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Displacement = Velocity / (2πf), where f is the frequency in Hz. Specifically, for peak values: d_0pk (μm) = v_peak (mm/s) / (2πf) × 1000. The peak-to-peak displacement is double the 0-peak value.

The standard reference for vibration velocity in dB is 10⁻⁹ m/s (= 1 nm/s = 10⁻⁶ mm/s). The formula is:

dB = 20 × log₁₀(v_RMS / 10⁻⁹)

where v_RMS is in m/s. For example, 1 mm/s RMS = 120 dB.

For a pure sinusoidal signal:

• Peak = RMS × √2 ≈ RMS × 1.414
• Peak-to-Peak = 2 × Peak
• RMS = Peak / √2 ≈ Peak × 0.7071

These ratios only hold for pure sine waves. For complex vibration signals with multiple harmonics, the crest factor (Peak/RMS) will differ from √2.

First convert velocity to acceleration using a = v × 2πf. With velocity in mm/s:

a (m/s²) = v (mm/s) × 2πf / 1000

Then divide by g = 9.80665 m/s² to get the value in g units. Note: this requires knowing the vibration frequency.

Velocity, displacement, and acceleration are related through calculus — each is the time derivative of the previous. For a sinusoid at frequency f, differentiating multiplies the amplitude by 2πf. Therefore, converting between these quantities requires knowing the frequency.

Only conversions within the same quantity (e.g., RMS to peak) are frequency-independent.