Polar Graphing

Convert the coordinate plane to a polar grid to explore circles, spirals, roses, limacons, and more.

Watch the video for an introduction to polar graphing, and read on to learn more.

The Desmos Graphing Calculator considers any equation or inequality written in terms of \(r\) and \(𝜃\) to be in polar form and will plot the equation or inequality as a polar curve or region.

By default, polar curves are plotted for values of \(𝜃\) in the interval \([0, 12π].\) If the calculator detects that a curve is periodic, it may adjust the curve's domain to plot one full period. You can also set the domain manually in the same line as your expression.

Polar inequalities will only display regions where the radius is positive to avoid many common cases, like \(r\lt 1\), where including regions of negative radius would shade the whole plane. If you want your inequality to include regions with negative radius, use its absolute value.

If you would like to display a polar grid, rather than the default Cartesian grid, click Graph Settings . Then, go to Grid and toggle between the Cartesian and polar grids.

Polar equations must be linear in \(r\), and it is currently not possible to plot polar equations of the form \(𝜃 = f(r).\)