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Root-mean-square value

Gives the root-mean-square value of a time-varying quantity over an interval of length T by squaring it, averaging over time, and taking the square root. It is used for alternating currents, voltages, and acoustic signals, where the RMS value is the equivalent constant level that delivers the same average power.

a_{\mathrm{eff}} = \sqrt{\frac{1}{T} \int_0^T a^2 \, \mathrm{d}t}

What the symbols mean

root-mean-square (effective) value of the quantity a
time-dependent quantity, such as voltage or current
duration of the averaging interval, in seconds
time, in seconds

About this formula

  • FieldEngineering
  • TopicSignal processing and electrical measurement
  • LevelUniversity
  • Also calledRMS value, effective value, root mean square, RMS formula, rms of a periodic signal, effective value of AC voltage
  • SourceWikidata Q369180

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