Hertz to Radians Per Second
Convert hertz to radians per second instantly — one hertz is 6.28319 radians per second.
| Hertz | Radians Per Second |
|---|---|
| 1 Hz | 6.283185 rad/s |
| 2 Hz | 12.566371 rad/s |
| 3 Hz | 18.849556 rad/s |
| 5 Hz | 31.415927 rad/s |
| 10 Hz | 62.831853 rad/s |
| 25 Hz | 157.079633 rad/s |
| 50 Hz | 314.159265 rad/s |
| 100 Hz | 628.318531 rad/s |
How to use
- Enter a value in the Hertz field.
- The Radians Per Second figure appears immediately — no button to press.
- Typing in the Radians Per Second field converts back to Hertz the same way.
- Use the reference table for the values that come up most often.
Hertz to Radians Per Second formula
Converting hertz to radians per second is a single multiplication by 6.28318531.
rad/s = Hz × 6.28318531
Why this factor: the hertz and the radian per second are both defined against the hertz, so dividing one definition by the other gives 6.28318531 directly. Both definitions are set out in full below.
To go the other way, divide by 6.28318531 — or use the Radians Per Second to Hertz converter, which is the same calculation reversed.
Worked example
Given 1000 Hz, multiplying by 6.28318531 yields 6283.185307 rad/s.
1000 Hz × 6.28318531 = 6283.185307 rad/s
The converter above does this for any value you type, in either direction.
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.
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.
Hertz vs Radians Per Second
The hertz and the radian per second 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 radians per second are in a hertz?
One hertz equals 6.28318531 radians per second.
What is the formula to convert hertz to radians per second?
Multiply the number of hertz by 6.28318531. To reverse it, divide by 6.28318531 instead.
How do I convert radians per second back to hertz?
Divide by 6.28318531, which is the same as multiplying by 0.159154943.
How many radians per second are in 10 hertz?
10 Hz works out to 62.831853 rad/s.
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 hertz defined?
Defined as one reciprocal second (s⁻¹). Named after Heinrich Hertz.