Root Mean Square (RMS) Calculator

The root mean square squares first, averages, then roots back — weighting large magnitudes more than a plain average. For 3 and 4: squares are 9 and 16, average 12.5, root ≈ 3.536, larger than the arithmetic mean 3.5 because squaring punishes the 4. Its killer application is alternating current: a 230 V RMS sine wave actually swings to 230×√2 ≈ 325.3 V peak, and RMS is the DC-equivalent that produces the same heating in a resistor, so a 230 V RMS supply powers a 2300 W kettle exactly like 230 V DC would. For a pure sine wave RMS = peak/√2 = 0.7071×peak. The calculator lists each square, the mean of squares, and the final root, plus a peak↔RMS converter for sinusoids and a note that RMS ≥ arithmetic mean for any data set with equality only when all values match.

1. 1

   Enter your samples

   Data values or instantaneous measurements

2. 2

   Square each one

   Every xᵢ² is shown — negatives become positive

3. 3

   Average the squares

   Sum them and divide by n

4. 4

   Take the square root

   The result is the quadratic mean, RMS

• 1

  Sine wave: RMS = peak/√2 ≈ 0.707 × peak

• 2

  RMS ≥ arithmetic mean, equality only for identical values

• 3

  Squaring makes RMS ignore sign — ideal for AC waveforms

• Averaging absolute values instead of squares — that is the mean absolute, not RMS

• Using peak voltage in power formulas; P = V²rms/R needs RMS

• Forgetting the final square root and reporting 12.5 for the 3,4 example

• Applying the /√2 shortcut to non-sinusoidal (square, sawtooth) waves