Langford Analytic · Knowledge Base

RMS & Variance Reference

A quick reference for the relationships between PSD, variance, RMS and standard deviation for random vibration signals.

Random Vibration2 min read
referenceRMSvariancestandard deviationPSD

Key Relationships

Variance = σ² = ∫ G(f) df = area under PSD

RMS = √(variance) = √(∫ G(f) df)

For zero-mean: RMS = σ = standard deviation

For Gaussian:
  P(|x| > 1σ) = 31.7%
  P(|x| > 2σ) = 4.6%
  P(|x| > 3σ) = 0.27%

RMS ≠ peak
RMS ≠ maximum
3σ is a screening level, not a maximum