Radians Per Second to Hertz
Convert radians per second to hertz instantly — one radian per second is 0.159155 hertz.
| Radians Per Second | Hertz |
|---|---|
| 1 rad/s | 0.159155 Hz |
| 2 rad/s | 0.31831 Hz |
| 3 rad/s | 0.477465 Hz |
| 5 rad/s | 0.795775 Hz |
| 10 rad/s | 1.591549 Hz |
| 25 rad/s | 3.978874 Hz |
| 50 rad/s | 7.957747 Hz |
| 100 rad/s | 15.915494 Hz |
How to use
- Enter a value in the Radians Per Second field.
- The Hertz figure appears immediately — no button to press.
- Typing in the Hertz field converts back to Radians Per Second the same way.
- Use the reference table for the values that come up most often.
Radians Per Second to Hertz formula
Converting radians per second to hertz is a single multiplication by 0.159154943.
Hz = rad/s × 0.159154943
Why this factor: the radian per second and the hertz are both defined against the hertz, so dividing one definition by the other gives 0.159154943 directly. Both definitions are set out in full below.
To go the other way, divide by 0.159154943 — or use the Hertz to Radians Per Second converter, which is the same calculation reversed.
Worked example
Given 1000 rad/s, multiplying by 0.159154943 yields 159.154943 Hz.
1000 rad/s × 0.159154943 = 159.154943 Hz
The converter above does this for any value you type, in either direction.
What is a radian per second?
Radians per second is the SI measure of angular velocity — how fast an angle is swept out.
Definition: One full revolution is 2π radians, so 1 rad/s equals 1/(2π) hertz, about 0.159155 Hz.
Where it is used: Rotational dynamics, control systems, signal processing, and motor modeling.
Worth knowing: Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
What is a hertz?
The hertz is the SI unit of frequency — one cycle per second.
Definition: Defined as one reciprocal second (s⁻¹). Named after Heinrich Hertz.
Where it is used: Mains electricity (50 or 60 Hz), audio frequencies, and display refresh rates.
Radians Per Second vs Hertz
The radian per second and the hertz belong to the same family of units, so converting between them is usually a matter of shifting a decimal point or applying a small whole-number factor.
Frequently asked questions
How many hertz are in a radian per second?
One radian per second equals 0.159154943 hertz.
What is the formula to convert radians per second to hertz?
Multiply the number of radians per second by 0.159154943. To reverse it, divide by 0.159154943 instead.
How do I convert hertz back to radians per second?
Divide by 0.159154943, which is the same as multiplying by 6.28318531.
How many hertz are in 10 radians per second?
10 rad/s works out to 1.591549 Hz.
Is there anything to watch out for with radians per second?
Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
How is the radian per second defined?
One full revolution is 2π radians, so 1 rad/s equals 1/(2π) hertz, about 0.159155 Hz.