About the Hz to rad/s Converter
Hertz count cycles per second, while radians per second count how fast an angle sweeps around, and engineers and physicists often need both. The link is ω = 2πf: one full cycle is 2π radians, about 6.283185 radians. This converter multiplies a frequency in hertz by 2π and shows the angular frequency in radians per second at once. It also lists the same speed in kilohertz, revolutions per minute and degrees per second, so you can move between an electrical frequency such as 50 Hz, a motor speed in rpm and the ω used in AC circuit formulas. It runs in your browser and sends nothing anywhere. Results appear as you type.
Updated October 2026
How to use the Hz to rad/s Converter
- 1Type the frequency in hertz.
- 2Read the angular frequency in radians per second at the top.
- 3See kHz, rpm and degrees per second in the rows below.
- 4Press Copy to copy the sentence, for example 50 Hz = 314.1592654 rad/s.
- 5Change the number to try another frequency.
The formula
ω = 2π × f. A frequency of 1 Hz means one full turn each second, which is 2π radians per second, about 6.2832 rad/s.
To go back, divide rad/s by 2π using the rad/s to Hz converter.
Examples
- 1 Hz = 6.283185 rad/s
- 50 Hz mains = 314.159 rad/s
- 60 Hz mains = 376.991 rad/s
- 1 kHz = 6,283.185 rad/s
- 440 Hz, concert A = 2,764.601 rad/s
Where angular frequency is used
In AC circuit analysis, inductive reactance is ωL and capacitive reactance is 1 divided by ωC, so ω appears in every calculation. In mechanics, a rotating shaft or a pendulum is often described with its angular velocity. In waves, ω pairs with the wave number k in the formula for a travelling wave.
A common slip is to use f where ω is needed, which makes results off by a factor of about 6.28. Convert first, then substitute.
Hertz, rpm and degrees
Three ways to describe the same turning speed are hertz, revolutions per minute and degrees per second. A shaft turning at 10 Hz does 600 rpm, sweeps 3,600 degrees each second and has an angular frequency of 62.83 rad/s. The rows under the answer show all of these, so you can match the unit a formula needs.
Use hertz for cycles, rad/s for formulas and rpm for machines. Mixing them up is the commonest cause of a result that is out by 6.28 or by 60.
Phone and computer
The calculator updates as you type, with the answer below the box on a phone. Angular frequency shows up in circuits and waves as often as hertz. Convert back with the rad/s to Hz Converter, find where a circuit rings with the Resonant Frequency Calculator, and see how a coil reacts with the Inductive Reactance Calculator.
Features
- Exact formula ω = 2πf
- Revolutions per minute and degrees per second shown
- Kilohertz row for quick scaling
- Ten significant digits
- Copy button
- Private, works in your browser
Frequently asked questions
How do I convert Hz to rad/s?
Multiply the frequency by 2π, about 6.283185307. For 50 Hz the answer is about 314.159 rad/s.
What is angular frequency?
It is how fast something turns or oscillates measured as an angle per second. One complete cycle is 2π radians.
What is 60 Hz in rad/s?
About 376.991 rad/s, the angular frequency of mains power in North America.
How do I convert Hz to rpm?
Multiply by 60. A motor turning at 25 Hz turns at 1,500 rpm. The rpm row shows it.
Why do circuit formulas use ω?
Reactance and impedance formulas such as X_L = ωL are simpler with ω than with 2πf, so engineers convert once and reuse it.
Are rad/s and Hz the same unit?
No. They differ by a factor of 2π. Both describe rate, but a hertz counts whole cycles and a radian per second counts angle.
Is my data uploaded?
No.
Can I use this for sound or light?
Yes. Any wave or oscillation has a frequency in hertz and an angular frequency in radians per second. For sound at 1,000 Hz the angular frequency is 6,283 rad/s, and for AC mains at 50 Hz it is 314 rad/s.