Polar graph paper, A4
Concentric rings at 10 mm with radial spokes, on A4, for polar coordinates, phasor diagrams and anything naturally described by an angle and a distance.
Opens with these settings already loaded. Change anything you like, then download as PDF, PNG or SVG.
When polar coordinates are the honest choice
Some curves are ugly in Cartesian coordinates and simple in polar ones. A circle centered on the origin is r = a. A spiral is r = aθ. Rose curves, cardioids and lemniscates all have short polar equations and unpleasant Cartesian ones. If the thing you are plotting is defined by a distance from a center and an angle, plotting it on a square grid means converting every point by hand for no benefit.
Reading the angular scale
The spokes give you the angular reference; the number of them determines how finely you can place a point by eye. Fifteen degrees between spokes gives 24 divisions and is a reasonable default for hand plotting. Ten degrees is finer but starts to look crowded near the center, where the spokes converge. Whatever you choose, the rings should stay evenly spaced, unevenly spaced rings turn a linear radial scale into something that misrepresents the data.
Beyond mathematics
Polar sheets do real work outside math class: antenna radiation patterns, loudspeaker and microphone polar response, wind roses in meteorology, phasor diagrams in AC circuit analysis, and light distribution curves in lighting design. All of them share the same structure, a magnitude that varies with direction, and all of them are conventionally plotted on exactly this grid.
Printing it accurately
This only measures correctly if your printer doesn't rescale the page. In the print dialog set Scale: 100%, not "Fit to page" or "Shrink oversized pages". If you're not sure it worked, print the calibration page, measure the ruler on it with a real ruler, and it will tell you exactly what your printer is doing to the page.