Queries, comments, suggestions? Please contact us.



Area Mathematics - Functions / Means

IEV ref103-02-02

en
root-mean-square value
RMS value
quadratic mean
quantity representing the quantities in a finite set or in an interval,

  1. for n quantities x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaaGymaaqabaGccaGGSaGaaGjbVlaadIhadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaaGjbVlaaykW7cqWIMaYscaaMc8UaaGPaVlaaysW7ca WG4bWaaSbaaSqaaiaad6gaaeqaaaaa@4713@ , by the positive square root of the mean value of their squares:

    X q = ( 1 n ( x 1 2 + x 2 2 ++ x n 2 )) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGa aGymaaGcbaGaamOBaaaacaGGOaGaamiEamaaDaaaleaajug4aiaaig daaSqaaKqzGdGaaGOmaaaakiabgUcaRiaadIhadaqhaaWcbaqcLboa caaIYaaaleaajug4aiaaikdaaaGccqGHRaWkcaaMc8UaaGjbVlaayk W7cqWIMaYscaaMc8UaaGPaVlaaysW7cqGHRaWkcaWG4bWaa0baaSqa aiaad6gaaeaajug4aiaaikdaaaGccaGGPaaacaGLBbGaayzxaaWaaW baaSqabeaajug4aiaaigdacaGGVaGaaGOmaaaaaaa@5F01@

  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) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaacUfacaWG0bWaaS baaSqaaKqzGdGaaGimaaWcbeaakiaacYcacaaMe8UaamiDamaaBaaa leaajug4aiaaicdaaSqabaGccqGHRaWkcaWGubGaaiyxaaaa@418C@ of the variable:

    X q = ( 1 T t 0 t 0 +T ( x(t) ) 2 dt ) 1/2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcbaqcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWdXaqaamaadmaabaGaamiEaiaacIcacaWG0bGaaiykaaGaay5waiaaw2faamaaCaaaleqabaGaaGOmaaaaaeaacaaMi8UaamiDamaaBaaameaacaaIWaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaaicdaaeqaaSGaey4kaSIaamivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaGaay5waiaaw2faamaaCaaaleqabaqcLboacaaIXaGaai4laiaaikdaaaaaaa@553C@

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.


fr
valeur moyenne quadratique, f
moyenne quadratique, f
grandeur représentant les grandeurs d’un ensemble fini ou d’un intervalle,

  1. pour n grandeurs x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaaGymaaqabaGccaGGSaGaaGjbVlaadIhadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaaGjbVlaaykW7cqWIMaYscaaMc8UaaGPaVlaaysW7ca WG4bWaaSbaaSqaaiaad6gaaeqaaaaa@4713@ , par la racine carrée positive de la valeur moyenne de leurs carrés:

    X q = ( 1 n ( x 1 2 + x 2 2 ++ x n 2 )) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGa aGymaaGcbaGaamOBaaaacaGGOaGaamiEamaaDaaaleaajug4aiaaig daaSqaaKqzGdGaaGOmaaaakiabgUcaRiaadIhadaqhaaWcbaqcLboa caaIYaaaleaajug4aiaaikdaaaGccqGHRaWkcaaMc8UaaGjbVlaayk W7cqWIMaYscaaMc8UaaGPaVlaaysW7cqGHRaWkcaWG4bWaa0baaSqa aiaad6gaaeaajug4aiaaikdaaaGccaGGPaaacaGLBbGaayzxaaWaaW baaSqabeaajug4aiaaigdacaGGVaGaaGOmaaaaaaa@5F01@

  2. pour une grandeur x fonction de la variable t, par la racine carrée positive de la valeur moyenne du carré de la grandeur prise sur un intervalle donné ( t 0 , t 0 +T) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaacUfacaWG0bWaaS baaSqaaKqzGdGaaGimaaWcbeaakiaacYcacaaMe8UaamiDamaaBaaa leaajug4aiaaicdaaSqabaGccqGHRaWkcaWGubGaaiyxaaaa@418C@ de la variable:

    X q = ( 1 T t 0 t 0 +T ( x(t) ) 2 dt ) 1/2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcbaqcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWdXaqaamaadmaabaGaamiEaiaacIcacaWG0bGaaiykaaGaay5waiaaw2faamaaCaaaleqabaGaaGOmaaaaaeaacaaMi8UaamiDamaaBaaameaacaaIWaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaaicdaaeqaaSGaey4kaSIaamivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaGaay5waiaaw2faamaaCaaaleqabaqcLboacaaIXaGaai4laiaaikdaaaaaaa@553C@

Note 1 à l'article: La valeur moyenne quadratique d'une grandeur périodique est généralement prise sur un intervalle d'intégration dont l’étendue est le produit de la période par un entier naturel.

Note 2 à l'article: La valeur moyenne quadratique d'une grandeur est notée en ajoutant l'indice q au symbole de la grandeur.

Note 3 à l'article: L’abréviation anglaise RMS était anciennement écrite r.m.s. ou rms, mais ces notations sont maintenant déconseillées.


ar
الوسط التربيعى
قيمة الجذر التربيعى لمتوسط المربعات(1)

de
quadratischer Mittelwert, m

es
valor medio cuadrático

it
radice della media dei quadrati
valore efficace
media quadratica

ko
실효값, <관련엔트리: 103-02-03>
아르엠에스 값
평방평균

ja
二乗平均平方根値
RMS値
平方平均

pl
średnia kwadratowa, f
wartość średnia kwadratowa, f

pt
valor eficaz
valor médio quadrático

sr
ефективна вредност, ж јд
rms вредност, ж јд
средња квадратна вредност, ж јд

sv
kvadratiskt medelvärde

zh
方均根值, <相关条目:IEV 103-02-03>
二次均值

Publication date: 2017-07
Copyright © IEC 2018. All Rights Reserved.