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.
ListPolarPlot
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
- ListPolarPlot [list] by default plots each element of list as a separate point.
- ListPolarPlot [list,Joined->True ] draws a line through the list of points.
- The angle is measured in radians, counterclockwise from the positive axis.
- The , position corresponding to , is , . The value of need not be between 0 and .
- In ListPolarPlot [{r1,…,rn}], r1 is taken to be associated with , and rn with .
- ListPolarPlot [Tabular […]cspec] extracts and plots values from the tabular object using the column specification cspec.
- The following forms of column specifications cspec are allowed for plotting tabular data:
-
{colθ,colr} plot column r against column θ{{colθ1,colr1},{colθ2,colr2},…} plot column r1 against column θ1, r2 against θ2, …colr, {colr} plot column r as a sequence of values{{colr1},…,{colri},…} plot columns y1, y2, … as sequences of values
- The following wrappers w can be used for the listi:
-
- Wrappers w can be applied at multiple levels:
-
{…,w[ri],…} wrap the value ri in data{…,w[{θ1,r1}],…} wrap the point {θ1,r1}w[listi] wrap the dataw[{list1,…}] wrap a collection of listiw1[w2[…]] use nested wrappers
- Callout , Labeled and Placed can use the following positions pos:
-
Automatic automatically placed labels{x,y} at a position {x,y}{pos,epos} epos in label placed at relative position pos of the data
- ListPolarPlot has the same options as ListPlot , with the following changes: [List of all options]
-
- ColorData ["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle .
- Possible settings for ScalingFunctions include:
-
sr scale the r axis{sx,sy} scale the r axis{sx,sy,sθ,sr} scale x, y, θ and r
- Common built-in scaling functions s include:
-
"Log" log scale with automatic tick labeling"Log10" base-10 log scale with powers of 10 for ticks"SignedLog" log-like scale that includes 0 and negative numbers"Reverse" reverse the coordinate direction"Infinite" infinite scale
- In general, you cannot scale both x or y and r simultaneously.
- Highlight options with settings specific to ListPolarPlot
-
ImageMargins 0. the margins to leave around the graphicPlotLayout "Overlaid" how to position dataPreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic
List of all options
Examples
open all close allBasic Examples (3)
Plot a list of radii r equally spaced in angle:
Join the points with a line:
Use θ, r coordinates for the data:
Show multiple sets of data with a legend:
Scope (30)
Data (9)
For regular data consisting of r values, the θ data range is uniformly spaced:
Provide an explicit θ data range by using DataRange :
Plot multiple sets of regular data:
For irregular data consisting of θ, r value pairs, the θ data range is inferred from data:
Plot multiple sets of irregular data:
Ranges where the data is nonreal are excluded:
Use MaxPlotPoints to limit the number of points used:
PlotRange is selected automatically:
Use PlotRange to focus on areas of interest:
Plot a TimeSeries :
Tabular Data (1)
Get tabular data:
Specify which columns to use as angle and radius:
Plot a list of radii r equally spaced in angle:
Show multiple sets of θ, r pairs:
Labeling and Legending (11)
Add labels to each point:
Use Callout to add a label to a set of points:
Place the label at a position:
Place the label at scaled position:
Place the labels relative to the inside of the data:
Place the labels relative to the outside of the data:
Label the data with PlotLabels :
Label multiple curves:
Use a scaled position:
Specify the text position relative to the point:
Specify the label at {x,y} position:
Reverse the direction of the x axis:
Use a log scale for the radius:
Presentation (9)
Use Joined to connect datasets with lines:
Multiple datasets are automatically colored to be distinct:
Provide explicit styling to different sets:
Add labels:
Provide an interactive Tooltip for the data:
Use shapes to distinguish different datasets:
Use legends:
Use Legended to add an additional legend:
Use InterpolationOrder to smooth joined data:
Use a theme with dark background and simple ticks:
Options (102)
ColorFunction (5)
ColorFunction only applies to Joined datasets:
Color by scaled x, y, theta, and r coordinates:
Color with a named color scheme:
ColorFunction has higher priority than PlotStyle for coloring the curve:
Use Automatic in MeshShading to use ColorFunction :
ColorFunctionScaling (3)
ColorFunctionScaling only applies to Joined datasets:
Color the line based on the scaled r value:
Manually scale the r value:
DataRange (4)
Lists of radii are equally spaced in angle around the origin:
Give the starting and ending angles:
Each dataset is scaled to the same domain:
Pairs are interpreted as θ, r coordinates:
Specifying DataRange in this case has no effect, since θ values are part of the data:
ImageSize (7)
Use named sizes such as Tiny , Small , Medium and Large :
Specify the width of the plot:
Specify the height of the plot:
Allow the width and height to be up to a certain size:
Specify the width and height for a graphic, padding with space if necessary:
Setting AspectRatio Full will fill the available space:
Use maximum sizes for the width and height:
Use ImageSize Full to fill the available space in an object:
Specify the image size as a fraction of the available space:
