Polar Graph Equations Simplified

Polar Graphs are best suited for displaying comparison insights into your data.

Why?

The charts are amazingly easy to interpret. Essentially, they use a strategic combination of colors and coordinates to compare key data points.

Google Sheets is one of the data visualization tools used widely across the world. The main reason why the tool is incredibly popular among professionals and business owners is that it’s free of charge.

But Google Sheets does not have Polar Graphs. Yes, you read that right.

It turns out you can visualize your data using Polar Graphs in your Google Sheets.

How?

To access ready-made and visually appealing Polar Graphs, you need only download and install a third-party application (add-on).

Table of Contents:

1. What is a Polar Coordinates & Polar Graph, and Why Do We Use it?
2. When Should We Use a Polar Graph Equation?
3. How to Write a Polar Graph Equation?
4. What is a Polar Curve?
5. Polar Equations Graphs Examples
6. How to Make a Polar Graph in a Few Clicks? Graphing Polar Equations?
7. How to Use the Polar Graph Equation?
8. Advantages of a Polar Graph Equation
9. Limitation of a Polar Graph Equation
10. FAQ About Polar Graph Equation
11. Wrap Up

What is a Polar Coordinates & Polar Graph, and Why Do We Use it?

Definition: A system of coordinates in which the location of a point is determined by its distance from a fixed point at the center of the coordinate space (called the pole), and by the measurement of the angle formed by a fixed line (the polar axis, corresponding to the x-axis in Cartesian coordinates) and a line from the pole through the given point. The polar coordinates of a point are given as (r, θ), where r is the distance of the point from the pole, and θ is the measure of the angle.

The chart is immensely similar to the multilayered Donut Chart. In other words, interpreting this chart is just as easy as getting insights from any other Chart.

Each layer is longer than the preceding one and has a varying radius and angle.

Like a Radar chart, the layers in this chart represent the changes in variables in your data. The sizes of the almost circular shapes, similar to a Circular chart, depict the magnitude of change in variables.

The visualization design has multiple monikers, such as the Spider or Web Chart.

When Should We Use a Polar Graph Equation?

We should use a polar graph equation when we want to represent data that has circular, periodic, or radial symmetry. Polar graphs are ideal for visualizing angles, directions, and waveforms, or when working with data that depends on distance from a central point, like in physics, navigation, or astronomy.

How to Write a Polar Graph Equation?

1. Identify Variables: A polar graph uses radial distance (r) and angle (θ) as its variables.
2. Choose the Equation: Common forms are $)$, where r is a function of the angle.
3. Set Relationships: Establish the mathematical relationship between r and θ (e.g., r=2+3sin(θ).
4. Plot the Equation: Use the angle θ on the polar axis and plot the corresponding r values.
5. Graph Symmetry: Many polar equations exhibit symmetry, which can simplify plotting.

In the next section, we’ll address the following question: what is a Polar curve?

What is a Polar Curve?

Polar curves (also known as Radar Charts) can help you understand plot equations with a different coordinate system.

The curve results from the polar equation defined by r and θ.

Use polar grids or polar planes to plot the polar curve and this graph is defined by all sets of (r, θ), that satisfy the given polar equation, r=f(θ).

In the coming section, we’ll expound more on graphs of polar equations.

Polar Equations Graphs Examples

Plotting a Polar equation is similar to rectangular equations.

When plotting rectangular equations by point-plotting, you normally pick values for x and then evaluate the equation to determine its corresponding y value.

• Limacons

If the polar equation has a general form of r=a±bcosθ or r=a±bsinθ, where a,b>0, its curve becomes a limacon (it’s French for snail).

Check out the variations of Limacons below.

• Rose

If the polar equation has a general form of r=acos(nθ) or r=asin(nθ), where a > 0, its curve is a Rose.

Each segment of the chart is called rose petals. The number of petals depends on whether n is even or odd.

• If n is even, the polar curve (rose) will show 2n petals.
• If n is odd, the polar curve (rose) will show n petals.

• Lemniscate

If the polar equation has a general form of r²=a²cos2θ or r=a²sin2θ, where a > 0, its curve is a Lemniscate.

How to Make a Polar Graph in a Few Clicks? Graphing Polar Equations?

There are a plethora of tools out there you can use to visualize your data using a Polar Graph equation.

Google Sheets is one of them.

It’s very understandable why people trust Google Sheets as their chosen tool for visualizing data. For starters, the tool has been there for decades. Furthermore, Google Sheets’s interface is familiar and friendly to a majority of business owners and professionals.

But, generating Polar Graph equations in Google Sheets is not a walk in the park. Google Sheets lacks ready-made Polar Graphs you can use to visualize data.

Besides, customizing existing charts to create a Polar Visualization is time-consuming and complex.

Here’s the kicker.

You don’t have to do away with Google Sheets. You can simply download and install a third-party add-in called ChartExpo.

What is ChartExpo?

