About the rad/s to Hz Converter
An angular frequency ω in radians per second tells you how fast an angle changes, but a signal generator, a motor label or a mains supply is specified in hertz. This converter divides the angular frequency by 2π to give the ordinary frequency, f = ω ÷ 2π. Type radians per second and read hertz at once, with kilohertz, revolutions per minute and degrees per second listed under it. For example ω = 314.16 rad/s is almost exactly 50 Hz. It helps when a formula or a simulation gives you ω and you want to know what to set on a real instrument. Everything is worked out in your browser, so your numbers stay private.
Updated October 2026
How to use the rad/s to Hz Converter
- 1Type the angular frequency in radians per second.
- 2Read the frequency in hertz at the top.
- 3Check rpm and degrees per second in the rows below.
- 4Press Copy to copy the sentence.
- 5Change the number to try another value.
The formula
f = ω ÷ 2π. A full turn is 2π radians, so dividing the angle swept each second by the angle in one turn gives the number of turns per second.
For the opposite direction use the Hz to rad/s converter.
Examples
- 6.283185 rad/s = 1 Hz
- 314.159 rad/s = 50 Hz
- 376.991 rad/s = 60 Hz
- 1,000 rad/s = 159.155 Hz
- 10 rad/s = 1.59155 Hz = 95.49 rpm
Turning a formula result into a setting
A resonant circuit has ω₀ = 1 divided by √(LC). If L is 10 mH and C is 100 nF, then ω₀ = 31,623 rad/s. Divide by 2π to get 5,033 Hz, which is the frequency you would set on a signal generator to find the resonance.
The same step turns the angular speed of a spinning part into a motor setting: 150 rad/s corresponds to 23.87 Hz, or about 1,432 rpm.
Checking your answer
A quick sanity check: dividing by 6.28 is roughly dividing by six. So 600 rad/s should come out a bit under 100 Hz, and it does, at 95.49 Hz. If your result is larger than the input, something went wrong.
When ω comes from a simulation or a textbook problem, also check whether the source meant angular frequency or an ordinary frequency, since some documents write both as f or w.
Why 2π?
A radian is defined so that a full circle is 2π of them. That is why every conversion between turns and radians carries the factor 6.283185. If a calculation seems to give a frequency that is oddly large or small, check that you divided by 2π exactly once.
Phone and computer
Results update as you type, in one column on a phone. Angular frequency makes circuit sums easier, while hertz is more familiar. Convert back with the Hz to rad/s Converter, find a circuit's natural frequency with the Resonant Frequency Calculator, and find a coil's reaction with the Inductive Reactance Calculator.
Features
- Exact formula f = ω ÷ 2π
- Revolutions per minute and degrees per second shown
- Kilohertz row for large values
- Ten significant digits
- Copy button
- No upload
Frequently asked questions
How do I convert rad/s to Hz?
Divide by 2π, about 6.283185307. For example 628.3185 rad/s is 100 Hz.
What is 100 rad/s in Hz?
About 15.9155 Hz.
What is 1 rad/s in rpm?
About 9.5493 rpm, because rpm is 60 times Hz and Hz is 1 divided by 2π times rad/s.
Why is ω written in rad/s?
Because the radian is the natural unit of angle for calculus and physics, so formulas involving oscillation and rotation are simpler in radians.
Is the result a frequency or a speed?
Both. For a rotating shaft, hertz are turns per second, and for a signal they are cycles per second.
Does the tool handle negative values?
Yes. A negative angular frequency means rotation in the opposite direction and gives a negative frequency.
Is my number uploaded?
No.
How do I convert rad/s to rpm?
Multiply by 60 and divide by 2π, which is about 9.5493. The rpm row shows it. A drive shaft at 188.5 rad/s turns at 1,800 rpm.