Graph paper sizes and spacing explained
Short answer: standard US graph paper is quad ruled, 4 squares per inch, so each square is 1/4 in (6.35 mm). Engineering paper has 5 squares per inch (1/5 in), and finer US grids have 8 or 10. Outside the US, graph paper is measured in millimetres: 5 mm squares for exercise books, 1 cm for young children, and 2 mm or 1 mm with heavier centimetre lines for plotting. None of these is fixed by a standard; they are the rulings the paper is sold in.
How graph paper is named
US graph paper is named by squares per inch: "4 × 4" or "4 sq/in" means four squares each way in every inch. "Quad ruled" and "quadrille" usually mean 4 per inch, though some sellers use the words for any square grid, so check the count. "Cross-section" paper has a heavier line every inch on top of the fine grid. Metric paper is named by the square size, sometimes with its heavier lines: "1:5:10 mm" is millimetre squares with heavier lines every 5 and 10 mm.
| Square | Also called | Per inch | Per cm | On Letter | On A4 | Heavier lines | Typical use |
|---|---|---|---|---|---|---|---|
| 1 in | 1 per inch | 1 | 0.39 | 7 × 10 | 7 × 10 | None | Large diagrams, game boards, early counting |
| 1/2 in | 2 × 2 | 2 | 0.79 | 15 × 20 | 14 × 21 | None | Young students, big charts, low vision |
| 1/4 in | Quad ruled, quadrille, 4 × 4 | 4 | 1.57 | 30 × 40 | 29 × 42 | Usually none | US school maths, sketching, floor plans |
| 1/5 in | Engineering, 5 × 5 | 5 | 1.97 | 37 × 50 | 37 × 53 | Every inch on cross-section paper | Engineering calculations and sketches |
| 1/8 in | 8 × 8 | 8 | 3.15 | 60 × 80 | 59 × 85 | Often every inch | Detailed drawings and plans |
| 1/10 in | 10 × 10 | 10 | 3.94 | 75 × 100 | 74 × 106 | Every inch | Data plots, cross-stitch charts |
| 1 cm | 1 cm squared | 2.54 | 1 | 19 × 25 | 19 × 27 | None | Primary maths in metric countries |
| 5 mm | 5 mm squared | 5.08 | 2 | 38 × 50 | 38 × 54 | Usually none | Exercise books, maths, journals |
| 2 mm | 2 mm graph | 12.7 | 5 | 95 × 127 | 95 × 135 | 1 cm, often 2 cm too | School graphs and plotting |
| 1 mm | Millimetre paper | 25.4 | 10 | 190 × 254 | 190 × 270 | 5 mm and 1 cm | Precise plots and drawings |
Whole squares across × down on portrait sheets with 1/2 in margins (Letter) or 10 mm margins (A4), as the graph paper generator draws them with no heavy lines.
Quad ruled paper
The everyday US school and office pad: Letter-size sheets with 4 squares per inch, usually in light blue and often printed on both sides. There are usually no heavier lines; you count inches by fours. With 1/2 in margins a Letter sheet holds 30 × 40 squares. It is the usual graph paper for school maths in the US, from plotting points to drawing shapes for area, and its 1/4 in square matches the common 1/4 in = 1 ft drawing scale.
Engineering paper
Engineering computation pads have a 5-square-per-inch grid with a heavier line every inch, on green-tinted paper. The grid is printed on the back of the sheet and shows faintly through to the front, which carries only a frame of margin lines: you write on a clean surface with the grid as a guide. A home printer can't print through the paper, but you can get close: 1/5 in squares with a heavy line every 5, in engineering green, with a header for the name, date and project.
Five squares to the inch suits decimal inches: each square is 0.2 in, so measurements in tenths of an inch fall on a line or halfway between, and the heavier inch lines keep counts easy. The 10-per-inch grid gives tenths directly but is harder to read.
