Histograms
Histograms play a fundamental role in any kind of physical analysis. Histograms not only serve to visualize measurements, but also represent a powerful form of data reduction. ROOT supports histograms up to three dimensions.
Binned data
A histogram is used for continuous data, where the bins represent ranges of data. ROOT supports constant and variable bin widths.
A graph or chart is a plot of categorical variables, this is unbinned data, see → Graphs.
Histogram tutorials
Histogram classes
ROOT supports the following histogram types:

Histograms up to three dimensions (1D, 2D, 3D).

Profile histograms, which are used to display the mean value of Y and its standard deviation for each bin in X.
All histogram classes are derived from the TH1 base class.
The following histogram classes are available in ROOT, among others:
1D histograms

 TH1C
 One byte per channel. Maximum bin content = 127.

 TH1S
 One short per channel. Maximum bin content = 32767.

 TH1I
 One int per channel. Maximum bin content = 2147483647.

 TH1F
 One float per channel. Maximum precision 7 digits.

 TH1D
 One double per channel. Maximum precision 14 digits.
2D histograms

 TH2C
 One byte per channel. Maximum bin content = 127.

 TH2S
 One short per channel. Maximum bin content = 32767.

 TH2I
 One int per channel. Maximum bin content = 2147483647.

 TH2F
 One float per channel. Maximum precision 7 digits.

 TH2D
 One double per channel. Maximum precision 14 digits.
3D histograms

 TH3C
 One byte per channel. Maximum bin content = 127.

 TH3S
 One short per channel. Maximum bin content = 32767.

 TH3I
 One int per channel. Maximum bin content = 2147483647.

 TH3F
 One float per channel. Maximum precision 7 digits.

 TH3D
 One double per channel. Maximum precision 14 digits.
Profile histograms

 TProfile
 Profile histogram to display the mean value of Y and its error for each bin in X.

 TProfile2D
 Profile2D histograms are used to display the mean value of Z and its RMS for each cell in X,Y.

 TProfile3D
 Profile3D histograms are used to display the mean value of T and its RMS for each cell in X,Y,Z.
Bin numbering
All histogram types support fixed or variable bin sizes. 2D histograms may have fixed size bins along X and variable size bins along Y or viceversa.
Conventions
For all histogram types: nbins
, xlow
, xup
:

bin# 0 contains the underflow.

bin# 1 contains the first bin with lowedge (
xlow
INCLUDED). 
The second to last bin (bin# nbins) contains the upperedge (
xup
EXCLUDED). 
The last bin (bin#
nbins+1
) contains the overflow. 
In case of 2D or 3D histograms, a global bin number is defined.
Example
Assuming a 3D histogram h
with binx
, biny
, binz
, the function returns a global/linear bin number.
Int_t bin = h>GetBin(binx, biny, binz);
This global bin is useful to access the bin information independently of the dimension.
Rebinning
You can rebin a histogram via the TH1::Rebin() method. It returns a new histogram with the rebinned contents. If bin errors were stored, they are recomputed during the rebinning.
Working with histograms
Creating and copying a histogram
 Use a histogram constructor to create a histogram object.
Examples
In the following examples, histograms are created for the classes TH1I , TH2F , TH3D :
– or –
 Clone/copy an existing histogram with the
Clone()
method.
Example
Filling a histogram
 Fill a histogram with the TH1::Fill() method.
Examples
The Fill()
method computes the bin number corresponding to the given x, y or z argument and increments this bin by the given weight.
The Fill()
method returns the bin number for 1D histograms or global bin number for 2D and 3D histograms.
Filling a histogram with random numbers
 Fill a histogram with random numbers with the TH1::FillRandom() method.
The FillRandom()
method uses the contents of an existing TF1
function or another TH1
histogram (for all dimensions).
Example
A histogram is randomly filled 10 000 times with a default Gaussian distribution of mean 0 and sigma 1.
Use the TH1::GetRandom() method to get a random number distributed according the contents of a histogram.
Adding, multiplying and dividing histograms
Following operations are supported on histograms or between histograms:

Addition of a histogram to the current histogram.

