# How is RMS calculated in ROOT?

Hello,

I’m starting to question what the definition of RMS is in ROOT.
It seems, to really calculated the
"RMS" = <x^2>= (X1^2 + X2^2 +…)/N , mean of squares,
instead of the Mathematical/Statistical definition of
RMS= sqrt(<x^2>), Root of mean of squares.

I haven’t been able to successfully find the definition in the documentation. Could someone point me in the right direction please?

See, for example, the TH1::GetRMS and the TH1::GetStdDev method descriptions.

If I am not mistaken, the Standard Deviation from ROOT TMath returns Variation value, without the square-root still.

according to these lines:

```stddev2 = TMath::Abs(stats[axm+1]/stats -x*x); 7057 if (axis<10) 7058 return TMath::Sqrt(stddev2); 7059 else { 7060 // The right formula for StdDev error depends on 4th momentum (see Kendall-Stuart Vol 1 pag 243) 7061 // formula valid for only gaussian distribution ( 4-th momentum = 3 * sigma^4 ) 7062 Double_t neff = GetEffectiveEntries(); 7063 return ( neff > 0 ? TMath::Sqrt(stddev2/(2*neff) ) : 0. );```
at here: root.cern.ch/doc/master/TH1_8cx … tml#l07047

the square-root should be performed, but the value seems to be exactly the square of standard deviation I am able to calculate.

Pseudo code logic: