Vibration Calculator (Frequency / Displacement / Velocity / Acceleration)

Features

• Enter a frequency plus one amplitude — displacement, velocity or acceleration — and get the rest
• Displacement as peak, peak-to-peak and RMS; the three differ by up to 2.83×, so mixing them flips the answer
• Velocity as peak and RMS in mm/s — the velocity RMS that ISO 10816 bearing criteria use
• Acceleration as peak and RMS, plus the equivalent in g
• The value you supplied is labelled so it cannot be confused with the derived ones
• The assumption behind the arithmetic — simple harmonic motion — is stated in the output
• A frequency of zero or below, or a negative amplitude, is reported with the reason instead of yielding Infinity
• Clearing a number box empties the output rather than silently substituting a default
• Everything runs locally in the browser

How to use

1. Enter the frequency (50 Hz, mains, by default)
2. Enter the amplitude and say whether it is displacement, velocity or acceleration
3. The results appear at once, grouped by displacement, velocity and acceleration

FAQ

What is the difference between peak, peak-to-peak and RMS?

They describe different features of the same vibration. Peak is the distance from zero to the maximum, peak-to-peak the distance from maximum to minimum (twice the peak for a sine), and RMS the equivalent steady value (the peak divided by √2 for a sine). The three differ by as much as 2.83× — compare a peak-to-peak figure against a bearing limit meant for RMS and you conclude "grossly out of tolerance" when the machine may be fine. So all three are listed here.

Why the caveat that RMS only holds for a pure sine?

Because RMS = peak ÷ √2 is a consequence of the simple harmonic motion assumption, not a general definition. Real vibration containing impacts, friction, gear meshing or beating is not sinusoidal, and the ratio between its peak and RMS changes (an impulsive signal has a high peak and a modest RMS, so the ratio is well above √2). Condition monitoring uses velocity RMS against ISO 10816, so the figure here is best read as an estimate of the sinusoidal part.

What is the velocity row for?

The general severity criterion for machine vibration is velocity RMS in mm/s. ISO 10816 divides the velocity RMS in the 10–1000 Hz band into zones marking a machine as good, acceptable or unsatisfactory. So if you are asking "is 4.5 mm/s too much for this pump?", that 4.5 is velocity RMS — and this table has that row directly.

Why does acceleration grow so fast with frequency?

Because differentiating displacement once gives velocity (multiplying by ω = 2πf) and differentiating again gives acceleration (multiplying by another ω) — so acceleration is proportional to the square of frequency. The same displacement at 50 Hz instead of 25 Hz is four times the acceleration. That is also why high-frequency vibration shows a tiny displacement but a substantial acceleration.

Is my data uploaded?

No. The arithmetic runs entirely in browser memory; the page makes no requests and works offline.