Additions of two histograms with coefficients and storage into the current histogram.

Multiplications and divisions are supported in the same way as additions.
You can use the operators (+, *, /) or the TH1
methods Add()
, Multiply()
and Divide()
.
Examples
Multiplying a histogram object with a constant:
Creating a new histogram without changing the original one:
Multiplying two histograms and put the result in the third one:
Drawing a histogram

Use the TH1::Draw() method to draw a histogram.
It creates a THistPainter object that specializes the drawing of the histogram. The
THistPainter
class is separated from the histogram, so that the histogram does not contain the graphics overhead. 
Use the TH1::DrawCopy() method to create a copy of the histogram when drawing it.

Use the TH1::DrawNormalized() method to draw a normalized copy of a histogram.
Example
Figure: Histogram drawn with Draw().
Getting the bin width
 Use the GetBinWidth() method to get the bin width of a histogram.
Drawing options
Note
The drawing options are not case sensitive.
Drawing options for all histogram classes
For detailed information on the drawing options for all histogram classes, refer to THistPainter.
AXIS
: Draws only the axis.
HIST
: When a histogram has errors, it is visualized by default with error bars. To visualize it without errors, use HIST together with the required option (for example “HIST SAME C
”).
SAME
: Superimposes on previous picture in the same pad.
CYL
: Uses cylindrical coordinates.
POL
: Uses polar coordinates.
SPH
: Uses spherical coordinates.
PSR
: Uses pseudorapidity/phi coordinates.
LEGO
: Draws a lego plot with hidden line removal.
LEGO1
: Draws a lego plot with hidden surface removal.
LEGO2
: Draws a lego plot using colors to show the cell contents.
SURF
: Draws a surface plot with hidden line removal.
SURF1
: Draws a surface plot with hidden surface removal.
SURF2
: Draws a surface plot using colors to show the cell contents.
SURF3
: Same as SURF with a contour view on the top.
SURF4
: Draws a surface plot using Gouraud shading.
SURF5
: Same as SURF3
but only the colored contour is drawn. Used with option CYL
, SPH
or PSR
, it allows to draw colored contours on a sphere, a cylinder or in a pseudo rapidly space. In Cartesian or polar coordinates, option SURF3 is used.
Example
Figure: Histogram drawn with Draw(“LEGO1”).
Figure: Histogram drawn with Draw(“LEGO1 POL”).
Drawing options for 1D histogram classes
For detailed information on the drawing options for 1D histogram classes, refer to THistPainter.
AH
: Draws the histogram, but not the axis labels and tick marks.
B
: Draws a bar chart.
C
: Draws a smooth curve through the histogram bins.
E
: Draws error bars.
E0
: Draws error bars including bins with 0 contents.
E1
: Draws error bars with perpendicular lines at the edges
E2
: Draws error bars with rectangles.
E3
: Draws a filled area through the end points of the vertical error bars.
E4
: Draws a smoothed filled area through the end points of the error bars.
L
: Draws a line through the bin contents.
P
: Draws a (poly)marker at each bin using the histogram’s current marker style.
P0
: Draws current marker at each bin including empty bins.
PIE
: Draws a pie chart.
H
: Draws a histogram with a * at each bin.
LF2
: Draws a histogram with option L
but with a filled area. L
also draws a filled area if the histogram fill color is set but the fill area corresponds to the histogram contour.
9
: Forces a histogram to be drawn in high resolution mode. By default, the histogram is drawn in low resolution in case the number of bins is greater than the number of pixels in the current pad.
][
: Draws a histogram without the vertical lines for the first and the last bin. Use it, when superposing many histograms on the same picture.
Drawing options for 2D histogram classes
For detailed information on the drawing options for 2D histogram classes, refer to THistPainter .
By default, 2D histograms are drawn as scatter plots.
ARR
: Arrow mode. Shows gradient between adjacent cells.
BOX
: Draws a box for each cell with surface proportional to contents.
BOX1
: A sunken button is drawn for negative values, a raised one for positive values
COL
: Draws a box for each cell with a color scale varying with contents.
COLZ
: Same as COL
with a drawn color palette.
CONT
: Draws a contour plot (same as CONT0
).
CONTZ
: Same as CONT
with a drawn color palette.
CONT0
: Draws a contour plot using surface colors to distinguish contours.
CONT1
: Draws a contour plot using line styles to distinguish contours.
CONT2
: Draws a contour plot using the same line style for all contours.
CONT3
: Draws a contour plot using fill area colors.
CONT4
: Draws a contour plot using surface colors (SURF2
option at theta = 0
).
CONT5
: Uses Delaunay triangles to compute the contours.
LIST
: Generates a list of TGraph
objects for each contour.
FB
: To be used with LEGO
or SURFACE
, suppresses the FrontBox.
BB
: To be used with LEGO
or SURFACE
, suppresses the backbox.
A
: To be used with LEGO
or SURFACE
, suppresses the axis.
SCAT
: Draws a scatterplot (default).
SPEC
: Uses the TSpectrum2Painter
tool for drawing.
TEXT
: Draws bin contents as text (format set via gStyle>SetPaintTextFormat
).
TEXTnn
: Draws bin contents as text at angle nn (0 < nn < 90).
[cutg]
: Draws only the subrange selected by the TCutG
name “cutg
”.
Z
: The Z option can be specified with the options: BOX
, COL
, CONT
, SURF
, and LEGO
to display.
Drawing options for 3D histogram classes
For detailed information on the drawing options for 3D histogram classes, refer to THistPainter .
By default, 3D histograms are drawn as scatter plots.
BOX
: Draws a box for each cell with volume proportional to the contents.
LEGO
: Same as BOX
.
ISO
: Draws an iso surface.
FB
: Suppresses the frontbox.
BB
: Suppresses the backbox.
A
: Suppresses the axis.
Drawing a histogram with error bars
You can draw a histogram with error bars.
Example
A canvas with the histogram is displayed.

