WOLFRAM

ListPolarPlot[{r1,r2,}]

plots points equally spaced in angle at radii ri.

ListPolarPlot[{{θ1,r1},{θ2,r2},}]

plots points at polar coordinates θi, ri.

ListPolarPlot[{list1,list2,}]

plots several lists of values.

Details and Options

Examples

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Basic Examples  (3)Summary of the most common use cases

Plot a list of radii r equally spaced in angle:

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Join the points with a line:

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Use θ, r coordinates for the data:

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Show multiple sets of data with a legend:

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Scope  (30)Survey of the scope of standard use cases

Data  (9)

For regular data consisting of r values, the θ data range is uniformly spaced:

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Provide an explicit θ data range by using DataRange:

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Plot multiple sets of regular data:

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For irregular data consisting of θ, r value pairs, the θ data range is inferred from data:

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Plot multiple sets of irregular data:

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Ranges where the data is nonreal are excluded:

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Use MaxPlotPoints to limit the number of points used:

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PlotRange is selected automatically:

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Use PlotRange to focus on areas of interest:

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Plot a TimeSeries:

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Tabular Data  (1)

Get tabular data:

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Specify which columns to use as angle and radius:

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Plot a list of radii r equally spaced in angle:

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Show multiple sets of θ, r pairs:

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Labeling and Legending  (11)

Add labels to each point:

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Use Callout to add a label to a set of points:

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Place the label at a position:

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Place the label at scaled position:

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Place the labels relative to the inside of the data:

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Place the labels relative to the outside of the data:

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Label the data with PlotLabels:

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Label multiple curves:

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Use a scaled position:

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Specify the text position relative to the point:

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Specify the label at {x,y} position:

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Reverse the direction of the x axis:

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Use a log scale for the radius:

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Presentation  (9)

Use Joined to connect datasets with lines:

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Multiple datasets are automatically colored to be distinct:

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Provide explicit styling to different sets:

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Add labels:

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Provide an interactive Tooltip for the data:

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Use shapes to distinguish different datasets:

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Use legends:

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Use Legended to add an additional legend:

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Use InterpolationOrder to smooth joined data:

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Use a theme with dark background and simple ticks:

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Options  (92)Common values & functionality for each option

ColorFunction  (5)

ColorFunction only applies to Joined datasets:

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Color by scaled x, y, theta, and r coordinates:

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Color with a named color scheme:

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ColorFunction has higher priority than PlotStyle for coloring the curve:

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Use Automatic in MeshShading to use ColorFunction:

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ColorFunctionScaling  (3)

ColorFunctionScaling only applies to Joined datasets:

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Color the line based on the scaled r value:

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Manually scale the r value:

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DataRange  (4)

Lists of radii are equally spaced in angle around the origin:

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Give the starting and ending angles:

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Each dataset is scaled to the same domain:

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Pairs are interpreted as θ, r coordinates:

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Specifying DataRange in this case has no effect, since θ values are part of the data:

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ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

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Specify the width of the plot:

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Specify the height of the plot:

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Allow the width and height to be up to a certain size:

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Specify the width and height for a graphic, padding with space if necessary:

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Setting AspectRatioFull will fill the available space:

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Use maximum sizes for the width and height:

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Use ImageSizeFull to fill the available space in an object:

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Specify the image size as a fraction of the available space:

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InterpolationOrder  (5)

Joined lines can be interpolated:

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By default, linear interpolation is used:

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Use zero-order or piecewise-constant interpolation:

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Use third-order spline interpolation:

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Interpolation order zero to 5:

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Joined  (3)

Join the dataset with a line:

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Join the first dataset with a line, but use points for the second dataset:

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Join the dataset with a line and show the original points:

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LabelingFunction  (7)

By default, points are automatically labeled with strings:

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Use LabelingFunction->None to suppress the labels:

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Put the labels above the points:

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Put them in a tooltip:

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Use Callout to label the points:

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Label the points with their values:

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Label the points with their indices:

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Specify an overall label with PlotLabels and put individual labels in Tooltip:

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LabelingSize  (2)

Textual labels are shown at their actual sizes:

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Specify the size of the text:

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Image labels are resized to fit in the plot:

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Specify the labeling size:

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MaxPlotPoints  (2)

All points are included by default:

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Uniformly spaced data is downsampled:

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In this case, downsample from to points:

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Mesh  (6)

Mesh only applies to Joined datasets:

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The initial and final sampling meshes are typically the same:

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Interpolated data may introduce points:

