Root Mean Square Calculator
Calculate the RMS value of a list of numbers.
How Root Mean Square Is Calculated
Root mean square, or RMS, measures the effective magnitude of a set of values. Unlike an ordinary average, RMS squares each value before averaging, so positive and negative values do not cancel each other out.
Formula
RMS = √[(x₁² + x₂² + … + xₙ²) ÷ n].
Worked Example
For the values 3 and 4, RMS = √[(9 + 16) ÷ 2] = √12.5 ≈ 3.5355.
Factors That Affect the Result
Larger-magnitude observations have extra influence because values are squared. RMS is therefore especially useful for alternating signals, errors, velocities and other quantities where magnitude matters more than sign.
Frequently Asked Questions
Is RMS the same as the arithmetic mean?
No. RMS squares the values first, so it is usually equal to or greater than the absolute arithmetic mean.
Why is RMS used for AC voltage?
It expresses the equivalent effective magnitude of a varying voltage or current for power calculations.
Can RMS include negative numbers?
Yes. Squaring removes the sign before averaging, so negative inputs are handled naturally.
Methodology, Assumptions and Interpretation
Root mean square is √(Σx²/n) for a set of values. RMS emphasizes larger magnitudes and is not interchangeable with the arithmetic mean; for AC waveforms, voltage/current RMS relationships also depend on waveform shape.