Click
View
, and then clickEditor
. 
Click on the histogram.
In the Style
tab, you can select the error bars to displayed for the histogram.
Figure: Selection of error bars for a histogram.
 Select
Simple
.
The size of the error bars is equal to the square root of the number of events in the histogram.
Figure: Error bars for a histogram.
Instead of using the Editor
, you also can simply draw the error bars by:
Example: Histogramming a data analysis
In Example: Using a ROOT macro for data analysis was shown how to create a ROOT macro for analyzing a tree in a ROOT file.
Here it is shown, how to create a histogram for a variable hPosX
for this data analysis.
Example
A 1D histogram TH1F
is created for the X position of particles (hPosX
).
Profile histograms
Profile histograms are used to display the mean value of Y
and its error for each bin in X
.
When you fill a profile histogram with the TProfile.Fill() method:

H[j]
contains for each binj
the sum of they
values for this bin. 
L[j]
contains the number of entries in the binj
. 
e[j]
ors[j]
will be the resulting error depending on the selected option.
The following formulae show the cumulated contents (capital letters) and the values displayed by the printing or plotting routines (small letters) of the elements for bin J
.
E[j] = sum Y**2
L[j] = number of entries in bin J
H[j] = sum Y
h[j] = H[j] / L[j]
s[j] = sqrt[E[j] / L[j]  h[j]**2]
e[j] = s[j] / sqrt[L[j]]
The displayed bin content for bin J
of a TProfile
is always h(J).
The corresponding bin error is by default e(J).
In case the option s
is used (in the constructor or by calling TProfile::BuildOptions) the displayed error is s(J)
.
In the special case where s[j]
is zero, when there is only one entry per bin, e[j]
is computed from the average of the s[j]
for all bins. This approximation is used to keep the bin during a fit operation.
Example
Figure: A profile histogram example.