Calculate the root mean square (quadratic mean) of a list of numbers.
The RMS (Root Mean Square) Calculator finds the quadratic mean of a set of numbers — the square root of the average of their squares.
RMS is widely used in electronics (AC voltage and current), physics, and statistics because it gives a meaningful average for values that include both positive and negative numbers.
RMS = √( (x1² + x2² + ... + xn²) ÷ n ), where n is the number of values.
For the values 3, 4, 5, and 6, the RMS is √((9+16+25+36)/4) = √21.5 ≈ 4.64.
An average that accounts for positive and negative fluctuations, used for effective values like AC voltage.
Square each value, average the squares, then take the square root of that average.
A simple average of a sine wave is zero, while RMS gives a meaningful effective value.