is an option for graphics functions that specifies what range of coordinates to include in a plot.


  • PlotRange can be used for both two- and three-dimensional graphics.
  • The following settings can be used:
  • Allall points are included
    Automaticoutlying points are dropped
    Fullinclude full range of original data
    maxexplicit limit for each function (see below)
    {min,max}explicit limits for y (2D), z (3D), or array values
    {{xmin,xmax},{ymin,ymax}}explicit limits for x and y
    {{xmin,xmax},{ymin,ymax},{zmin,zmax}}explicit limits for x, y, and z (3D)
  • When no explicit limits are given for a particular coordinate, a setting of Automatic is assumed.
  • With the Automatic setting, the distribution of coordinate values is found, and any points sufficiently far out in the distribution are dropped. Such points are often produced as a result of singularities in functions being plotted.
  • Any explicit limit or pair {min,max} can be replaced by a specification such as All or Automatic.
  • A setting such as {min,Automatic} gives a particular minimum value for a coordinate, with a maximum value to be determined automatically.
  • If a particular minimum or maximum is specified as {Automatic,α}, this means that the range should in effect be cut off beyond a fraction α of points in the plot. When smooth curves or surfaces are plotted, the measure of points is based on projected length or area.
  • The setting Full can be used in Plot and related functions to specify that a range determined by the original input to the plotting function should be used. »
  • Plot[f,{x,xmin,xmax},PlotRange->Full] specifies that the full range {xmin,xmax} should be used, even if no actual values of f are plotted in part of that range.
  • With the setting PlotRange->s, the following ranges are used: »
  • Graphics{{-s,s},{-s,s}}
    ListPlot and ListLinePlot {Full,{0,s}}
    ParametricPlot and RegionPlot {{-s,s},{-s,s}}
    ContourPlot and ListContourPlot{Full,Full,{-s,s}}
    DensityPlot and ListDensityPlot{Full,Full,{-s,s}}
    Plot3D and ListPlot3D{Full,Full,{-s,s}}
    ParametricPlot3D and RegionPlot3D{{-s,s},{-s,s},{-s,s}}
    ContourPlot3D and ListContourPlot3D{Full,Full,Full,{-s,s}}
  • AbsoluteOptions gives the explicit form of PlotRange specifications when Automatic settings are given.
  • The final absolute range of coordinates to include in a plot is determined by PlotRangePadding as well as PlotRange itself.


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Basic Examples  (3)

Automatically drop outlying points:

Explicitly choose and ranges:

Explicitly choose a range:

Choose the range to show all the existing points:

Use the full , range:

Scope  (8)

Normally, plot functions drop outlying points, which is equivalent to PlotRange->Automatic:

PlotRange->All shows all of the points:

PlotRange for Graphics and Graphics3D is All, by default:

Drop outlying points, by setting PlotRange->Automatic:

Use PlotRange->All to include all points:

Use PlotRange->Full to include all the points and the original domain:

An explicit range can be given in each direction by {min,max}:

One value of the explicit range can be a symbol such as All or Automatic:

The interpretation of PlotRange->max depends on the function:

Any valid range specification can be given to each direction:

Applications  (1)

Plot the CDF of the normal distribution with , :

Properties & Relations  (7)

Use ClippingStyle to style the region clipped by PlotRange:

In ordinary graphics, objects can extend beyond the plot range:

Use PlotRangeClipping->True to clip objects to the range:

Normally, plot functions clip objects to the range:

By default, 2% of padding is added to the plot range in each direction:

Prevent padding by setting PlotRangePadding to None:

Include 1 coordinate unit of padding on all sides:

No padding is added if the plot range is explicit:

Scaled coordinates are given by fractions of the plot range:

Neat Examples  (3)

An elementary function with pole singularities:

A function with a curve singularity:

A function with random poles:

Wolfram Research (1988), PlotRange, Wolfram Language function, (updated 2017).


Wolfram Research (1988), PlotRange, Wolfram Language function, (updated 2017).


Wolfram Language. 1988. "PlotRange." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017.


Wolfram Language. (1988). PlotRange. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_plotrange, author="Wolfram Research", title="{PlotRange}", year="2017", howpublished="\url{}", note=[Accessed: 16-June-2024 ]}


@online{reference.wolfram_2024_plotrange, organization={Wolfram Research}, title={PlotRange}, year={2017}, url={}, note=[Accessed: 16-June-2024 ]}