Convert Hertz to Radians per Second (Hz to rad/s)
1 hertz (Hz) = 6.283185307 radians per second (rad/s). 1 rad/s = 0.1591549431 Hz. Example: 50 Hz = 50 × 6.283185307 = 314.1592654 rad/s.
Also searched as Hz to rad/s, frequency to angular frequency and hertz to radians per second.
1 Hz = 6.283185307 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk hertz to radian per second converter to paste a column from Excel.
How to Convert Hertz to Radian per Second
- 1 Hz = 6.283185307 rad/s
- 1 rad/s = 0.1591549431 Hz
- Example: convert 50 Hz to rad/s: 50 Hz = 50 × 6.283185307 rad/s = 314.1592654 rad/s
Formula
rad/s = Hz × 6.28318530718
Derivation from SI units:
- 1 Hz = 1 s⁻¹, one cycle per second.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
Both units are defined exactly, so the factor is exact. Hertz definition: hertz; Radian per Second definition: radian per second.
Worked examples
- Mains at 50 Hz has ω = 314.1592654 rad/s.
50 Hz × 6.283185307 = 314.1592654 rad/s - A frequency of 1 Hz is 6.283185307 rad/s.
1 Hz × 6.283185307 = 6.283185307 rad/s
Hertz to Radian per Second conversion table
| Hertz (Hz) | Radians per Second (rad/s) |
|---|---|
| 1 Hz | 6.283185307 rad/s |
| 10 Hz | 62.83185307 rad/s |
| 50 Hz | 314.1592654 rad/s |
| 60 Hz | 376.9911184 rad/s |
| 100 Hz | 628.3185307 rad/s |
| 440 Hz | 2764.601535 rad/s |
| 1000 Hz | 6283.185307 rad/s |
| 20000 Hz | 125663.7061 rad/s |
Where it's used
Frequencies in hertz are converted to angular frequency ω in rad/s for AC circuit impedance (X = ωL, 1/ωC), oscillators and wave equations. Multiply by 2π.
Hertz to other frequency units
| Conversion | 1 Hz equals |
|---|---|
| hertz to radian per second | 6.283185307 rad/s |
| hertz to megahertz | 0.000001 MHz |
| hertz to gigahertz | 1 × 10⁻⁹ GHz |
| hertz to revolution per minute | 60 rpm |
| hertz to kilohertz | 0.001 kHz |
| hertz to revolution per second | 1 rps |
| hertz to degree per second | 360 °/s |
| hertz to beat per minute | 60 bpm |
Show 1 more units
| hertz to terahertz | 1 × 10⁻¹² THz |
|---|
Frequently asked questions
Why is ω = 2πf?
One cycle is a full turn of 2π radians, so f cycles per second sweep 2πf radians per second: 50 Hz gives 314.16 rad/s.
How many radians per second are in 1 hertz?
1 Hz = 6.283185307 rad/s.
How do I convert hertz to radians per second?
Multiply the value in Hz by 6.283185307. For example, 50 Hz × 6.283185307 = 314.1592654 rad/s.
Is the Hz 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 Hertz to Radians per Second (Hz to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/hertz-to-radians-per-second/
IEEE
Scientific Converters, "Convert Hertz to Radians per Second (Hz to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/hertz-to-radians-per-second/