians per second are a measure of angular frequency, or rotational speed, equal to the change in orientation or angle of an object in radians per second.

Radians per second can be abbreviated as rad/s; for example, 1 radian per second can be written as 1 rad/s.

In formal expressions, the slash, or solidus (/), is used to separate units used to indicate division in an expression.[1]

Hertz

Hertz is formally defined as the frequency equalling one cycle per second.[2]

The hertz is the SI derived unit for frequency in the metric system. Hertz can be abbreviated as Hz; for example, 1 hertz can be written as 1 Hz.

Frequency in hertz can be expressed using the formula: Hz = CyclesTimes

Radian Per Second to Hertz Conversion Table

Radian per second measurements converted to hertz
Radians Per Second Hertz
1 rad/s 0.159155 Hz
2 rad/s 0.31831 Hz
3 rad/s 0.477465 Hz
4 rad/s 0.63662 Hz
5 rad/s 0.795775 Hz
6 rad/s 0.95493 Hz
7 rad/s 1.1141 Hz
8 rad/s 1.2732 Hz
9 rad/s 1.4324 Hz
10 rad/s 1.5915 Hz
11 rad/s 1.7507 Hz
12 rad/s 1.9099 Hz
13 rad/s 2.069 Hz
14 rad/s 2.2282 Hz
15 rad/s 2.3873 Hz
16 rad/s 2.5465 Hz
17 rad/s 2.7056 Hz
18 rad/s 2.8648 Hz
19 rad/s 3.0239 Hz
20 rad/s 3.1831 Hz
21 rad/s 3.3423 Hz
22 rad/s 3.5014 Hz
23 rad/s 3.6606 Hz
24 rad/s 3.8197 Hz
25 rad/s 3.9789 Hz
26 rad/s 4.138 Hz
27 rad/s 4.2972 Hz
28 rad/s 4.4563 Hz
29 rad/s 4.6155 Hz
30 rad/s 4.7746 Hz
31 rad/s 4.9338 Hz
32 rad/s 5.093 Hz
33 rad/s 5.2521 Hz
34 rad/s 5.4113 Hz
35 rad/s 5.5704 Hz
36 rad/s 5.7296 Hz
37 rad/s 5.8887 Hz
38 rad/s 6.0479 Hz
39 rad/s 6.207 Hz
40 rad/s 6.3662 Hz

References

  1. National Institute of Standards and Technology, NIST Guide to the SI, Chapter 6: Rules and Style Conventions for Printing and Using Units, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-6-rules-and-style-conventions-printing-and-using
  2. National Institute of Standards and Technology, SI Units - Time, https://www.nist.gov/pml/owm/si-units-time

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