Root mean square

The root mean square of a varying quantity is the square root of the mean of its squared values. It summarizes magnitude while accounting for both positive and negative values.

Mean: A measure found by adding values and dividing by their number, or by integrating over a continuous domain. The averaging step in root mean square is performed after each value has been squared.
RMS voltage: The root-mean-square value of an electrical voltage, representing its effective magnitude for resistive heating. It is the most familiar electrical use of the root-mean-square measure.
Square function: The function that maps a number to its second power. Squaring makes negative and positive signal values contribute positively to the RMS calculation.
Arithmetic mean: The sum of a set of values divided by the number of values. A symmetric alternating waveform can have zero arithmetic mean but a nonzero RMS magnitude.
Quadratic mean: A generalized mean equal to the square root of the arithmetic mean of squared values. Root mean square is the quadratic mean, applied to values such as signal samples.
RMS current: The root-mean-square value of an electrical current, related to its heating effect in a resistor. Current waveforms use the same calculation to quantify effective current.
Square root: A number whose square equals a specified value; the principal square root is nonnegative. Taking the square root restores the original units after averaging squared values.
Peak value: The greatest magnitude attained by a signal within a specified interval. Peak value records an extreme, whereas RMS reflects the signal’s overall squared magnitude.
Integral: A mathematical operation that accumulates a function’s values over an interval or region. For a continuous signal, its squared values are integrated over time before normalization and the square root.
Electric power: The rate at which electrical energy is transferred or converted. For a resistor, average power can be calculated from RMS voltage or current.

Linked from 14 pages