How to Plot Polar Coordinates

Polar points are (r, theta): count rings out from the centre for distance, then follow the spoke for the angle.

Quick answer

A polar point (r, theta) is not x then y. r is how many rings out from the centre you go, and theta is the angle from the positive horizontal axis, measured counter-clockwise. On the FreeGridPaper polar grid, spokes run every 15 degrees, angle labels run every 30 degrees, and the cardinal spokes at 0, 90, 180, and 270 degrees are bold.

Reference facts

r: Distance from the centre, counted in rings
Theta: Angle from the positive horizontal axis, counter-clockwise
Spokes: Every 15 degrees
Angle labels: Every 30 degrees, outside the outer circle
Default ring spacing: 10 mm, nine rings on Letter paper

Best for

Polar equations and trigonometry
Angles, circles, and circular motion
Converting between polar and rectangular thinking

Plot in two steps, angle then distance, or distance then angle

Either order works if you keep them separate. Find the angle first by following the labelled spoke from the centre, then count rings out along that spoke. Or count rings first on the 0 degree spoke, then rotate to the angle. Mixing the two, for example counting rings along the wrong spoke, is the usual error.

(3, 60 degrees) is three rings out along the 60 degree spoke, up and to the right.
(4, 180 degrees) is four rings out to the left, on the bold horizontal spoke.
(2, 270 degrees) is two rings straight down.

What about negative r and angles over 360 degrees

A negative r means go the same distance in the opposite direction: (3, 60 degrees) with r negated lands where (3, 240 degrees) lands. An angle over 360 degrees just wraps around the circle again, so 390 degrees is the same spoke as 30 degrees. Keep the centre marked, because every ring and spoke is measured from there, not from the edge of the page.

Common mistakes to check

Measuring the angle from the vertical axis instead of the horizontal axis rotates the whole plot by 90 degrees. Counting rings from the outer circle inward reverses r. Using radians when the labels are in degrees, or vice versa, shifts every point, so check the unit before you start.

Printing guidance

Print at Actual Size or 100% scale so ring spacing stays as selected. Lower the ring spacing in the generator for more, finer rings, and raise it for fewer, larger rings.

Best starting pages

Related templates

Related presets

Polar Grid 10 mm

Updated 2026-11-01