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Use 20 mesh levels evenly spaced in the θ direction:

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

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Use explicit styles at specific points:

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MeshFunctions  (3)

MeshFunctions only applies to Joined datasets:

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

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Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

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MeshShading  (7)

MeshShading only applies to Joined datasets:

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Alternate red and blue segments of equal angles in the θ direction:

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Use None to remove segments:

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MeshShading can be used with PlotStyle:

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MeshShading has higher priority than PlotStyle for styling the curve:

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Use PlotStyle for some segments by setting MeshShading to Automatic:

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MeshShading can be used with ColorFunction and has higher priority:

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MeshStyle  (5)

MeshStyle only applies to Joined datasets:

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Color the mesh the same color as the plot:

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Use a red mesh in the direction:

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

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Use big red mesh points in the θ direction:

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PlotLabels  (5)

Add labels to the data:

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Place the labels above the data:

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Place the labels in different locations:

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Use scaled position to place the labels:

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Place labels relatively to the data:

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Use None to not add a label:

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PlotLegends  (7)

No legend is used, by default:

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Use a list of labels for a legend:

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Generate a legend using placeholders:

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Legends use the same styles as the plot:

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Use Placed to specify the legend placement:

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Place the legend inside the plot:

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Legend layout changes automatically along with position:

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Use PointLegend to change the legend appearance:

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PlotMarkers  (8)

ListPolarPlot normally uses distinct colors to distinguish different sets of data:

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Automatically use colors and shapes to distinguish sets of data:

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Use shapes only:

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Change the size of the default plot markers:

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Use arbitrary text for plot markers:

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Use explicit graphics for plot markers:

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Use the same symbol for all the sets of data:

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Explicitly use a symbol and size:

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PlotRange  (2)

PlotRange is automatically calculated:

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Show the whole dataset:

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PlotStyle  (7)

Use different style directives:

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By default, different styles are chosen for multiple datasets:

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Explicitly specify the style for different datasets:

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PlotStyle applies to both lines and points:

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PlotStyle can be combined with ColorFunction:

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PlotStyle can be combined with MeshShading and has lower priority:

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MeshStyle by default uses the same style as PlotStyle:

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PlotTheme  (1)

Use a theme with detailed ticks and simple grid lines:

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Add a theme with detailed polar grid lines:

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Add a color function:

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ScalingFunctions  (3)

By default, ListPolarPlot uses natural scale in both axes:

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Use ScalingFunctions to reverse the coordinate direction in the y direction:

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Use a log scale for the radius:

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Properties & Relations  (13)Properties of the function, and connections to other functions

ListPolarPlot is a special case of ListPlot:

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Use PolarPlot for functions:

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Use ListPlot and ListLinePlot for Cartesian plots:

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Use ListLogPlot, ListLogLogPlot, and ListLogLinearPlot for logarithmic plots:

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Use DateListPlot to show data over time:

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Use ListPointPlot3D to show three-dimensional points:

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Use ListPlot3D to create surfaces from data:

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Use ListContourPlot to create contours from continuous data:

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Use ListDensityPlot to create densities from continuous data:

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Use ArrayPlot and MatrixPlot for arrays of discrete values:

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Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:

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Use ParametricPlot for parametric curves:

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RadialAxisPlot displays coordinates of -dimensional points around a circle:

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Neat Examples  (1)Surprising or curious use cases

Parametrized butterflies:

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Wolfram Research (2007), ListPolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListPolarPlot.html (updated 2025).
Wolfram Research (2007), ListPolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListPolarPlot.html (updated 2025).

Text

Wolfram Research (2007), ListPolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListPolarPlot.html (updated 2025).

Wolfram Research (2007), ListPolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListPolarPlot.html (updated 2025).

CMS

Wolfram Language. 2007. "ListPolarPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ListPolarPlot.html.

Wolfram Language. 2007. "ListPolarPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ListPolarPlot.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_listpolarplot, author="Wolfram Research", title="{ListPolarPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ListPolarPlot.html}", note=[Accessed: 28-May-2025 ]}

@misc{reference.wolfram_2025_listpolarplot, author="Wolfram Research", title="{ListPolarPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ListPolarPlot.html}", note=[Accessed: 28-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_listpolarplot, organization={Wolfram Research}, title={ListPolarPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ListPolarPlot.html}, note=[Accessed: 28-May-2025 ]}

@online{reference.wolfram_2025_listpolarplot, organization={Wolfram Research}, title={ListPolarPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ListPolarPlot.html}, note=[Accessed: 28-May-2025 ]}