Mathematics & Physics•9 min read•Updated Aug 2026

Polar Coordinates & Radial Graphing Tutorial

Unlike Cartesian grids that describe location using horizontal \(x\) and vertical \(y\) offsets, polar graph paper defines points using distance \(r\) from the origin and angular angle \(\theta\). Here is how to master radial plotting.

Cartesian to Polar Conversion Formulas

To convert between rectangular \((x, y)\) coordinates and polar \((r, \theta)\) coordinates, use the fundamental trigonometric identities:

Coordinate Conversion Equations:

\(r = \sqrt(x^2 + y^2)\)

\(\theta = \arctan(y / x)\)

\(x = r \cdot \cos(\theta)\)

\(y = r \cdot \sin(\theta)\)

Plotting Rose Curves and Cardiods

Polar paper makes it simple to sketch periodic trigonometric curves:

Cardioid Curve (\(r = a(1 - \cos\theta)\)): Creates a heart-shaped boundary widely used to represent cardioid directional microphones.
Rose Curve (\(r = a \cos(n\theta)\)): Produces symmetric flower petals. If \(n\) is odd, the rose has \(n\) petals; if \(n\) is even, it has \(2n\) petals.

Download Printable Polar Graph Paper10-degree and 15-degree radial ray presets.

Get Polar Grid Paper PDF