Explore our free online **polar function grapher**, world's best polar function graphing calculator, easy-to-use and sophisticated.

## What is a *Polar* Function Grapher?

A ** polar function grapher** is a

*function grapher*that draws the graph of a function in the polar coordinate system on its domain of definition. A function graph in the polar coordinate system is called the

**polar graph**or

**polar curve**of the function.

## Features of Our *Polar* Function Grapher

**Animated Polar Graphs**: Experience the most captivating polar graph**animation**. Our online*polar*function grapher uses a unique**animation**algorithm to visualize the step-by-step construction of polar graphs of functions. This makes it easy to see how even the most complicated polar graphs are created.**Rotating Angular (Radial) Axes**: In**animating**the construction of polar graphs, our online*polar*function graphing calculator is unmatched in its ability to rotate radial axes. This allows you to create stunning visualizations that help you understand the intricacies of polar graphing of functions.**Seamless Switching Between Polar and Cartesian Graphs**: Our*polar*function grapher makes it easy to switch between polar and Cartesian coordinate systems by checking/unchecking the**Polar checkbox**. This allows you to visualize the**polar graph**and**Cartesian graph**of a given functions in either coordinate system with remarkable ease.

## How Our *Polar* Function Grapher Works

Our ** polar function grapher** plots

**function graphs**in the

**polar coordinate system**in a similar way to how you would graph them on paper.

The **polar function graphing calculator** does this by drawing **angular (radial) axes** for the values of `θ`

that increase incrementally.

For each value of `θ`

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

with the **polar axis**. The ** polar function graphing calculator** calculates 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 **thus completes the polar graph of the given function.**

*polar*function graphing calculator
*You can watch the entire polar graphing process by running the animation feature as described 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 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.`∞`