IEVref: 103-02-02 ID: Language: en Status: Standard Term: root-mean-square value Synonym1: RMS value [Preferred] Synonym2: quadratic mean [Preferred] Synonym3: Symbol: Definition: quantity representing the quantities in a finite set or in an interval,for n quantities ${x}_{1},\text{\hspace{0.17em}}{x}_{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{x}_{n}$, by the positive square root of the mean value of their squares: ${X}_{\text{q}}={\left(\frac{1}{n}\left({x}_{1}^{2}+{x}_{2}^{2}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{x}_{n}^{2}\right)\right)}^{1/2}$ 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 $\left({t}_{0},\text{\hspace{0.17em}}{t}_{0}+T\right)$ of the variable:${X}_{\text{q}}={\left(\frac{1}{T}{\int }_{\text{ }{t}_{0}}^{\text{ }{t}_{0}+T}{\left(x\left(t\right)\right)}^{2}\text{d}t\right)}^{1/2}$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. Publication date: 2017-07 Source: Replaces: 103-02-02:2009-12 Internal notes: CO remarks: 2017-08-25: Added tag before list. LMO TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: