**Visualize functions in a new way with our free online polar function grapher!** Compare **function graphs** in Cartesian and polar coordinate systems seamlessly, or explore the unique world of graphs of function in **oblique coordinate systems** - all in one powerful tool.

This dedicated **polar function grapher** uses a unique **animation** algorithm to visualize the step-by-step construction of the graph of a function in the **polar coordinate system** like no other grapher. With its ability to **rotate radial axes**, it helps you understand the **polar graphing process for functions** in stunning animation.

Our **polar grapher** makes it easy to switch between **polar** and **Cartesian** coordinate systems by checking or unchecking the **Polar checkbox**. This allows you to visualize the **polar graph** and **Cartesian graph** of a given function in either coordinate system with remarkable ease.

## How Our Polar Function Grapher Works

Our **polar function grapher** plots **graphs of functions** in the **polar coordinate system**, similarly to how you would graph them on paper.

For each value of `θ`

, a temporary **radial axis** is drawn, making an angle of `θ`

with the **polar axis**. The **polar function graphing calculator** computes the signed distance `r(θ)`

and locates that point along the radial axis.

The **polar function grapher** then connects this point to the next point located using the same method with a slightly larger value of `θ`

. The online **polar function graphing calculator** thus completes the polar graph of the given function.

*Our polar function grapher allows you to watch the entire animated graphing process, as detailed below*.

**Lines**

**Semi-circles**

**Semi-ellipses**

**Parabolas**

**Semi-hyperbolas**

**Other graphs**

**Lines**

**Circles**

**Spirals**

**Roses**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Cardioids**

**Limacons**

**Lemniscates**

**Butterfly curve**

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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the context (pop-up) menu.

As you type:

**..t**is replaced by. (You can also use`θ`

`x`

or`t`

; they are internally replaced by`θ`

).**pi**is replaced by.`π`

**inf**(**infinity**) is replaced by.`∞`