ChartExpo is loaded with a ready-to-use Polar Graph equation Chart, plus many insightful and visually appealing advanced graphs such as Pareto Chart, Likert Scale Chart, Sankey Chart, etc.

You don’t have to be armed with coding/programming skills to use ChartExpo. You only need basic knowledge of visualization to operate the Google Sheets add-on without hitches.

Example

This section will use a Polar Graph equation to display insights into the table below.

Period	Inventory	Sales
Previous	Paints	612
Previous	Garden tools	553
Previous	Plumbing Items	628
Previous	Electrical Supplies	594
Previous	Power tools	604
Current	Paints	949
Current	Garden tools	956
Current	Plumbing Items	559
Current	Electrical Supplies	922
Current	Power tools	903

To Get Started with the Polar Graph in Google Sheets, install the ChartExpo add-on for Google Sheets from the link, and then follow the simple and easy steps below.

• Click the Add-on button>ChartExpo>Open.

• Click the Add New Chart button to access your fully stocked library of charts.

• You will see the list of charts available by ChartExpo in the right section of Google Sheets.

• Now Click the Search Box and type Radar Chart. It should pop up together with other charts. We will use Radar Chart as this chart has the option to convert into a Polar Graph as well.

• Select the sheet holding your data and select the Metrics option. Fill in the numerical numbers (in our scenario, we’ll fill in inventory and sales count)
• Select the Dimensions field and fill in the dimensional data (in our example, we’ll use period).

• Now you will see the radar chart by clicking the Create Chart button.

Now click on the Edit Chart button, click on the right top section Chart Settings then find Chart Type and Select “Polar” from the drop-down.  This Radar Chart visualization will be converted into a Polar Graph.

Below will be a look of the Polar Chart.

How to Edit Polar Graph?

As you can see there is no dollar sign with the data values, you can add prefixes with values by again clicking on Edit Chart and then finding the pencil icon near the data values and clicking on it.

Similarly, you can add a header on top of this chart and show a legend from the properties. If you follow the instructions above, your Polar Graph should look like the below:

Insights

• Previous data is shown in blue while current is shown in orange.
• All the products in the inventory except Plumbing Items performed better in the current period than in the previous period.
• In Previous data Garden tools were the worst performing whereas in current data it is highlighted as the best performers.

How to Use the Polar Graph Equation?

1. Input Values: Begin by plugging different angle values (θ) into the equation.
2. Calculate r: Solve for r based on the input θ values.
3. Plot Points: Plot the points using polar coordinates, where r represents the radius and θ the angle.
4. Connect the Points: Connect the points to form the graph, noting any symmetry.
5. Analyze the Shape: Observe patterns or shapes, such as circles, spirals, or roses, formed by the graph.

Advantages of a Polar Graph Equation

1. Effective for Circular Data: Polar graphs represent circular or periodic data, making them perfect for angles, directions, or oscillations.
2. Simplifies Complex Relationships: They display complex mathematical relationships between variables with radial symmetry.
3. Intuitive Visualization: Polar graphs provide a clear and intuitive way to visualize data with varying magnitudes and angles.
4. Flexible Representation: Useful in fields like physics, engineering, and navigation where radial data representation is essential.
5. Enhanced Clarity: Polar graphs reduce clutter by organizing data points around a central axis.

Limitation of a Polar Graph Equation

1. Complexity in Interpretation: Polar graphs can be harder to interpret compared to Cartesian graphs, especially for complex equations.
2. Limited Data Representation: They are best suited for cyclical or angular data, limiting their use for other types of data.
3. Difficult Plotting: Plotting polar graphs manually can be more challenging due to the need for precise angle measurements.
4. Not Ideal for Large Datasets: Polar graphs are less effective for displaying large or detailed datasets.
5. Symmetry Constraints: Many polar graphs inherently emphasize symmetry, which might not always be useful for non-symmetrical data.

FAQ About Polar Graph Equation

What is the Polar Chart used for?

A Polar Graph equation is a version of Bar Graphs plotted on a polar coordinate system rather than a Cartesian one.

You can use the chart to display trends, patterns, and relationships of key variables in your data. The chart is best suited for visualizing bulky data.

Wrap Up

Polar Graphs are best suited for displaying comparison insights into your data.

The charts are amazingly easy to interpret. Essentially, they use a strategic combination of colors and coordinates to compare key data points.

Google Sheets is one of the data visualization tools used widely across the world. The main reason why the tool is incredibly popular among professionals and business owners is that it’s free of charge.

But Google Sheets does not have Polar Graphs.

To access ready-made Polar Graph equations, we recommend you install third-party apps, such as ChartExpo, into your Google Sheets.

ChartExpo is an add-on you can easily download and install in your Google Sheets app. The tool comes loaded with ready-to-use Polar Charts, plus over 50 more ready-to-go visualization designs.

Sign up for a 7-day trial to enjoy unlimited access to ready-to-go and visually appealing Polar Charts.