Kilohertz is 1000 hertz units.
Kilohertz to Radians per second Converter — kHz to rad/s
Convert Kilohertz (kHz) to Radians per second (rad/s) using the exact conversion factor (1 kilohertz = 6,283.185307 radians per second). See the formula, worked examples, and conversion table.
Kilohertz to Radians per second converter
Converter
Frequency Converter
Convert hertz, SI frequency prefixes, RPM, beats per minute, and angular frequency.
Context values
Some unit families need one extra value for a physically accurate result.
Angular frequency converted by one revolution equals 2*pi radians.
Result = input x 1000 / 0.1591549431.
Frequency uses hertz as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Kilohertz to Radians per second
Kilohertz and Radians per second both describe how fast something cycles or rotates, and the conversion is a routine part of reading a car tachometer or motor spec sheet against a scientific frequency figure. Specifically: Kilohertz is 1000 hertz units, and angular frequency converted by one revolution equals 2*pi radians.
Formula
radians per second = kilohertz × 6283.18530718
This factor comes from each unit's defined relationship to the category's base unit: 1 kilohertz equals 1000 base units, and 1 radians per second equals 0.159154943092 base units, so dividing one by the other gives the direct kilohertz-to-radians per second factor of 6283.18530718.
Simple example
1 kHz × 6283.185307 = 6,283.185307 rad/s
1 kilohertz = 6,283.185307 radians per second.
Real-world example
1,000 kHz × 6283.185307 = 6,283,185.307 rad/s
1,000 kilohertz = 6,283,185.307 radians per second.
Conversion table
| Kilohertz (kHz) | Radians per second (rad/s) |
|---|---|
| 60 kHz | 376,991.1184 rad/s |
| 600 kHz | 3,769,911.184 rad/s |
| 1,000 kHz | 6,283,185.307 rad/s |
| 3,000 kHz | 18,849,555.92 rad/s |
| 6,000 kHz | 37,699,111.84 rad/s |
| 10,000 kHz | 62,831,853.07 rad/s |
Reverse conversion: Radians per second to Kilohertz
1 rad/s × 0.0001591549431 = 0.0001591549 kHz
1 radians per second = 0.0001591549 kilohertz.
kilohertz = radians per second × 0.000159154943092
For a page dedicated to this direction, see Radians per second to Kilohertz.
Understanding the Kilohertz (kHz)
Kilohertz is 1000 hertz units.
Understanding the Radians per second (rad/s)
Angular frequency converted by one revolution equals 2*pi radians.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians per second are in 1 kilohertz?
1 kilohertz equals 6,283.185307 radians per second, using the exact defined conversion factor rather than an estimate.
How do I convert kilohertz to radians per second?
Multiply the kilohertz value by 6283.185307. The converter above does this instantly to whatever precision you set.
How do I convert radians per second back to kilohertz?
Use the reverse factor: 1 radians per second equals 0.0001591549 kilohertz. You can also use the swap control in the converter above to flip the direction instantly.
What is a kilohertz?
Kilohertz (kHz) is a unit of frequency.
What is a radians per second?
Radians per second (rad/s) is a unit of frequency.
Is the kilohertz to radians per second conversion exact?
Yes. Both kilohertz and radians per second are defined by fixed standards rather than physical artifacts, so the factor of 6283.185307 used above is exact to as many digits as you choose to display.