Velocity in in/sec Peak to Displacement in Mils Peak-to-Peak Calculator
Convert between peak vibration velocity in in/sec, peak-to-peak displacement in mils, and frequency in CPM. Enter any two variables to solve the third for a discrete sinusoidal frequency.
US + metric
Formula shown
Shareable results
Velocity, Displacement & Frequency
in/s pk
mil pk-pk
CPM
Enter any two variables
The highlighted field is calculated automatically using a single-frequency sinusoidal relationship.
Filtered, discrete frequency only
Velocity must be peak amplitude and displacement must be peak-to-peak. This conversion does not apply to broadband, random, shock, transient, or unfiltered overall vibration.
For the US vibration inputs shown, V(in/s pk) = 0.00005235987756 × X(mil pk-pk) × CPM. The coefficient includes the peak-to-peak to peak factor of two.
For preliminary analysis and educational use. Verify amplitude conventions, frequency filtering, sensor bandwidth, mounting, calibration, and signal-processing settings before using a result for machinery decisions.
This calculator converts among peak vibration velocity, peak-to-peak displacement, and frequency for one sinusoidal vibration component. Choose the variable to calculate, then enter the other two. US vibration units use in/sec peak, mils peak-to-peak, and cycles per minute (CPM); the metric view uses mm/s peak, micrometres peak-to-peak, and hertz.
The sinusoidal relationship
For sinusoidal displacement x(t) = Xpk sin(2πft), peak velocity is Vpk = 2πfXpk. Because the entered displacement is peak-to-peak, Xpk = Xpp/2, so Vpk = 2πfXpp/2. The inverse forms are Xpp = 2Vpk/(2πf) and f = Vpk/(πXpp). Frequency in hertz is CPM divided by 60.
Solve in any direction
Peak velocity (Vips) — enter peak-to-peak displacement and frequency.
Peak-to-peak displacement (Xpp) — enter peak velocity and frequency.
Frequency (CPM or Hz) — enter peak velocity and peak-to-peak displacement.
Worked example
A filtered sinusoidal vibration of 1 mil peak-to-peak at 3,600 CPM (60 Hz) has a peak displacement amplitude of 0.5 mil and a peak velocity of 0.188496 in/sec, equivalent to 4.78779 mm/s. Solving backward with that velocity and frequency returns 1 mil peak-to-peak.
Amplitude conventions matter
This tool pairs peak velocity with peak-to-peak displacement. Do not enter RMS velocity without converting it to peak for a sinusoid (peak = RMS × √2). Likewise, do not enter zero-to-peak displacement in the peak-to-peak field without doubling it.
Discrete-frequency assumption
The conversion is valid for a single sinusoidal component at a known frequency, such as a filtered spectral line. It does not convert broadband, random, transient, shock, or unfiltered overall vibration. For a spectrum, convert each frequency component separately while keeping consistent amplitude conventions.
Assumptions and limits
The vibration is sinusoidal and occurs at one discrete, filtered frequency.
Velocity is peak amplitude and displacement is peak-to-peak excursion.
CPM equals shaft rpm only for a 1× rotational vibration component.
The mathematical result does not account for sensor bandwidth, integration noise, filtering, mounting, or calibration uncertainty.
Brüel &Kjær Sound and Vibration Handbook sinusoidal relationshipsNIST SP 811 inch definition
Verified
Constants and formula two-source checked (PumpCalcs engineering review, 2026-08-26).
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