Hertz to Radians per Second Converter

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

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1 Hz = 6.283185 rad/s

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How to Convert Hertz to Radians per Second

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To convert a measurement in hertz to a measurement in radians per second, multiply the frequency by the following conversion ratio: 6.283185 radians per second/hertz.

Since one hertz is equal to 6.283185 radians per second, you can use this simple formula to convert:

radians per second = hertz × 6.283185

The frequency in radians per second is equal to the frequency in hertz multiplied by 6.283185.

For example, here's how to convert 5 hertz to radians per second using the formula above.
radians per second = (5 Hz × 6.283185) = 31.415927 rad/s
conversion scale showing hertz and equivalent radians per second frequency values

How Many Radians per Second Are in a Hertz?

There are 6.283185 radians per second in a hertz, which is why we use this value in the formula above.

1 Hz = 6.283185 rad/s

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

ω = 2πƒ

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

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

What is a Hertz?

One hertz is formally defined as the frequency of one cycle per second.[1]

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.

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.[2] For example, rad/s is expressing a change in angle relative to a change in time.

Learn more about radians per second.

Hertz to Radian per Second Conversion Table

Table showing various hertz measurements converted to radians per second.
Hertz Radians Per Second
1 Hz 6.2832 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 37.7 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
11 Hz 69.12 rad/s
12 Hz 75.4 rad/s
13 Hz 81.68 rad/s
14 Hz 87.96 rad/s
15 Hz 94.25 rad/s
16 Hz 100.53 rad/s
17 Hz 106.81 rad/s
18 Hz 113.1 rad/s
19 Hz 119.38 rad/s
20 Hz 125.66 rad/s
21 Hz 131.95 rad/s
22 Hz 138.23 rad/s
23 Hz 144.51 rad/s
24 Hz 150.8 rad/s
25 Hz 157.08 rad/s
26 Hz 163.36 rad/s
27 Hz 169.65 rad/s
28 Hz 175.93 rad/s
29 Hz 182.21 rad/s
30 Hz 188.5 rad/s
31 Hz 194.78 rad/s
32 Hz 201.06 rad/s
33 Hz 207.35 rad/s
34 Hz 213.63 rad/s
35 Hz 219.91 rad/s
36 Hz 226.19 rad/s
37 Hz 232.48 rad/s
38 Hz 238.76 rad/s
39 Hz 245.04 rad/s
40 Hz 251.33 rad/s

References

  1. National Institute of Standards and Technology, SI Units - Time, https://www.nist.gov/pml/owm/si-units-time
  2. 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

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