A random spectrum is presented as a set of frequency and amplitude breakpoint values. To compute the root mean square (RMS) from the values, we must calculate the area under the curve defined by them. The RMS Calculator provided by Vibration Research computes random acceleration, velocity, and displacement values from a breakpoint table.
RMS Online Calculator
Velocity is calculated as an RMS value. Displacement is calculated as peak-to-peak assuming 3-sigma peaks.