Generators
Polar Graph Paper
Polar coordinate paper: evenly spaced circles around a center point and rays every 15° (or your choice), with the angles marked in degrees.
Print at 100% (“Actual size”), not “Fit to page”, so the spacing measures true.
Preview of the one-page PDF.
The paper and PDF are made in your browser; nothing is uploaded.
Works in your browser. No account needed.
Frequently asked questions
What is polar graph paper used for?
Plotting points and curves in polar coordinates (r, θ): a distance r from the center, called the pole, and an angle θ measured counterclockwise from the horizontal ray to the right. Precalculus and calculus students use it to draw roses, cardioids, limaçons, spirals and circles, which are awkward on square grids. It is also handy for pie charts, radar charts, dials, compass roses and mandala designs.
How are the angles labelled?
In degrees, counterclockwise from 0° on the right, as in mathematics. With rays every 15° or more, each ray is labelled; with finer rays, every 30° is labelled. For radians, 15° is π/12, 30° is π/6, 45° is π/4 and 90° is π/2, so the 15° setting puts a ray on every standard angle.
Why do some rays stop before the center?
Near the center, rays at small angles would crowd into a dark blot. The main rays (every 30°) run all the way to the pole; the in-between rays start a ring or two out, as on professionally printed polar paper.
How many rings are there?
As many whole rings as fit inside the margins with room for the angle labels. On US Letter with ¼-inch rings that is 14 rings; the outermost ring is always a whole number of spacings from the center, so r can be read directly by counting.
Can I use it for a protractor or compass rose?
Yes. Printed at 100% the angles are exact, so a sheet makes a large paper protractor or a base for drawing a compass rose, a clock face or a spinner. Choose 5° or 10° rays for finer angle steps.
About this tool
Polar graph paper replaces the square grid with the natural grid of polar coordinates: circles centered on the pole mark the distance r, and straight rays from the pole mark the angle θ. Curves such as r = 2 cos 3θ (a three-petal rose) or r = 1 + sin θ (a cardioid) are quick to plot point by point on it and tedious on ordinary graph paper.
This page draws the rings at an exact spacing you choose, with a heavier ring every few circles, and rays every 5°, 10°, 15°, 30° or 45°. The horizontal and vertical axes are drawn heavier, the rays are labelled in degrees around the outside, and the whole figure is centered on the page and sized to the largest whole number of rings that fits.
Teachers can print a set with name and date headers for a unit on polar functions or complex numbers in polar form. Students can print a few sheets for homework, and designers use polar grids for radial layouts, dials, and dot mandalas.
Tip: before plotting, make a table of θ and r in steps that match the rays — every 15° on the default paper — then join the points with a smooth curve. Negative r values are plotted in the opposite direction, 180° around.