// multi-utility computation suite · offline · instant · precise
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sci.random-vibration-PSD-rms Calculator
Calculates rms acceleration from a power spectral density (PSD) profile: a_rms = √(∫PSD df) using trapezoidal integration over the frequency band. Random vibration qualification per MIL-STD-810G uses 0.04 g²/Hz flat spectrum from 20–500 Hz: a_rms = √(0.04 × 480) = 4.38 g.
Inputs
S0 M2 S3 Hz
Reference formula or conversion factor shown for context.
F1 Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
F2 Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Results
RMS acceleration a_rms
The proportional relationship between two quantities.
3σ peak (99.73% probability)
Reference formula or conversion factor shown for context.
frequency band (decades)
Sample size or count used in the calculation.
bandwidth (Hz)
The computed width.
a_rms = √(S₀·Δf)
Reference formula or conversion factor shown for context.
GRMS
Reference formula or conversion factor shown for context.