How do I switch between Cartesian and polar graphs?

Simply check or uncheck the 'Polar' checkbox. The grapher automatically updates your function variables—changing f(x) to r(θ) without altering the defining expression—allowing a direct comparison between coordinate systems.

What makes the polar graph animator unique?

Unlike instant plotters, our animator draws polar graphs step-by-step in real time. This controlled animation lets you clearly visualize how intricate curves and multiple loops are traced from start to finish.

Can I graph functions in an oblique coordinate system?

Yes. This versatile function plotter allows you to rotate the axes using your mouse, enabling you to graph functions in oblique (non-orthogonal) coordinate systems.

What are the text typing shortcuts for mathematical symbols?

While typing your function expressions: typing 't' or 'x' will automatically replace it with the theta symbol (θ), typing 'pi' will replace it with π, and typing 'inf' will automatically change to the infinity symbol (∞).

What are the default domains for Cartesian and polar systems?

The default domain for the Cartesian coordinate system is (-∞, ∞). For the polar coordinate system, the default domain is (0, 2π). Polar system endpoints must remain finite; any infinite values entered will be automatically adjusted.

Function Grapher | Cartesian & Polar Plot

Entering Function Expressions

By default, the function grapher plots in real time as you type. To explore graphs of functions in either the Cartesian or polar coordinate plane, type an expression into any input box—for example, f(x) or r(θ).

When you enter an expression, the grapher automatically adjusts the variables internally if necessary. To view these adjustments, simply hover your mouse over the expression type label located above the input box.

Note: You can instantly switch between Cartesian and polar graphs by checking or unchecking the Polar checkbox. This will redraw the function in the selected coordinate system—a feature unique to our function graphing calculator.

The function plotter automatically applies a suitable domain interval to your expressions and graphs them accordingly:

In the Cartesian Coordinate System: The default interval is dom=(-∞, ∞). You can customize these endpoints as needed.
In the Polar Coordinate System: The default interval is dom=(0, 2π). While you can modify these limits, they must remain finite to properly render polar graphs. If infinite values are entered, the grapher will automatically adjust them back to finite constraints.

How Our Polar Function Grapher Works

This unique, interactive polar function graphing calculator plots functions r(θ) directly in the polar coordinate plane. Unlike other graphers, it works exactly the way you would graph them on paper—without the need to convert to Cartesian coordinates.

For each value of the angular coordinate θ, a temporary radial axis is drawn at an angle of θ relative to the main polar axis. The plotter then computes the signed distance r(θ) and plots the point along that radial axis.
It then connects this point to the subsequent point, which is located using the same method with a slightly larger value of θ. This process continues sequentially until the polar graph is complete.

Our polar grapher also offers an animated graphing process—a feature vital for visualizing the detailed construction of polar graphs.

Polar Function Graph Animator

Why use animation? Polar curves can be intricate, often featuring multiple overlapping loops. Most other graphers only display the polar graph of a function instantly, without showing where it starts or ends, or how those loops—if present—are actively traced.

To address this, it is crucial to draw a polar graph step-by-step, allowing for a clear visualization of how the curve unfolds across its domain. Our polar graph animator, equipped with a sophisticated polar plotting algorithm, is specifically designed for this purpose.

It is the first tool to introduce the proper method for graphing functions in the polar coordinate system. It's the only polar function plotter that elegantly shows the rotating radial axis as the curve is progressively plotted to completion through a controlled animation.

This way, you can watch your polar graphs take shape in real time!

Function Grapher | Cartesian/Polar Plot

About the Function Grapher

Comprehensive Function Visualization

Entering Function Expressions

How Our Polar Function Grapher Works

Polar Function Graph Animator