Vibration & Reliability Calculators
Practical calculations for learning, measurement planning and maintenance analysis. Choose a tool, enter your values and calculate.
ISO 20816-3 guided check
Select your equipment and measurement conditions for a preliminary broadband velocity-zone assessment. This tool implements a limited bearing-housing check, not the complete standard.
Group selection must be verified: Group 1 uses power above 300 kW, or electrical-machine shaft height at least 315 mm; Group 2 uses power above 15 through 300 kW, or electrical-machine height 160 to less than 315 mm. Conflicting classifications need review. Support is a dynamic property in each direction, not simply concrete versus steel. Use all required bearing locations; this result assesses only the entered reading. This implementation withholds velocity-only zones at 600 RPM or below. Between 600 and 1000 RPM it conservatively requires the 2 Hz band. Zone boundaries are not automatic alarm or trip setpoints.
View severity tables
These are the velocity boundaries used by this calculator. Values are in mm/s RMS, measured on non-rotating bearing housings or pedestals. Select the correct group and support before comparing a reading.
| Machine group | Support | A/B | B/C | C/D |
|---|---|---|---|---|
| Group 1 | Rigid | 2.3 | 4.5 | 7.1 |
| Group 1 | Flexible | 3.5 | 7.1 | 11.0 |
| Group 2 | Rigid | 1.4 | 2.8 | 4.5 |
| Group 2 | Flexible | 2.3 | 4.5 | 7.1 |
| Zone | Reading | Practical interpretation |
|---|---|---|
| A | Below A/B | Low overall magnitude; faults may still be present. |
| B | At A/B, below B/C | Usually compatible with long-term operation; review trends. |
| C | At B/C, below C/D | Investigate promptly and plan corrective work. |
| D | At or above C/D | Urgent engineering review; follow approved site procedures. |
Example: Group 2 with rigid support, 3.7 mm/s RMS, falls in Zone C. Equality is assigned to the higher zone by this tool. These zones are not automatic alarm or shutdown settings.
Reference cross-check: Mobius Institute, Category II course manual (2016), Chapter 18, printed page 18-7, Figure 18-7, presents matching Group 1 and 2 velocity boundaries under the older ISO 10816-3 designation. This is an original RCM GLOBAL summary, not a scan of the manual. Older pump groups are not included. Displacement and shaft-vibration tables are not implemented here.
Basis: ISO 20816-3:2022, preliminary non-rotating-part velocity check. Verify measurement procedure and machine applicability against the full standard. No ISO endorsement or certification. ISO scope and edition status · Adash instrument guide: velocity boundaries. Reviewed 20 October 2026. Numerical limits do not diagnose bearing or gear defects; review trends and manufacturer limits separately.
RPM ↔ Hz
Convert rotational speed to shaft frequency.
Hz = RPM ÷ 60. Shaft frequency is not necessarily the dominant vibration frequency.
Vibration amplitude
Convert displacement, velocity and acceleration at one frequency.
Single sinusoid only: v = 2πfx; a = (2πf)²x. Peak = √2 × RMS; peak-to-peak = 2 × peak. Do not convert broadband overall values using one frequency. Standard gravity: 1 g = 9.80665 m/s². All results below use RMS.
Gear mesh frequency
Calculate mesh frequency from one gear’s speed and tooth count.
GMF = teeth × RPM ÷ 60. Use the speed and tooth count of the same gear. Mesh harmonics alone do not establish a fault.
Bearing frequencies
Estimate theoretical frequencies from bearing geometry.
Stationary outer ring, rotating inner ring, ideal rolling without slip. Use the manufacturer's internal geometry, not bore or outside diameter. Frequencies are diagnostic reference values, not proof of damage. BSF is spin frequency; a rolling-element defect may excite 2 × BSF.
MTBF, MTTR & availability
Summarise a repairable asset’s completed failure-and-repair history.
MTBF = operating hours ÷ failures; MTTR = active repair hours ÷ completed repairs. Use the same observation period and only completed failure-repair events. Inherent availability = MTBF ÷ (MTBF + MTTR). It excludes planned maintenance, logistics and administrative delays; it is not operational availability or a remaining-life prediction. With zero failures, MTBF and MTTR cannot be estimated by these ratios.
FFT measurement planner
Connect sample rate, record length, frequency spacing and shaft revolutions.
Record duration T = N/fs; bin spacing Δf = fs/N; revolutions = RPM × T/60. Nyquist frequency fs/2 is a mathematical boundary, not the usable bandwidth of an instrument. Set Fmax strictly below it and check the instrument's anti-alias filter. Bin spacing is not guaranteed peak separation: window choice and noise matter. No zero padding assumed.
Blade & vane passing
Find passing frequency, harmonics and first shaft-speed sidebands.
Passing frequency = blade count × RPM/60. Sideband markers = passing frequency ± shaft frequency. These are theoretical markers, not predicted amplitudes or a fault diagnosis.
Your alarm-limit comparison
Compare one reading with limits approved for your asset.
Enter your own limits from the equipment maker or your approved monitoring programme. No ISO limits are supplied. Reading and limits must share bandwidth, location, operating condition and RMS convention. At equality the higher category applies. A reading below warning does not prove the machine is healthy.
Waveform & phase simulator
Explore two equal-frequency sine waves and their sum.
A(t) = A sin(2πft); B(t) = B sin(2πft + φ). The plot spans two cycles. Resultant peak = √(A² + B² + 2AB cos φ); RMS = peak/√2. Educational signals only, not measured machine data.
Measurement references: NI: FFTs and windowing; SKF: introduction to vibration monitoring.
Formulas and references
Bearing formulas: r = (d/D) cos θ; shaft frequency f = RPM/60; BPFO = Zf(1−r)/2; BPFI = Zf(1+r)/2; FTF = f(1−r)/2; BSF = Df(1−r²)/(2d).
Reference reading: SKF: bearing vibration frequencies; IBM: MTTR and MTBF; IBM: availability formula.
Check units, measurement conventions and equipment data before using a result in an engineering decision. No values are uploaded by these calculators.
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