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RMS of a Signal Calculator

Enter your comma or space separated values to compute their RMS.

How it is calculated

The tool reads a list of numbers separated by commas or spaces. It squares each value, averages the squares, and takes the square root: RMS = √( (x₁² + x₂² + … + xₙ²) / n ). It also reports the arithmetic mean (Σx) / n, which shows any DC offset, and the peak, the largest absolute value. Values are in whatever unit you used (volts, amps, pascals), and RMS keeps that unit. Entries that are not numbers are skipped silently instead of raising an error, so n counts only the valid ones. A single value is enough. Results are rounded to four decimals. The result describes the list you give, so samples should cover whole cycles of a periodic signal.

Worked example

Eight samples taken over one cycle of a sine wave of amplitude 10: 0, 7.07, 10, 7.07, 0, −7.07, −10, −7.07. Squares: 0, 49.98, 100, 49.98, 0, 49.98, 100, 49.98, which add up to 399.94. Mean of squares: 399.94 / 8 = 49.9925. RMS = √49.9925 = 7.0705. The mean is 0.0000 because positive and negative halves cancel, and the peak is 10.0000. The RMS is about 0.707 of the peak, as expected for a sine wave.

Try this example →

Common mistakes

  • Using the plain average instead of RMS. For a symmetric AC signal the average is zero (as here), but the RMS is not.
  • Typing a decimal comma. A value like 2,5 is split into 2 and 5, which changes both n and the result. Use a decimal point.
  • Mistyping a number and not noticing. Text such as "1O" (letter O) is dropped without a warning, so the result is based on fewer values than you expect.
  • Sampling a partial cycle of a periodic signal. The list needs whole cycles, or the RMS will be biased toward the part you captured.
  • Mixing peak, peak-to-peak and RMS. This tool returns RMS of the numbers you enter; if you enter peak-to-peak readings, the result is not a voltage RMS.

About this calculator

The root mean square (RMS) of a set of values is the square root of the average of their squares — a way of measuring the “typical” magnitude of a signal that properly accounts for both positive and negative values, unlike a simple average which can cancel them out or understate their real effect.

RMS matters most for anything involving power or energy: for an AC voltage or current, RMS is the value that delivers the same heating/power effect as an equivalent DC signal, which is why household power like “120V” actually refers to an RMS value, not the peak voltage. Electrical engineers and audio/signal-processing engineers use RMS to size components for real power dissipation, specify audio equipment loudness, and characterize noise and vibration signals where the peak alone would be misleading.

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  • Editorial team

    Enter samples covering a whole number of cycles, or the RMS is biased. As a check, four samples of a sine, 0, 1, 0, -1, give 0.7071, which is peak divided by the square root of two. If the mean is not near zero, there is a DC offset and RMS includes it. What kind of waveform are you sampling?

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