RMS Calculator
This free RMS calculator converts between peak, RMS, peak-to-peak and average for common waveforms — with the crest factor — or computes the RMS of a list of values you paste in.
RMS (root mean square) is the equivalent steady value that carries the same power as a varying signal — it’s what tracks loudness and heating. The waveform conversions assume an ideal, symmetric sine, square, triangle or sawtooth. This is a calculator, not a measurement.
Peak ↔ RMS ↔ peak-to-peak
Edit any field — the others update. Values are unitless (use them as volts, amps, etc.).
RMS of a list of values
Enter numbers separated by commas or spaces. RMS = √(mean of the squares).
Waveform factors (relative to peak)
For a symmetric waveform of peak amplitude 1. Crest factor = peak ÷ RMS.
How RMS Works
RMS (root mean square) of a signal is the square root of the mean of its squared values: RMS = √(mean(x²)). It matters because the power delivered (and the heating, and roughly the perceived loudness) depends on the square of the amplitude — so RMS is the single number that represents a varying signal’s "equivalent steady" level. A 1 V RMS AC voltage delivers the same power to a resistor as 1 V DC. This is the foundation of how AC power grids specify their nominal voltages: mains electricity at 120 V or 230 V is an RMS value — the actual peak voltage swings to ±170 V or ±325 V respectively.
For a pure sine wave, the peak to RMS conversion is simply divide by √2 (≈ 0.707 × peak), and RMS to peak is multiply by √2. The ratio of peak to RMS is the crest factor (√2 ≈ 1.414 for a sine). Different shapes have different factors: a square wave has RMS = peak (crest 1), while triangle and sawtooth waves have RMS = peak ÷ √3 ≈ 0.577 (crest √3 ≈ 1.732). For audio signals, crest factor relates directly to headroom — the gap between the average (RMS) level and the instantaneous peak that must not clip. To measure how loud a signal actually sounds relative to full scale, see the decibel meter for a live dBFS reading.
Why the waveform matters
The simple "× 0.707" rule only applies to sine waves. The waveform RMS depends on the shape: real signals — music, speech, clipped or compressed audio — have their own crest factors that change with processing (dynamic range compression lowers the crest factor; sharp transients and unprocessed speech raise it). Heavily limited broadcast audio might have a crest factor as low as 1.5, while an orchestral recording can reach 6 or more. To get the true RMS of an arbitrary signal you must square every sample, average, and take the root — which is exactly what the "RMS of values" mode does for data you paste in. The audio spectrum analyzer can give you a visual sense of a signal's energy distribution across frequency, which complements the single-number RMS view.