Polar Graph Paper
Print polar coordinate graph paper for plotting points by distance and angle. Each grid is a set of evenly spaced rings round a centre point, crossed by spokes every 5°, 10°, 15° or 30°, or every π/12 or π/6 radians, with angle labels in degrees or as fractions of π. Choose 1, 2 or 4 grids per US Letter or A4 page, a full circle or a half circle (0° to 180°), the number of rings or a fixed distance between them such as 1 cm or ¼ in, a heavier ring every 2 or 5, numbered rings, degree ticks round the edge and a name and date line. Download a vector PDF, an SVG at real size or a 300 DPI PNG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). The PDF is vector, so rings and spokes stay sharp at any zoom.
Page
Angles
Rings
Style
Runs in your browser with our own code: nothing is uploaded and nothing is saved. Print at 100% (Actual size) so the ring spacing stays true. You may use what you make here, including commercially, with no credit needed.
How to print polar graph paper
- Choose US Letter or A4 and 1, 2 or 4 grids per page.
- Pick the spoke spacing: 15° or π/12 suits most trigonometry homework, 5° or 10° gives finer angles.
- Choose degree or radian labels, and the number of rings or the distance between them.
- Add a heavier ring every 5, numbered rings, degree ticks or a name and date line if you like.
- Download the PDF and print at 100% (Actual size).
What you can use it for
- Plotting polar equations such as roses, cardioids and spirals in precalculus
- Converting between polar and rectangular coordinates
- Antenna radiation patterns and microphone polar patterns
- Wind roses, compass bearings and navigation exercises
- Mandalas, radial designs and rotational symmetry sketches
- Pie-style data, clock faces and dial designs
Polar grid sizes on each page
| Paper | Grids per page | Outer radius (full circle) | Ring spacing with 10 rings | Outer radius (half circle) |
|---|---|---|---|---|
| US Letter | 1 | 91 mm (3.58 in) | 9.1 mm | 91 mm (3.58 in) |
| US Letter | 2 | 55.9 mm (2.2 in) | 5.58 mm | 91 mm (3.58 in) |
| US Letter | 4 | 40 mm (1.57 in) | 4 mm | 40 mm (1.57 in) |
| A4 | 1 | 88 mm (3.46 in) | 8.8 mm | 88 mm (3.46 in) |
| A4 | 2 | 60.3 mm (2.37 in) | 6.03 mm | 88 mm (3.46 in) |
| A4 | 4 | 38.5 mm (1.52 in) | 3.85 mm | 38.5 mm (1.52 in) |
Each grid fills its part of the page inside an 8 mm margin, with room for the angle labels round the outside. Choose fewer rings for wider spacing, or set an exact distance between rings.
Spokes and angle labels
| Spokes | Spokes in a full circle | Spokes in a half circle | Labels, 1 grid per page | Labels, 4 grids per page |
|---|---|---|---|---|
| Every 5° | 72 | 37 | every 10° | every 15° |
| Every 10° | 36 | 19 | every 10° | every 30° |
| Every 15° | 24 | 13 | every 15° | every 15° |
| Every 30° | 12 | 7 | every 30° | every 30° |
| Every π/12 rad = 15° | 24 | 13 | every 15° | every 15° |
| Every π/6 rad = 30° | 12 | 7 | every 30° | every 30° |
Labels are spaced so they never crowd: the smallest multiple of the spoke angle that divides 90° and leaves at least 9 mm of arc between labels. 0°, 90°, 180° and 270° are always labelled.
Degrees and radians
| Degrees | Radians (label) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0.0000 |
| 15° | π/12 | 0.2618 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 120° | 2π/3 | 2.0944 |
| 135° | 3π/4 | 2.3562 |
| 150° | 5π/6 | 2.6180 |
| 180° | π | 3.1416 |
| 210° | 7π/6 | 3.6652 |
| 225° | 5π/4 | 3.9270 |
| 240° | 4π/3 | 4.1888 |
| 270° | 3π/2 | 4.7124 |
| 300° | 5π/3 | 5.2360 |
| 315° | 7π/4 | 5.4978 |
| 330° | 11π/6 | 5.7596 |
Angles are measured anticlockwise from the line pointing right (the positive x-axis), as in most maths textbooks.