Metric squared paper
- 5 mm squares are the usual grid of maths exercise books in the UK and much of Europe, and a common dot and grid pitch in journals.
- 1 cm squares suit younger children, area and perimeter, and simple bar charts.
- 2 mm graph paper has heavier lines every 1 cm and 2 cm; UK school graph paper is sold as "2, 10 and 20 mm squared". In the generator, choose 2 mm squares with a heavy line every 10 and a medium line every 5.
- Millimetre paper has 1 mm squares with heavier lines every 5 and 10 mm ("1:5:10 mm"), for precise plots and technical drawing. It is often printed in blue, orange or red.
Inch and metric sizes that look alike
Some inch and metric squares are close enough to confuse but far enough apart to matter over a page. The inch is exactly 25.4 mm, so the differences are exact:
| Sizes | Inch size in mm | Difference | After 20 squares |
|---|---|---|---|
| 1/5 in and 5 mm | 5.08 mm | +1.6% | 1.6 mm |
| 1/10 in and 2.5 mm | 2.54 mm | +1.6% | 0.8 mm |
| 1/4 in and 6 mm | 6.35 mm | +5.8% | 7 mm |
| 3/8 in and 1 cm | 9.525 mm | −4.8% | 9.5 mm |
If a sheet has to line up with something you already have, such as a metric notebook, a US engineering pad or a pattern drawn on one of them, match the unit as well as the size.
Graph paper for scale drawings
Pick a square size and a drawing scale that make each square a round number. The US architectural scales of 1/4 in and 1/8 in to the foot, and the metric 1:50 and 1:100, all work cleanly:
| Square | Drawing scale | One square is | One sheet covers |
|---|---|---|---|
| 1/4 in | 1/4 in = 1 ft (1:48) | 1 ft | 30 × 40 ft on Letter |
| 1/4 in | 1/8 in = 1 ft (1:96) | 2 ft | 60 × 80 ft on Letter |
| 1/8 in | 1/8 in = 1 ft (1:96) | 1 ft | 60 × 80 ft on Letter |
| 1 cm | 1:100 | 1 m | 19 × 27 m on A4 |
| 1 cm | 1:50 | 50 cm | 9.5 × 13.5 m on A4 |
| 5 mm | 1:100 | 50 cm | 19 × 27 m on A4 |
Sheets as in the first table: portrait, 1/2 in margins on Letter, 10 mm on A4, no heavy lines.
For a bigger area, use landscape, a larger page such as Tabloid or A3, or a smaller scale. A scale drawing is only as accurate as the print, so print it at actual size and check the calibration ruler; the printing guide explains how.
Choosing a size
- Writing numbers in the squares (long division, column arithmetic): 1/4 in or 1 cm, depending on the writer.
- Plotting data: 1/10 in or 2 mm with heavier lines, so values can be read to a tenth of a division.
- Sketching and diagrams: 1/4 in, 1/5 in or 5 mm in a light colour.
- Counting crafts (cross-stitch, pixel art, perler beads): 1/10 in or 1/8 in with a heavy line every 10 or 8.
- Something other than squares: dot grid for journals, isometric for 3D drawings, hexagon for game maps, polar for angles and circles, and semi-log and log-log for data spanning powers of ten.
Sources
- Ampad (TOPS Products) quadrille pad listing: Letter sheets printed with 4 squares per inch on both sides.
- TOPS engineering computation pad listing: 5-square-per-inch cross-section ruling printed on the back and showing faintly through, frame margins on the front, green-tint paper.
- Rapid A4 graph paper, 1:5:10 mm listing: millimetre squares with 5 and 10 mm lines.
- Classmates graph paper, 2, 10 and 20 mm squared listing (UK school supplies).
- Wikipedia, Ruled paper: overview of national rulings, including 5 mm squared maths paper in the UK and Germany and 10 mm squared paper in UK primary schools.
- NIST, SI units: length: the inch is exactly 25.4 mm.
- ISO 216:2007: A4 is 210 × 297 mm.