Kilohertz to Radians Per Second
Convert kilohertz to radians per second instantly — one kilohertz is 6283.19 radians per second.
| Kilohertz | Radians Per Second |
|---|---|
| 1 kHz | 6283.185307 rad/s |
| 2 kHz | 12566.370614 rad/s |
| 3 kHz | 18849.555922 rad/s |
| 5 kHz | 31415.926536 rad/s |
| 10 kHz | 62831.853072 rad/s |
| 25 kHz | 157079.632679 rad/s |
| 50 kHz | 314159.265359 rad/s |
| 100 kHz | 628318.530718 rad/s |
How to use
- Enter a value in the Kilohertz field.
- The Radians Per Second figure appears immediately — no button to press.
- Typing in the Radians Per Second field converts back to Kilohertz the same way.
- Use the reference table for the values that come up most often.
Kilohertz to Radians Per Second formula
To convert kilohertz to radians per second, multiply by 6283.18531.
rad/s = kHz × 6283.18531
Why this factor: the kilohertz and the radian per second are both defined against the hertz, so dividing one definition by the other gives 6283.18531 directly. Both definitions are set out in full below.
To go the other way, divide by 6283.18531 — or use the Radians Per Second to Kilohertz converter, which is the same calculation reversed.
Worked example
Start with 60 kHz. Multiply by 6283.18531 to get 376991.118431 rad/s.
60 kHz × 6283.18531 = 376991.118431 rad/s
The converter above does this for any value you type, in either direction.
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.
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.
Kilohertz vs Radians Per Second
The kilohertz is a metric unit while the radian per second is an SI 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 radians per second are in a kilohertz?
One kilohertz equals 6283.18531 radians per second.
What is the formula to convert kilohertz to radians per second?
Multiply the number of kilohertz by 6283.18531. To reverse it, divide by 6283.18531 instead.
How do I convert radians per second back to kilohertz?
Divide by 6283.18531, which is the same as multiplying by 0.000159154943.
How many radians per second are in 10 kilohertz?
10 kHz works out to 62831.853072 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 kilohertz defined?
Exactly 1,000 hertz.