How is overall vibration level calculated from a spectrum?

The overall (broadband) vibration level is calculated as the root-sum-of-squares (RSS) of individual spectral components: Overall = √(a₁² + a₂² + ... + aₙ²). This applies to RMS amplitudes of individual frequency components.

What is the crest factor?

Crest factor is the ratio of peak value to RMS value. For a pure sine wave, CF = √2 ≈ 1.414. Higher crest factors indicate impulsive events like bearing faults. Normal machinery typically has CF = 2–4; CF > 4 may indicate developing faults.

Should I use peak or RMS amplitudes?

Use RMS amplitudes for overall level calculation. Most vibration analyzers display spectral lines as RMS values. If you have peak values, divide by √2 to convert to RMS before summing.

Why doesn't the overall level equal the sum of components?

Because vibration components at different frequencies are independent and combine as root-sum-of-squares, not arithmetic sum. The RSS method accounts for the statistical independence of different frequency components.

What units should I use?

Any consistent unit works — mm/s RMS for velocity, g RMS for acceleration, or μm for displacement. The key requirement is that all input components use the same unit and measurement type (all RMS or all peak).

Free Engineering Tool — #014

Overall Vibration Level Calculator

Calculate overall vibration level from spectrum components using root-sum-of-squares. Enter up to 10 amplitude values and optional peak value for crest factor.

RSS Method Crest Factor Up to 10 Components

Results

Overall RMS Level

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Crest Factor

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Number of Components

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Dominant Component

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Dominant Contribution

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Root-Sum-of-Squares (RSS)

The overall vibration level from independent spectral components is:

Where a_i are RMS amplitudes of individual spectral components.

Crest Factor

CF = √2 ≈ 1.414 — Pure sine wave
CF = 2–4 — Normal machinery
CF > 4 — Impulsive events (bearing defects)
CF > 6 — Severe impact or looseness

Practical Example

Example — Centrifugal Pump

Spectral components (mm/s RMS): 3.2, 1.8, 0.9, 0.4, 0.2

Overall = √(3.2² + 1.8² + 0.9² + 0.4² + 0.2²) = √(10.24 + 3.24 + 0.81 + 0.16 + 0.04)

Overall = √14.49 = 3.81 mm/s RMS

If peak = 8.5 mm/s → CF = 8.5 / 3.81 = 2.23 (normal)

ℹ️ Note: The dominant component (1×, usually) typically contributes the most to overall level. If one component is much larger than others, the overall ≈ that component’s amplitude.