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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:$X}_{\text{q}}={\left(\frac{1}{n}({x}_{1}^{2}+{x}_{2}^{2}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{x}_{n}^{2})\right)}^{1/2$ - 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 $({t}_{0},\text{\hspace{0.17em}}{t}_{0}+T)$ of the variable:$X}_{\text{q}}={\left(\frac{1}{T}{\int}_{\text{\hspace{0.05em}}{t}_{0}}^{\text{\hspace{0.05em}}{t}_{0}+T}{\left(x(t)\right)}^{2}\text{d}t\right)}^{1/2$
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. | ||

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: |

- 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:$X}_{\text{q}}={\left(\frac{1}{n}({x}_{1}^{2}+{x}_{2}^{2}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{x}_{n}^{2})\right)}^{1/2$

- 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 $({t}_{0},\text{\hspace{0.17em}}{t}_{0}+T)$ of the variable:$X}_{\text{q}}={\left(\frac{1}{T}{\int}_{\text{\hspace{0.05em}}{t}_{0}}^{\text{\hspace{0.05em}}{t}_{0}+T}{\left(x(t)\right)}^{2}\text{d}t\right)}^{1/2$

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.