generates a polar plot of a curve with radius r as a function of angle θ.


makes a polar plot of curves with radius functions r1, r2, .

Details and Options


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Basic Examples  (3)

Make a polar plot:

Make several polar plots:

Style the curves:

Scope  (22)

Sampling  (6)

More points are sampled when the function changes quickly:

The plot range is selected automatically:

Ranges where the function becomes nonreal are excluded:

The curve is split when there are discontinuities in the function:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Labeling and Legending  (7)

Use Callout to add the expressions as a label:

Use any text as a label:

Place the label along the curve:

Place the label at a scaled position:

Place the labels relative to the inside of the curve:

Place the labels relative to the outside of the curve:

Label the curve with PlotLabels:

Label multiple curves:

Use a scaled position:

Specify the text position relative to the point:

Specify the label at {x,y} position:

Presentation  (9)

Multiple curves are automatically colored to be distinct:

Provide explicit styling to different curves and regions:

Add labels:

Provide an interactive Tooltip for each curve:

Create an overlay mesh:

Style the areas between mesh levels:

Color by parameter values:

Legend multiple curves:

Use a theme with dark background and high-contrast colors:

Use a theme with minimal styling:

Options  (59)

ColorFunction  (4)

Color the curve by scaled , , , or value:

Use a named color gradient:

ColorFunction has higher priority than PlotStyle:

Use red for the parameter :

ColorFunctionScaling  (1)

Color the curve by angle:

EvaluationMonitor  (3)

Find the list of parameter values evaluated:

Find the coordinate values:

Count how many times the function is evaluated:

Exclusions  (3)

Automatically determine exclusions:

Provide an explicit list of points for exclusions:

Specify exclusions using equations:

ExclusionsStyle  (2)

Specify explicit styling for lines joining exclusion points:

Provide styling for both exclusion points and the lines joining them:

LabelingSize  (2)

Textual labels are shown at their actual sizes:

Specify the size of the text:

Image labels are resized to fit in the plot:

Specify the labeling size:

MaxRecursion  (1)

Each level of MaxRecursion will adaptively subdivide the initial mesh into a finer mesh:

Mesh  (4)

Show the initial and final sampling meshes:

Use 10 mesh points evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

Use explicit value and style for the mesh:

MeshFunctions  (2)

Use a mesh evenly spaced in the , , , and directions:

Show five mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue arcs in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

MeshStyle  (4)

Automatically choose the mesh style:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big red mesh levels in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotPoints  (1)

Use more initial points to get a smoother plot:

PlotLabels  (6)

PlotLabels->"Expressions" uses functions as curve labels:

Specify the text to label the curves:

Place the labels above the curves:

Place the labels differently for each curve:

Use callouts to identify the curves:

Put labels relative to the outside of the curves:

Use None to not add a label:

PlotLegends  (7)

Use the automatic legend:

No legends are used by default:

Use legends:

Show no legends:

PlotLegends automatically picks up PlotStyle option values:

Show expressions as legends in TraditionalForm:

Specify a list of labels for legends:

Place legends outside:

Place legends inside:

Legend layout changes automatically along with position:

Use LineLegend to adjust the appearance of the legend:

Specify LegendMarkers:

PlotRange  (2)

Show the curve where and :

With the natural range of values, the fine detail around the origin is not visible:

Use PlotRange to focus in on areas of interest:

PlotStyle  (5)

Use different style directives:

By default, different styles are chosen for multiple curves and regions:

Explicitly specify the style for different curves and regions:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with MeshShading:

PlotTheme  (1)

Use a theme with polar grid lines and bright colors:

Add another theme with legends:

Change plot styles:

RegionFunction  (1)

Show the plot where :

WorkingPrecision  (2)

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications  (4)

Plot a circle:

A spiral:

An oscillation around a circle:

Archimedean spirals of the form :

Archimedean spirals of the form :

Logarithmic spirals have the form :

Create a Guilloché pattern [more info]:

Properties & Relations  (5)

PolarPlot is a special case of ParametricPlot for curves:

Use ListPolarPlot for data:

Use Plot3D and ParametricPlot3D for function and parametric surfaces:

Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:

Use ContourPlot and RegionPlot for implicit curves and regions:

Neat Examples  (2)

Wolfram Research (2007), PolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PolarPlot.html (updated 2019).


Wolfram Research (2007), PolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PolarPlot.html (updated 2019).


@misc{reference.wolfram_2020_polarplot, author="Wolfram Research", title="{PolarPlot}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolarPlot.html}", note=[Accessed: 21-January-2021 ]}


@online{reference.wolfram_2020_polarplot, organization={Wolfram Research}, title={PolarPlot}, year={2019}, url={https://reference.wolfram.com/language/ref/PolarPlot.html}, note=[Accessed: 21-January-2021 ]}


Wolfram Language. 2007. "PolarPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/PolarPlot.html.


Wolfram Language. (2007). PolarPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolarPlot.html