Convert Radians per Second to Hertz (rad/s to Hz)
1 radian per second (rad/s) = 0.1591549431 hertz (Hz). 1 Hz = 6.283185307 rad/s. Example: 1000 rad/s = 1000 × 0.1591549431 = 159.1549431 Hz.
Also searched as radians per second to Hz, radians per second in Hz, radians per second into hertz, rad/s to Hz, rad/s in hertz, rad/s into hertz, radian per second to hertz, rad/s to hertz converter and how many hertz in a radian per second.
1 rad/s = 0.1591549431 Hz
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian per second to hertz converter to paste a column from Excel.
How to Convert Radian per Second to Hertz
- 1 rad/s = 0.1591549431 Hz
- 1 Hz = 6.283185307 rad/s
- Example: convert 1000 rad/s to Hz: 1000 rad/s = 1000 × 0.1591549431 Hz = 159.1549431 Hz
Formula
Hz = rad/s × 0.1591549430919
or Hz = rad/s ÷ 6.28318530718
Derivation from SI units:
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 Hz = 1 s⁻¹, one cycle per second.
Both units are defined exactly, so the factor is exact. Radian per Second definition: radian per second; Hertz definition: hertz.
Worked examples
- An angular frequency of 376.991 rad/s is 59.99998115 Hz.
376.991 rad/s × 0.1591549431 = 59.99998115 Hz - A resonance at 1000 rad/s is 159.1549431 Hz.
1000 rad/s × 0.1591549431 = 159.1549431 Hz
Radian per Second to Hertz conversion table
| Radians per Second (rad/s) | Hertz (Hz) |
|---|---|
| 1 rad/s | 0.1591549431 Hz |
| 2 rad/s | 0.3183098862 Hz |
| 3.14159 rad/s | 0.4999995777 Hz |
| 6.28318 rad/s | 0.9999991553 Hz |
| 10 rad/s | 1.591549431 Hz |
| 50 rad/s | 7.957747155 Hz |
| 100 rad/s | 15.91549431 Hz |
| 314.159 rad/s | 49.99995777 Hz |
| 376.991 rad/s | 59.99998115 Hz |
| 1000 rad/s | 159.1549431 Hz |
Where it's used
Angular frequencies in rad/s from circuit analysis and vibration formulas (ω = √(k/m)) are converted to hertz, the unit instruments display. Divide by 2π.
Radian per Second to other frequency units
| Conversion | 1 rad/s equals |
|---|---|
| radian per second to hertz | 0.1591549431 Hz |
| radian per second to megahertz | 1.591549431 × 10⁻⁷ MHz |
| radian per second to gigahertz | 1.591549431 × 10⁻¹⁰ GHz |
| radian per second to revolution per minute | 9.549296586 rpm |
| radian per second to kilohertz | 0.0001591549431 kHz |
| radian per second to revolution per second | 0.1591549431 rps |
| radian per second to degree per second | 57.29577951 °/s |
| radian per second to beat per minute | 9.549296586 bpm |
Show 1 more units
| radian per second to terahertz | 1.591549431 × 10⁻¹³ THz |
|---|
Frequently asked questions
How do I convert ω to f?
Divide by 2π: ω = 1000 rad/s gives f = 159.1549431 Hz.
How many hertz are in 1 radian per second?
1 rad/s = 0.1591549431 Hz.
How do I convert radians per second to hertz?
Multiply the value in rad/s by 0.1591549431, or divide it by 6.283185307. For example, 1000 rad/s × 0.1591549431 = 159.1549431 Hz.
Is the rad/s to Hz 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 Radians per Second to Hertz (rad/s to Hz). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/radians-per-second-to-hertz/
IEEE
Scientific Converters, "Convert Radians per Second to Hertz (rad/s to Hz)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/radians-per-second-to-hertz/