# Full width at half maximum for TGraph

Good evening to all;
I would like to know how can I calculate the FWHM for TGraph or TGraphErrors if someone can help me please.

I tried the following code but it doesn’t work :

Int_t firstBin= graph_Simulated2.GetHistogram()->FindFirstBinAbove(graph_Simulated2.GetHistogram()->GetMaximum()/2);

Int_t lastBin= graph_Simulated2.GetHistogram()->FindLastBinAbove(graph_Simulated2.GetHistogram()->GetMaximum()/2);

Double_t FWHMvalue= graph_Simulated2.GetHistogram()->GetBinCenter(lastBin) - graph_Simulated2.GetHistogram()->GetBinCenter(firstBin);

some help, please !!

cordially

``````void fwhm()
{
auto Canvas = new TCanvas();
auto h1 = new TH1F("h1", "", 50, -5.0, 5.0);
for (Int_t i = 0; i < 10000; i++) h1->Fill(gRandom->Gaus());
h1->Draw();

// method 1
auto firstBin = h1->FindFirstBinAbove(h1->GetMaximum()/2);
auto lastBin  = h1->FindLastBinAbove(h1->GetMaximum()/2);
auto FWHMvalue= h1->GetBinCenter(lastBin)-h1->GetBinCenter(firstBin);
cout << "1. FWHM: " << FWHMvalue << std::endl;

// method 2 , more accurate if the distribution is Gaussian
TFitResultPtr r = h1->Fit("gaus","SQ");
auto height = r->Parameter(0);
auto mean   = r->Parameter(1);
auto width  = r->Parameter(2);
cout << "2. FWHM: " << 2.355*width << std::endl;
}
``````

TGraph::GetHistogram always returns a completely “empty” histogram, which is only used to draw the axes.

In general, you would need to take the array pointers returned by TGraph::GetX and TGraph::GetY (together with the array sizes returned by TGraph::GetN) and then use some standard C++ functions to find FWHM (just make sure that you TGraph::Sort it first).

If your graph is a scatter-plot of some “well defined” known distribution, then you could use TGraph::GetRMS (and TGraph::GetMean, if needed) and “calculate” FWHM from it:

``````{
TGraph *g = new TGraph(10000);
for (int i = 0; i < g->GetN(); i++)
g->SetPoint(i, gRandom->Rndm(), gRandom->Gaus());
// g->Sort();
g->Draw("AP");
cout << "X Mean (exact 0.5)      = " << g->GetMean(1) << endl;
cout << "X RMS  (exact " << sqrt(1. / 12.) << ") = " << g->GetRMS(1) << endl;
cout << "Y Mean (exact 0.0)      = " << g->GetMean(2) << endl;
cout << "Y RMS  (exact 1.0)      = " << g->GetRMS(2) << endl;
}
``````
1 Like

Thanks, @Wile_E_Coyote, and @Eddy_Offermann for your reply.
I found the solution for this problem
cordialy

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