InterpolationOrder (5)
Joined lines can be interpolated:
By default, linear interpolation is used:
Use zero-order or piecewise-constant interpolation:
Use third-order spline interpolation:
Interpolation order zero to 5:
Joined (3)
Join the dataset with a line:
Join the first dataset with a line, but use points for the second dataset:
Join the dataset with a line and show the original points:
LabelingFunction (7)
By default, points are automatically labeled with strings:
Use LabelingFunction->None to suppress the labels:
Put the labels above the points:
Put them in a tooltip:
Use Callout to label the points:
Label the points with their values:
Label the points with their indices:
Specify an overall label with PlotLabels and put individual labels in Tooltip :
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:
LabelingTarget (6)
Labels are automatically placed to maximize readability:
Show all labels:
Use a denser layout for the labels:
Show the half of the labels that are easiest to read:
Only allow labels that are orthogonal to the points:
Only allow labels that are diagonal to the points:
Restrict labels to be above or to the right of the points:
Allow labels to be clipped by the edges of the plot:
MaxPlotPoints (2)
All points are included by default:
Uniformly spaced data is downsampled:
In this case, downsample from to points:
Mesh (6)
MeshFunctions (3)
MeshFunctions only applies to Joined datasets:
Use a mesh evenly spaced in the , , , and directions:
Show 5 mesh levels in the direction (red) and 10 in the direction (blue):
MeshShading (7)
MeshShading only applies to Joined datasets:
Alternate red and blue segments of equal angles in the θ direction:
Use None to remove segments:
MeshShading can be used with PlotStyle :
MeshShading has higher priority than PlotStyle for styling the curve:
Use PlotStyle for some segments by setting MeshShading to Automatic :
MeshShading can be used with ColorFunction and has higher priority:
MeshStyle (5)
PlotLabels (5)
Add labels to the data:
Place the labels above the data:
Place the labels in different locations:
Use scaled position to place the labels:
Place labels relatively to the data:
Use None to not add a label:
PlotLegends (7)
No legend is used, by default:
Use a list of labels for a legend:
Generate a legend using placeholders:
Legends use the same styles as the plot:
Use Placed to specify the legend placement:
Place the legend inside the plot:
Legend layout changes automatically along with position:
Use PointLegend to change the legend appearance:
PlotMarkers (8)
ListPolarPlot normally uses distinct colors to distinguish different sets of data:
Automatically use colors and shapes to distinguish sets of data:
Use shapes only:
Change the size of the default plot markers:
Use arbitrary text for plot markers:
Use explicit graphics for plot markers:
Use the same symbol for all the sets of data:
Explicitly use a symbol and size:
PlotRange (2)
PlotRange is automatically calculated:
Show the whole dataset:
PlotStyle (7)
Use different style directives:
By default, different styles are chosen for multiple datasets:
Explicitly specify the style for different datasets:
PlotStyle applies to both lines and points:
PlotStyle can be combined with ColorFunction :
PlotStyle can be combined with MeshShading and has lower priority:
PlotTheme (1)
Use a theme with detailed ticks and simple grid lines:
Add a theme with detailed polar grid lines:
Add a color function:
PolarAxes (1)
Use polar axes:
Add polar grid lines:
Turn on the polar axis but not the radial axis:
PolarAxesOrigin (1)
Reorient the polar and radial axes so that they intersect where and :
Turn off the polar ticks and move the radial axis below the plot:
PolarGridLines (1)
Use automatic polar grid lines:
Specify particular polar grid lines and ticks:
Change the style of the specified grid lines:
PolarTicks (1)
Use automatic polar ticks:
Change the labels for some of the ticks so the angle runs from to instead of to :
Display polar ticks in degrees and specify the radial ticks:
ScalingFunctions (3)
By default, ListPolarPlot uses natural scale in both axes:
Use ScalingFunctions to reverse the coordinate direction in the y direction:
Use a log scale for the radius:
Properties & Relations (13)
ListPolarPlot is a special case of ListPlot :
Use PolarPlot for functions:
Use ListPlot and ListLinePlot for Cartesian plots:
Use ListLogPlot , ListLogLogPlot , and ListLogLinearPlot for logarithmic plots:
Use DateListPlot to show data over time:
Use ListPointPlot3D to show three-dimensional points:
Use ListPlot3D to create surfaces from data:
Use ListContourPlot to create contours from continuous data:
Use ListDensityPlot to create densities from continuous data:
Use ArrayPlot and MatrixPlot for arrays of discrete values:
Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:
Use ParametricPlot for parametric curves:
RadialAxisPlot displays coordinates of -dimensional points around a circle:
Neat Examples (1)
Parametrized butterflies:
Related Guides
History
Introduced in 2007 (6.0) | Updated in 2008 (7.0) ▪ 2012 (9.0) ▪ 2019 (12.0) ▪ 2022 (13.1) ▪ 2025 (14.2) ▪ 2025 (14.3)
Text
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.
APA
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: 05-December-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: 05-December-2025]}