Root Mean Square Calculator
Calculate the root mean square (RMS) of a set of values, used in physics and signal processing.
Root Mean Square
4.082483
Root Mean Square vs Value 1
Formula
## How to Calculate the Root Mean Square ### Formula **RMS = sqrt( (v1^2 + v2^2 + ... + vn^2) / n )** 1. Square each value 2. Compute the arithmetic mean of the squares 3. Take the square root The RMS is always greater than or equal to the absolute value of the arithmetic mean. In electrical engineering, RMS voltage represents the equivalent DC voltage that delivers the same power.
Exemplo Resolvido
Compute the RMS of 3, 4, 5.
- 01Squares: 9, 16, 25
- 02Mean of squares = (9 + 16 + 25) / 3 = 50 / 3 ≈ 16.6667
- 03RMS = sqrt(16.6667) ≈ 4.0825
- 04Compare: Arithmetic mean = (3 + 4 + 5) / 3 = 4
Perguntas Frequentes
Why is RMS used instead of the regular average?
RMS gives more weight to larger values and accounts for sign (since squaring removes negatives). It is the correct measure of magnitude for alternating signals and error measurements.
Is RMS always larger than the arithmetic mean?
For non-negative values that are not all identical, yes. The inequality RMS >= AM follows from the power mean inequality. They are equal only when all values are the same.
Where is RMS used in practice?
RMS is used for AC voltage and current, audio signal levels (dBFS), RMSE in regression analysis, and molecular speeds in kinetic theory of gases.
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