GRMS Calculator

GRMS is a measure of the overall intensity or severity of a random vibration spectrum. Enter frequency and acceleration PSD breakpoints to calculate GRMS using log-log power-law integration.

Frequency (Hz)	PSD (g²/Hz)

Number format

Decimal places

Segment results

Segment	f₁	f₂	PSD₁	PSD₂	Slope n	Area (g²)	% area

How GRMS is calculated

For a PSD defined by straight segments on log-log axes, each segment is represented as a power law, PSD(f) = C·fⁿ, where the exponent n comes from the two bounding breakpoints. The area of every segment is integrated and summed. Overall GRMS is the square root of that total mean-square area and condenses the energy in the full PSD curve into a single RMS acceleration value. Higher GRMS generally indicates a more severe overall random vibration environment, although two spectra with the same GRMS can distribute that energy differently across frequency.

Important: This calculator assumes the breakpoint pairs describe straight line segments on a log-log PSD plot. All frequencies and PSD amplitudes must be greater than zero, and frequencies must increase from row to row.

Why not use the trapezoidal rule?

A straight segment on log-log axes is generally curved on linear axes. Power-law integration preserves the intended log-log PSD shape instead of approximating it with a linear trapezoid.

Units

If PSD is entered in g²/Hz and frequency in Hz, the integrated area is in g² and its square root is the RMS acceleration in g, or GRMS. The same method applies to other compatible PSD units; the RMS result has the corresponding base unit.