Radians Per Second to Kilohertz
Type a value in either box to convert between radians per second and kilohertz. The factor is 0.000159155.
| Radians Per Second | Kilohertz |
|---|---|
| 1 rad/s | 0.000159 kHz |
| 2 rad/s | 0.000318 kHz |
| 3 rad/s | 0.000477 kHz |
| 5 rad/s | 0.000796 kHz |
| 10 rad/s | 0.001592 kHz |
| 25 rad/s | 0.003979 kHz |
| 50 rad/s | 0.007958 kHz |
| 100 rad/s | 0.015915 kHz |
How to use
- Enter a value in the Radians Per Second field.
- The Kilohertz figure appears immediately — no button to press.
- Typing in the Kilohertz 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 Kilohertz formula
To convert radians per second to kilohertz, multiply by 0.000159154943.
kHz = rad/s × 0.000159154943
Why this factor: the radian per second and the kilohertz are both defined against the hertz, so dividing one definition by the other gives 0.000159154943 directly. Both definitions are set out in full below.
To go the other way, divide by 0.000159154943 — or use the Kilohertz to Radians Per Second converter, which is the same calculation reversed.
Worked example
Take 50 rad/s and multiply by the factor 0.000159154943: the result is 0.007958 kHz.
50 rad/s × 0.000159154943 = 0.007958 kHz
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 kilohertz?
A kilohertz is 1,000 cycles per second.
Definition: Exactly 1,000 hertz.
Where it is used: AM radio frequencies, audio sample rates (44.1 kHz for CD audio), and ultrasonic ranges.
Radians Per Second vs Kilohertz
The radian per second is an SI unit while the kilohertz is a metric unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many kilohertz are in a radian per second?
One radian per second equals 0.000159154943 kilohertz.
What is the formula to convert radians per second to kilohertz?
Multiply the number of radians per second by 0.000159154943. To reverse it, divide by 0.000159154943 instead.
How do I convert kilohertz back to radians per second?
Divide by 0.000159154943, which is the same as multiplying by 6283.18531.
How many kilohertz are in 10 radians per second?
10 rad/s works out to 0.001592 kHz.
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.