Rings at a fixed spacing
| Distance between rings | Rings, US Letter (1 grid) | Rings, A4 (1 grid) | Rings, US Letter (4 grids) |
|---|---|---|---|
| 5 mm | 18 | 17 | 7 |
| 10 mm (1 cm) | 9 | 8 | 3 |
| ¼ in | 14 | 13 | 6 |
| ½ in | 7 | 6 | 3 |
| 1 in | 3 | 3 | 1 |
Only whole rings are drawn, so the outer ring sits at an exact multiple of the spacing.
Polar paper or square graph paper?
| You want | Use |
|---|---|
| Points given as a distance and an angle (r, θ), roses, cardioids, spirals, bearings | Polar graph paper (this page) |
| Points given as x and y, straight-line graphs, floor plans | Graph Paper |
| 3D sketches at 30° | Isometric Graph Paper |
| Measuring an angle on screen | Online Protractor |
The Graph Paper generator draws square, engineering, dot, isometric and hexagon grids but no circles; this page adds the circular grid. For 3D drawing use Isometric Graph Paper, measure angles on screen with the Online Protractor, and turn rotational patterns into art with the Mandala Maker or the Spirograph Generator.
Printing tips
- Print at 100% (Actual size) so a 1 cm ring spacing measures 1 cm.
- Light grey or light blue lines leave your pencil or pen graph easy to see.
- For a worksheet, choose 4 grids per page and turn on the name and date line.
- The SVG opens in drawing programs at real size if you want to add your own labels.
More free tools
More paper for maths and drawing
Printable grids and drawing helpers that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What is polar graph paper?
Polar graph paper is a grid of concentric circles crossed by straight lines from the centre. A point is found by its distance from the centre (r, counted in rings) and its angle (θ, measured anticlockwise from the line pointing right), instead of by x and y as on square graph paper.
How do you read polar graph paper?
Start at the centre, turn to the angle θ (0° points to the right, 90° straight up, 180° to the left), then count r rings outward along that spoke. For a negative r, go the same distance in the opposite direction, which is the angle θ + 180°.
Should I use degrees or radians?
Use whatever your class uses. Radian labels follow the spokes as fractions of π: with spokes every π/12 (15°), the labels read π/12, π/6, π/4 and so on, and π/2 is straight up. The table on this page lists the common angles in both.
How many spokes should the grid have?
Spokes every 15° (24 spokes) match the special angles of trigonometry: 30°, 45°, 60° and their multiples all sit on a spoke. Every 5° (72 spokes) or 10° (36) gives finer angles for engineering or navigation, and every 30° (12) keeps a small grid uncluttered. There are 6 spoke settings plus rings only.
Can I print several polar grids on one page?
Yes. Choose 2 or 4 grids per page for worksheets and quizzes. Each grid gets the same rings, spokes and labels, centred in its part of the page.
What is a half polar grid?
A half circle from 0° to 180°, centred on its straight edge. It is used for antenna and speaker patterns that are symmetrical, protractor-style angle practice and graphs that only need the upper half plane.
Can I set the distance between the rings?
Yes. Choose Distance between rings and pick 5 mm, 1 cm, ¼ in, ½ in or 1 in, or type your own in mm or inches. The grid uses as many whole rings as fit, so each ring is an exact distance from the centre when printed at 100%.
Why are the fine spokes missing near the centre?
Near the centre, spokes every 5° or 10° crowd into a solid blot. Keep the centre clear starts the fine spokes at the first ring where they are at least 1.5 mm apart; the 30° spokes start at the first ring and the axes run all the way to the centre. Turn it off to draw every spoke from the centre.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. Everything is drawn by JavaScript in your browser and never leaves your device. Only the free fonts load from a public font CDN, and nothing is saved when you close the page.