Convert Kilohertz to Radians per Second (kHz to rad/s)
1 kilohertz (kHz) = 6283.185307 radians per second (rad/s). 1 rad/s = 0.0001591549431 kHz. Example: 15 kHz = 15 × 6283.185307 = 94247.77961 rad/s.
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1 kHz = 6283.185307 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk kilohertz to radian per second converter to paste a column from Excel.
How to Convert Kilohertz to Radian per Second
- 1 kHz = 6283.185307 rad/s
- 1 rad/s = 0.0001591549431 kHz
- Example: convert 15 kHz to rad/s: 15 kHz = 15 × 6283.185307 rad/s = 94247.77961 rad/s
Formula
rad/s = kHz × 6283.18530718
Derivation from SI units:
- 1 kHz = 10³ Hz.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 kHz = 1000 Hz ÷ 0.1591549430919 Hz per rad/s = 6283.18530718 rad/s
Both units are defined exactly, so the factor is exact. Kilohertz definition: kilohertz; Radian per Second definition: radian per second.
Worked examples
- A reading of 16 kHz converts to 100530.9649 rad/s.
16 kHz × 6283.185307 = 100530.9649 rad/s - A value of 48 kHz is 301592.8947 rad/s.
48 kHz × 6283.185307 = 301592.8947 rad/s
Kilohertz to Radian per Second conversion table
| Kilohertz (kHz) | Radians per Second (rad/s) |
|---|---|
| 1 kHz | 6283.185307 rad/s |
| 4 kHz | 25132.74123 rad/s |
| 8 kHz | 50265.48246 rad/s |
| 16 kHz | 100530.9649 rad/s |
| 20 kHz | 125663.7061 rad/s |
| 44.1 kHz | 277088.472 rad/s |
| 48 kHz | 301592.8947 rad/s |
| 100 kHz | 628318.5307 rad/s |
| 531 kHz | 3336371.398 rad/s |
| 1600 kHz | 10053096.49 rad/s |
Where it's used
Kilohertz are used for audio sample rates, while radians per second appear in angular velocity in physics and dynamics. Both measure frequency and rotational speed, so the conversion is a fixed factor.
Kilohertz to other frequency units
| Conversion | 1 kHz equals |
|---|---|
| kilohertz to radian per second | 6283.185307 rad/s |
| kilohertz to hertz | 1000 Hz |
| kilohertz to megahertz | 0.001 MHz |
| kilohertz to gigahertz | 0.000001 GHz |
| kilohertz to revolution per minute | 60000 rpm |
| kilohertz to revolution per second | 1000 rps |
| kilohertz to degree per second | 360000 °/s |
| kilohertz to beat per minute | 60000 bpm |
Show 1 more units
| kilohertz to terahertz | 1 × 10⁻⁹ THz |
|---|
Frequently asked questions
How many radians per second are in 1 kilohertz?
1 kHz = 6283.185307 rad/s.
How do I convert kilohertz to radians per second?
Multiply the value in kHz by 6283.185307. For example, 15 kHz × 6283.185307 = 94247.77961 rad/s.
Is the kHz to rad/s conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 7 (SI prefixes); hertz, Table 4.
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Kilohertz to Radians per Second (kHz to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/kilohertz-to-radians-per-second/
IEEE
Scientific Converters, "Convert Kilohertz to Radians per Second (kHz to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/kilohertz-to-radians-per-second/