Engineering reference – source controlled
Single-Frequency Sinusoidal Vibration Converter
Convert the RMS velocity magnitude of one sinusoidal component to acceleration and displacement magnitudes at that same frequency. RMS, peak and peak-to-peak descriptors remain explicit.
Single-component record
All fields are required. Velocity may be zero; frequency must be positive. Decimal point and decimal comma are accepted, while grouped numbers, exponents and unit suffixes are rejected.
Equations and descriptor discipline
Single sinusoidal component
aRMS = omega vRMS
aPeak = sqrt(2) aRMS
xRMS = vRMS / omega
xPeak = sqrt(2) xRMS
xPP = 2 xPeak
Velocity is converted to m/s before the equations. Acceleration is in m/s² and displacement in metres before display conversion. The magnitudes are related at one common frequency; differentiation introduces a 90-degree phase shift between velocity and acceleration, while this page reports magnitude only.
Conventional standard acceleration
The BIPM SI Brochure records the conventional standard acceleration as 980.665 cm/s², equal to 9.80665 m/s². Here “g_n” is a ratio to that conventional reference; m/s² remains the coherent SI acceleration unit.
Why an overall RMS value cannot use one representative frequency
Differentiation weights each frequency component by its own angular frequency. A multi-frequency or random signal therefore requires frequency-domain processing of each complex component, or a validated instrument/time-domain method with the stated filters. Peak = sqrt(2) x RMS is also a sine-wave relation, not a general crest-factor rule.
Standard and source record
| Sumber | 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 measurement/evaluation framework; different quantities and methods require clear definition and limitations. | It is not the source of these elementary sine equations and does not make this an “ISO 20816 calculator”. |
| ISO 20816-3:2022, Edition 1 | Published; stage 90.92, to be revised. | Illustrates why evaluation scope matters: coupled industrial machines above 15 kW and 120 to 30,000 r/min, with specified measurement/application conditions. | It does not justify universal “good/acceptable/alarm” acceleration bands or a generic g threshold. |
| ISO 2041:2018, Edition 4 | Published and confirmed in 2024; stage 90.93. | Current mechanical-vibration, shock and condition-monitoring vocabulary reference. | A vocabulary standard is not a machine-severity table. |
| Brüel & Kjær, Measuring Vibration, br0094, PDF metadata modified 2016, pp. 5-7 | Official manufacturer primer; pages visually checked. | Sine RMS/peak/peak-to-peak descriptors; sinusoidal displacement/velocity/acceleration relationship; multi-frequency wideband measurements weight parameters differently. | Its historical practical bands are not imported as current universal ISO limits. |
| 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 alone does not establish vibration severity. |
Worked sine example
For one 25 Hz sinusoidal component with velocity 4.5 mm/s RMS: omega = 157.0796327 rad/s, aRMS = 0.7068583471 m/s², aPeak = 0.9996486611 m/s², xRMS = 28.64788976 µm and xPP = 81.02846845 µm. The button loads these values but deliberately leaves the confirmations unchecked. This arithmetic example applies the published sine relationships; it is not an ISO acceptance example.
Common invalid uses
- Using an overall 10-1000 Hz velocity RMS and shaft speed to claim overall acceleration.
- Using one dominant-frequency estimate when significant harmonics, gear mesh, bearing bands, impacts, modulation or random vibration are present.
- Converting RMS to peak with sqrt(2) for a non-sinusoidal waveform, shock or envelope signal.
- Comparing the calculated g value to generic condition bands without the exact machine/product/standard procedure.
- Treating RPM as vibration frequency when the component is at another order, blade/vane pass, gear mesh or bearing-defect frequency.
- Ignoring sensor response, integration drift, high-pass/low-pass filters, spectral leakage, window correction and noise.
Soalan lazim
Can I convert overall velocity RMS to acceleration using running speed?
Only if the measured signal is demonstrably one sinusoid at running speed. A broadband overall contains multiple components, each of which is weighted by its own frequency during differentiation.
Does the result comply with ISO 20816?
The arithmetic is not an ISO 20816 formula or evaluation. An ISO assessment requires the applicable part, machine scope, measurement quantity and descriptor, frequency band, point/direction, support, operating state and all stated criteria.
Why are RMS, peak and peak-to-peak shown separately?
They are different amplitude descriptors. For one sine wave only, peak equals sqrt(2) times RMS and peak-to-peak equals twice peak. Those factors do not describe an arbitrary waveform.
Is g the local acceleration due to gravity?
No. This page uses the conventional standard acceleration g_n = 9.80665 m/s² as a reference ratio. It does not use location-dependent free-fall acceleration.
