Hertz to Radians Per Second Conversion

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

Results in Radians Per Second:
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1 Hz = 6.283185 rad/s

How to Convert Hertz to Radians Per Second

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

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 hertz multiplied by 6.283185.

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

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.


Hertz is formally defined as the frequency equalling 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 = Cycles / Times

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.[2]

Hertz to Radian Per Second Conversion Table

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


  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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