1. for n quantities $x_1,x_2,\dots x_n$, by the positive square root of the mean value of their squares:

   ${\displaystyle X_{\text{q}}={\left(\frac{1}{n}(x_1^2+x_2^2+\dots +x_n^2)\right)}^{1/2}}$

2. for a quantity x depending on a variable t, by the positive square root of the mean value of the square of the quantity taken over a given interval $(t_0,t_0+T)$ of the variable:

   ${\displaystyle X_{\text{q}}={\left(\frac{1}{T}{\int }_{t_0}^{t_0+T}{\left(x(t)\right)}^2\text{d}t\right)}^{1/2}}$

Note 1 to entry: The root-mean-square value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number.

Note 2 to entry: The root-mean-square value of a quantity is denoted by adding the subscript q to the symbol of the quantity.

Note 3 to entry: The abbreviation RMS was formerly denoted as r.m.s. or rms, but these notations are now deprecated.

tag before list. LMO