Polar Graph Paper Template

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• January 3, 2022 Updated
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The Polar Vortex comes down every so often, making us reach for our winter jackets, hats, and gloves. But the Polar Graph template has nothing to do with cold weather, and more to do with simplifying complex circular data and displaying it on paper. The polar graph template is useful for visually representing circular motion, using polar coordinates. This template contains a worksheet with a blank graph and another worksheet with a ready-to-use table, which allows you to enter your values and instantly plot them on a polar graph in Excel.

Template Contents

Here is a list of worksheets included in this template.

Blank Graph

A blank polar graph in portrait orientation, ideally used as a printout for plotting by hand.

(Graph) With Values

An automated polar graph in landscape orientation. This worksheet allows you to enter your circular coordinate data - R (radius) and θ (theta, angle), in rows A and B, which are then used to instantly calculate degrees, using the “SIN” and “COS” function, to be plotted on a polar graph.

Using the Template

Personalize and Print

Add a personal touch! Each worksheet has a built-in header. Use the header to include information, such as name, title, and date.

Go ahead and hit print - each tab is configured to print in its appropriate orientation type.

Graphing Polar Coordinates

Polar coordinates are represented as (r,θ) where -

R = Radius (or distance).

Θ = Theta, which represents angle.

To graph polar coordinates, make a table with distance (r) and angles (θ) values.

For example, if R = 0 and Θ = 0, the coordinate is plotted at the center of the polar graph. If the next coordinate in this circular motion is R = 6 and Θ = π/6 the coordinate is plotted at a radius of 6 to the right and a curved line is used to show the angle (Θ) of π/6 .

To get more insight into graphing polar equations - this WikiHow article is a good place to start.

Youtube videos can also be helpful to further your understanding of graphing polar equations.

A good video tutorial on how to graph polar equations can be found on StraighterLine YouTube channel

Working in Excel

Blank Graph

The polar blank graph template is ideal for printing and plotting by hand, but working in Excel is also an option. You can work out the mathematics on a separate worksheet and plot the coordinates by inserting plot points and curved lines.

To insert linear objects and plot points, select “Illustrations”, and then select “Shapes”, under the “Insert” menu. In the example above, we use a curve line from the “Lines” category and a circular icon for plot points.

While using the curve line, click on each plot point to extend the line until it meets the original starting plot point.

Excel Graph with Values

The Excel graph worksheet can do the graphing for you, as long as you know the polar coordinates you are trying to plot. Enter the “R” and “Theta” values (columns A and B) and the rest happens automatically - calculations are applied using the SIN and COS functions to determine degrees, and plot the coordinates on the polar graph.

Note: do not enter values in columns C and D; these columns are automatic calculations

Customize

Add Some Color

Background graph paper color can be jazzed up just the way you like it. To modify graph paper background, right-click on the “Chart Area” (outside of the grid lines) and select “Fill” to pick a new color.

Grid line color can also be changed by right-clicking on each segment of grid lines and selecting “Outline” to change the line color. Line style and weight can also be altered using the same menu.

If you want to get really fancy you can change the color of individual graph segments by right-clicking on each line segment and using the “Fill” option to change color.

Titles

In addition to changing the color of your chart, you may also want to add “Chart Title”, as well as title the axes.

To add axis titles, go to the “Design” menu and select “Add Chart Element”. Next, select “Axis Titles” (horizontal and/or vertical). A textbox will appear along the axis - click on the textbox to type in axis title. To add a chart title, repeat the same steps and select “Chart Title” under the “Add Chart Element” dropdown menu.

Displaying Data Points

In addition to circular visual representation, some people crave numbers! You can choose to display the coordinates directly on the polar graph for numeric presentation purposes.

To display data points on the polar graph, click on the circular plot results inside the graph. Tip: clicking other segments of the graph (outside of the plot results) will bring in unwanted data points. Next, go to the “Design” menu, select “Add Chart Elements”, then “Data Labels”, and finally select the desired placement of the data points.

We hope this article was helpful.

If you have suggestions or comments about your user experience, let us know!