Radians per Second to Hertz Converter

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

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1 rad/s = 0.159155 Hz

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How to Convert Radians per Second to Hertz

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To convert a measurement in radians per second to a measurement in hertz, multiply the frequency by the following conversion ratio: 0.159155 hertz/radian per second.

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 frequency in radians per second multiplied by 0.159155.

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

How Many Hertz Are in One Radian per Second?

There are 0.159155 hertz in one radian per second, which is why we use this value in the formula above.

1 rad/s = 0.159155 Hz

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.

What Are Radians per Second?

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

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

In the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.[1] For example, rad/s is expressing a change in angle relative to a change in time.

Learn more about radians per second.

What is a Hertz?

One hertz is formally defined as the frequency of 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 = CyclesTime in Seconds

Learn more about hertz.

Radian per Second to Hertz Conversion Table

Table showing various 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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