Pump Selection Interactive engineering tool

Acceleration in G’s to Displacement in Mils Calculator

Convert between peak acceleration in g, peak-to-peak displacement in mils, and vibration frequency in CPM. Enter any two variables to solve the third for a discrete sinusoidal frequency.

  • US + metric
  • Formula shown
  • Shareable results

Acceleration, Displacement & Frequency

g pk
mil pk-pk
CPM

Enter any two variables The highlighted field is calculated automatically using a single-frequency sinusoidal relationship.

Peak acceleration 0.18405 g pk (1.805 m/s² pk)

Filtered, discrete frequency only Acceleration 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.

Peak acceleration (A) 0.18405 g pk
Peak acceleration — SI 1.805 m/s² pk
Peak-to-peak displacement (X) 1 mil pk-pk
Displacement amplitude (peak) 0.5 mil pk
Discrete frequency (f) 3,600 CPM (60 Hz)
Angular frequency (ω) 376.99 rad/s
Peak velocity 0.1885 in/s pk
Formula & method

Apk = (2πf)² Xpk = (2πf)² Xpp / 2  ·  f = CPM / 60

f = 3,600 / 60 = 60 Hz
Apk = (2π × 60)² × (1 mil × 0.001 in/mil × 0.0254 m/in) / 2
Apk = 1.80495 m/s² = 0.184054 g pk

For the US vibration inputs shown, A(g pk) = 1.4201698269 × 10⁻⁸ × X(mil pk-pk) × CPM². The coefficient is derived from standard gravity and the exact international inch.

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 acceleration, displacement, and frequency for one sinusoidal vibration component. Choose the variable to calculate, then enter the other two. US vibration units use peak acceleration in g, peak-to-peak displacement in mils, and cycles per minute (CPM); the metric view uses g peak, micrometres peak-to-peak, and hertz.

The sinusoidal relationship

For displacement x(t) = Xpk sin(2πft), differentiating twice gives a peak acceleration magnitude of Apk = (2πf)²Xpk. Because the entered displacement is peak-to-peak, Xpk = Xpp/2, so Apk = (2πf)²Xpp/2. Frequency in hertz is CPM divided by 60.

Solve in any direction

  • Acceleration (A) — enter peak-to-peak displacement and frequency.
  • Displacement (Xpp) — enter peak acceleration and frequency.
  • Frequency (CPM or Hz) — enter peak acceleration 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 acceleration of 0.18405 g, equivalent to 1.80495 m/s². Solving backward with 0.18405 g and 3,600 CPM returns 1 mil peak-to-peak.

Amplitude conventions matter

This tool pairs peak acceleration with peak-to-peak displacement. Do not enter RMS acceleration 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 a consistent amplitude convention.

Assumptions and limits

  • The vibration is sinusoidal and occurs at one discrete, filtered frequency.
  • Acceleration is peak amplitude and displacement is peak-to-peak excursion.
  • CPM means cycles per minute. It 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.

Variables

Symbol Meaning US unit SI unit
A Peak sinusoidal acceleration amplitude g peak g peak
Xpp Peak-to-peak sinusoidal displacement mil pk-pk micrometre pk-pk
f Discrete vibration frequency CPM Hz
omega Angular frequency rad/s rad/s

Related calculators

Standards referenced

Brüel &amp Kjær Sound and Vibration Handbook sinusoidal relationships NIST SP 811 standard gravity and inch definition

Verified Constants and formula two-source checked (PumpCalcs engineering review, 2026-08-26).

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