PSD Integration to RMS Calculator
Calculate the RMS from a general PSD by numerical integration. Shows the equation, variables, substitution and result.
Calculator
RMS = √( ∫ G(f) df )
where:
G(f) = PSD value at frequency f [g²/Hz]
f = frequency [Hz]
RMS = root mean square [g]
For numerical integration (trapezoidal):
σ² ≈ Σ [ (G_i + G_{i+1})/2 × (f_{i+1} − f_i) ]
RMS = √(σ²)
Enter PSD values at frequency points to
calculate the overall RMS.Assumptions
- PSD is correctly defined in g²/Hz
- Frequency points span the full PSD range
- Resolution is fine enough to capture peaks
- Zero-mean process (RMS = standard deviation)
Limitations
The accuracy depends on the frequency resolution. Coarse resolution can miss narrow peaks and underestimate the RMS. For PSDs with sharp resonant peaks, use at least 5-10 points within the half-power bandwidth.