This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


PolarPlot[r, {, min, max}]
generates a polar plot of a curve with radius r as a function of angle .
PolarPlot[{f1, f2, ...}, {, min, max}]
makes a polar plot of curves with radius functions f1, f2, ....
  • The angle theta is measured in radians, counterclockwise from the positive x axis.
  • The x, y position corresponding to r, theta is r cos(theta), r sin(theta). The value of theta need not be between 0 and 2 pi.
  • PolarPlot has attribute HoldAll, and evaluates functions only after assigning specific numerical values to theta.
  • In some cases it may be more efficient to use Evaluate to evaluate functions symbolically before specific numerical values are assigned to theta.
  • No curve is drawn in any region where a function evaluates to None.
  • PolarPlot has the same options as Graphics, with the following additions and changes:
AxesTruewhether to draw axes
AxesOrigin{0,0}the origin where axes cross
ColorFunctionAutomatichow to determine the coloring of curves
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
EvaluationMonitorNoneexpression to evaluate at every function evaluation
ExclusionsAutomaticpoints in theta to exclude
ExclusionsStyleNonewhat to draw at excluded points
MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
MeshNonehow many mesh points to draw on each curve
MeshFunctions{#3&}how to determine the placement of mesh points
MeshShadingNonehow to shade regions between mesh points
MeshStyleAutomaticthe style for mesh points
MethodAutomaticthe method to use for refining curves
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotPointsAutomaticinitial number of sample points
PlotRangeAutomaticthe range of values to include
PlotRangeClippingTruewhether to clip at the plot range
PlotStyleAutomaticgraphics directives to specify the style for each curve
RegionFunction(True&)how to determine whether a point should be included
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • PolarPlot[Tooltip[{f1, f2, ...}], {, min, max}] specifies that the fi should be displayed as tooltip labels for the corresponding curves.
  • Tooltip[f, label] specifies an explicit tooltip label for a curve.
  • PolarPlot initially evaluates functions at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
  • You should realize that with the finite number of sample points used, it is possible for PolarPlot to miss features in your function. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
  • On[PolarPlot::accbend] makes PolarPlot print a message if it is unable to reach a certain smoothness of curve.
  • With Mesh->All, PolarPlot will explicitly draw a point at every position on each curve where each function was sampled.
  • The functions are evaluated all along each curve.
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