Engineering reference – source controlled
Single-Frequency Vibration Displacement Converter
Convert the displacement magnitude of one scalar sinusoidal vibration component to velocity and acceleration magnitudes at that same frequency. Units and RMS, peak and peak-to-peak descriptors remain explicit.
Single-component displacement record
All fields are required. Displacement may be zero; frequency must be positive. Decimal point and decimal comma are accepted. Grouped numbers, exponents and unit suffixes are rejected.
Equations, descriptors and units
Normalize the displacement descriptor
input peak: xRMS = x / sqrt(2)
input peak-to-peak: xRMS = x / (2 sqrt(2))
These descriptor factors apply to one sine wave. The page first converts the selected displacement unit to metres, then normalizes it to RMS.
Single sinusoidal component
vRMS = omega xRMS
aRMS = omega² xRMS
peak = sqrt(2) RMS
peak-to-peak = 2 peak
Velocity leads displacement by 90 degrees and acceleration is 180 degrees from displacement for the stated sine convention. This page reports magnitudes only; it does not reconstruct a time waveform or preserve phase.
Exact unit factors and conventional standard acceleration
1 mm = 10^-3 m
1 mil = 0.001 in = 25.4 µm
1 in = 0.0254 m
a[g_n] = a[m/s²] / 9.80665
The metre and inch conversion is exact. BIPM records the conventional standard acceleration as 980.665 cm/s², equal to 9.80665 m/s². A value in g_n is a reference ratio and not a severity category.
Why the former general recommendations were removed
- A broadband overall displacement cannot be converted with one representative frequency. Each complex frequency component has its own omega weighting.
- “Displacement below 10 Hz, velocity from 10 to 1000 Hz, acceleration above 1000 Hz” is not a universal ISO rule. Quantity and band depend on the machine, measurement purpose, sensor/probe response, point, direction and applicable procedure.
- Peak = sqrt(2) x RMS and peak-to-peak = 2 x peak are sine-wave relationships, not general rules for shocks, runout, non-sinusoidal motion or an orbit.
- RPM is a rotational rate. It equals the component frequency only for the 1x rotational order; harmonics, blade/vane pass, gear mesh and bearing components have other frequencies.
- A displacement magnitude alone cannot establish shaft-to-bearing clearance, stress, rub risk, orbit shape, phase, machine condition or acceptance.
Standard and source record
| Source | Status checked 16 Jul 2026 | What it supports here | What it does not support |
|---|---|---|---|
| ISO 20816-1:2016, Edition 1 | Published; stage 90.92, to be revised; ISO/FDIS 20816-1 is under development. | General machine-vibration measurement/evaluation framework and the need to define quantities, measurement types and scope. | It is not the source of these elementary sine equations and does not make this an ISO severity or shaft-clearance calculator. |
| ISO 2041:2018, Edition 4 | Published and confirmed in 2024; stage 90.93. | Current mechanical-vibration, shock and condition-monitoring vocabulary record. | A vocabulary standard is not a machine alarm or clearance table. |
| Brüel & Kjær, Measuring Vibration, br0094, pp. 5-7 | Official manufacturer full-text primer; relevant printed pages visually checked. | Sine RMS/peak/peak-to-peak descriptors, scalar sinusoidal displacement/velocity/acceleration relationships, phase relationships and frequency weighting. | Historical practical discussion is not imported as a current universal ISO band or limit. |
| BIPM SI Brochure, 9th edition, version 4.01, June 2026, Appendix 1 p. 154 | Current official SI brochure version at the audit date. | Conventional standard acceleration g_n = 980.665 cm/s² = 9.80665 m/s². | g_n conversion does not establish vibration severity. |
Worked sine example
For one scalar 25 Hz sinusoidal component with displacement 100 µm peak-to-peak: xPeak = 50 µm, xRMS = 35.35533906 µm, vRMS = 5.553603673 mm/s, vPeak = 7.853981634 mm/s, aRMS = 0.872358025 m/s² and aPeak = 1.233700550 m/s². The button loads these values but leaves every scope confirmation unchecked. This is an arithmetic example, not an acceptance limit.
Questions fréquemment posées
Can I use overall displacement and running speed?
Only when the value is demonstrably one scalar sinusoidal component at that frequency. A broadband overall or waveform containing harmonics requires component-wise or validated time-domain processing.
Is peak-to-peak always twice peak?
For one centered sine wave, yes. It is not a general relation for arbitrary waveforms, runout, transients or a two-dimensional orbit.
Does the result comply with ISO 20816?
No compliance verdict is produced. An evaluation needs the applicable part, machine scope, absolute or relative quantity, descriptor, frequency band, measurement point/direction, support and operating state.
Can the result be compared directly with shaft clearance?
No. Probe geometry, runout, scale factor, reference position, orbit, phase, thermal position and the applicable machinery procedure must be considered. This page calculates one scalar component magnitude only.
Why is g_n written with a subscript?
It identifies the conventional standard acceleration 9.80665 m/s² used as a reference ratio, not location-dependent free-fall acceleration and not a severity class.
