What is vibration displacement?

Vibration displacement is the total distance a vibrating object moves from its rest position. It is typically measured in micrometers (μm) and can be expressed as peak (0-peak, the maximum excursion from center) or peak-to-peak (the full range of motion). Displacement is most useful for evaluating low-frequency vibration below about 10 Hz.

How do you convert vibration velocity to displacement?

To convert velocity (mm/s RMS) to displacement (μm peak-to-peak), use the formula: d_pp = v_RMS × √2 × 1000 / (π × f), where f is the frequency in Hz. The √2 factor converts RMS to peak, and dividing by (π × f) is the integration from velocity to displacement. The factor 1000 converts mm to μm.

What is the relationship between displacement, velocity, and acceleration?

For sinusoidal vibration, displacement, velocity, and acceleration are mathematically related through frequency. Velocity is the time derivative of displacement (v = 2πf × d), and acceleration is the time derivative of velocity (a = 2πf × v). This means higher frequencies amplify acceleration relative to displacement, which is why displacement measurements are preferred at low frequencies and acceleration at high frequencies.

When should I use displacement instead of velocity for vibration monitoring?

Displacement is most useful for low-frequency vibration monitoring, typically below 10 Hz (600 RPM). At low frequencies, velocity and acceleration values become very small even when displacement is significant. Large slow-speed machines like paper mill rolls, cooling tower fans, and reciprocating compressors often require displacement-based monitoring. Velocity (mm/s RMS) is preferred for general machinery in the 10–1000 Hz range, while acceleration is best above 1000 Hz.

Free Engineering Tool

Vibration Displacement Calculator

Convert vibration velocity (mm/s RMS) to displacement (μm peak-to-peak) and acceleration (m/s², g) at any frequency. Enter velocity and frequency to get all vibration parameters.

Velocity → Displacement Hz / RPM Peak & Peak-to-Peak

Results

Displacement (peak-to-peak)

—

Displacement (0-peak)

—

Velocity RMS

—

Velocity Peak

—

Acceleration Peak

—

Acceleration (g)

—

Frequency

—

Displacement (peak-to-peak)

Displacement (0-peak)

Acceleration (peak)

Where:

v_RMS — vibration velocity RMS (mm/s)
f — frequency (Hz). If RPM: f = RPM / 60
√2 — converts RMS to peak (sinusoidal signals)
g — 9.80665 m/s² (standard gravity)

Note: d_p-p = 2 × d_peak. The factor 1000 converts mm to μm.

Practical Example

Example — Machine at 50 Hz, 3.5 mm/s RMS

Velocity peak = 3.5 × √2 = 4.950 mm/s

Displacement p-p = 3.5 × √2 × 1000 / (π × 50) = 31.50 μm

Displacement 0-peak = 31.50 / 2 = 15.75 μm

Acceleration peak = 3.5 × √2 × 2π × 50 / 1000 = 1.556 m/s²

Acceleration in g = 1.556 / 9.80665 = 0.159 g

Vibration Parameters — Quick Reference

Parameter	Symbol	Unit	Best Range
Displacement	d	μm (mils)	Low frequency < 10 Hz
Velocity	v	mm/s (in/s)	10 – 1000 Hz
Acceleration	a	m/s² (g)	> 1000 Hz

Vibration displacement is the total distance a vibrating object moves from its rest position. It is measured in micrometers (μm) or mils (1 mil = 25.4 μm) and can be expressed as peak (0-peak) or peak-to-peak.

Displacement is the most important vibration parameter for low-frequency machinery — typically below 10 Hz (600 RPM). At low frequencies, velocity and acceleration values become very small even when physical movement is significant.

Peak displacement (0-peak) measures the maximum excursion from the center rest position in one direction. Peak-to-peak displacement measures the total range of motion — from the maximum positive to the maximum negative excursion.

For sinusoidal vibration, peak-to-peak equals exactly twice the peak value: d_p-p = 2 × d_peak. Most specifications use peak-to-peak values.

To convert velocity (mm/s RMS) to displacement (μm peak-to-peak), use:

d_p-p = v_RMS × √2 × 1000 / (π × f)

where f is frequency in Hz. The √2 converts RMS to peak, dividing by (π × f) integrates velocity to displacement, and × 1000 converts mm to μm. If you know RPM instead of Hz, divide RPM by 60 first.

For sinusoidal vibration, these parameters are related through frequency via calculus. Velocity is the derivative of displacement: v_peak = 2πf × d_peak. Acceleration is the derivative of velocity: a_peak = 2πf × v_peak = (2πf)² × d_peak.

Higher frequencies amplify acceleration relative to displacement. A small displacement at high frequency produces large acceleration, while large displacement at low frequency may produce negligible acceleration.

Use displacement for low-frequency vibration monitoring, typically below 10 Hz (600 RPM). Large slow-speed machines such as paper mill rolls, cooling tower fans, wind turbines, and reciprocating compressors require displacement monitoring.

Velocity (mm/s RMS) is the standard for general machinery in the 10–1000 Hz range (ISO 10816). Acceleration is preferred above 1000 Hz for bearing defects and gear mesh.

The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.