Root Mean Square Calculator
Calculate the quadratic mean: sqrt(sum(x^2) / n).
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Enter your values separated by commas or spaces. The calculator squares each value, takes the mean of those squares, then returns the square root. This is also called the quadratic mean. The arithmetic mean is shown for comparison.
About Root Mean Square
RMS gives a measure of magnitude that accounts for both positive and negative values. It is always greater than or equal to the absolute arithmetic mean. RMS is critical in electrical engineering (RMS voltage of AC signals), physics (RMS speed of gas molecules), and signal processing (RMS amplitude). For a sine wave, the RMS value is the peak divided by the square root of 2.
Frequently Asked Questions
How is RMS different from the arithmetic mean?
RMS squares values first, which gives more weight to larger magnitudes and always produces a non-negative result. For all-positive identical values, RMS equals the arithmetic mean. Otherwise RMS is larger.
Why is RMS important in electronics?
RMS voltage tells you the effective voltage of an alternating current signal. A 120V AC outlet has an RMS voltage of 120V, with a peak voltage of about 170V. RMS is the equivalent DC voltage that would deliver the same power.
What is the relationship between RMS and standard deviation?
If the mean of the data is zero, the RMS equals the population standard deviation. In general, RMS squared equals the mean squared plus the variance. This relationship connects the concepts of magnitude and spread.