Radians per Second to Hertz Converter
Enter the frequency in radians per second below to convert it to hertz.
Result in Hertz:
Do you want to convert hertz to radians per second?
On this page:
- Radians per Second to Hertz Converter
- How to Convert Radians per Second to Hertz
- How Many Hertz Are in One Radian per Second?
- What Are Radians per Second?
- What Is a Hertz?
- Radian per Second to Hertz Conversion Table
- References
- More Radian per Second & Hertz Conversions
- Convert from Radians per Second
- Convert to Hertz
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How to Convert Radians per Second to Hertz
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
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 = ω / 2π
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 = Cycles / Time in Seconds
Learn more about hertz.
Radian per Second to Hertz Conversion Table
| 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
- 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
- National Institute of Standards and Technology, SI Units - Time, https://www.nist.gov/pml/owm/si-units-time