Grid spacing is a convention, not a standard
There is no international standard for how far apart the lines on graph paper should be, which is why a pad bought in one country feels wrong to someone taught in another. Metric graph paper settled on 5 mm squares for general school and engineering use, often with a lighter 1 mm subdivision inside each square and a heavier index line every 10 mm. Imperial paper is specified the other way round — by squares per inch rather than by spacing — so you buy 4, 5, 8 or 10 squares to the inch. Quad-ruled 4×4 is the common American school pad at 6.35 mm, while engineering pads are usually 5×5 or 10×10.
Lined paper is more codified. American wide ruled is 8.7 mm between lines, college ruled is 7.1 mm, and narrow ruled is 6.35 mm; wide ruled is intended for younger writers still forming letters, and many schools switch to college ruled around age eleven. French Seyès ruling takes a different approach again, using 8 mm squares subdivided by lighter 2 mm horizontal lines so that letter heights are explicitly guided rather than left to judgement.
The practical upshot is to choose spacing by what you are doing, not by habit. Fine 1–2 mm grids suit dense plotting and shrink handwriting to the point of illegibility; 5 mm is the general-purpose middle; 10 mm and above suits sketching, planning and anything a group needs to read from a distance.
The geometry under isometric, hex and polar
Isometric paper is ruled at 30 degrees from the horizontal, which places the three drawing axes 120 degrees apart and lets you draw all three faces of a box on a single sheet without perspective. There is a subtlety worth knowing: in true isometric projection all three axes are foreshortened to about 0.8165 of their real length, but nobody draws that way. Conventional isometric drawing plots full-size measurements straight onto the axes, so the finished drawing is roughly 22.5 percent larger than a geometrically true projection. It is a deliberate trade — the shape stays correct and every length remains directly measurable — but it means an isometric sketch is not a scale drawing unless you say which convention you used.
Hexagonal grids come in two orientations and the choice is not cosmetic. Pointy-top hexes sit in offset columns and have neighbours to the east and west, which suits maps read left to right; flat-top hexes stack in offset rows with neighbours to the north and south. For a hexagon with circumradius R, a pointy-top cell is 2R tall and √3·R wide, and successive rows sit 1.5R apart rather than 2R, because the rows interlock. That interlocking is exactly why hex grids are popular for games and tiling studies: every neighbour is the same distance away, which is not true of a square grid, where diagonal neighbours are √2 further off.
Polar paper trades the grid for concentric circles and radial spokes, usually every 15 or 30 degrees. It is the right paper for anything expressed as angle and distance — antenna patterns, wind roses, polar equations — and the wrong paper for anything else, because the area represented by one cell grows with the radius and the eye reads the outer ring as more important than it is.
Printing it so the grid is the size you asked for
The most common complaint about generated graph paper is that the printed squares do not measure what they should, and the cause is almost always the print dialog rather than the file. Settings named Fit to page, Shrink oversized pages or Scale to fit are enabled by default in several browsers and PDF viewers, and they resize the page to clear the printer's unprintable border. A 5 mm grid printed at 96 percent measures 4.8 mm. If the spacing matters, set scaling to 100 percent or Actual size before printing, then check one square with a ruler.
The border exists because most consumer inkjet and laser printers cannot print to the edge of the sheet, typically reserving a few millimetres on each side and sometimes more at the trailing edge. Generating the paper with a margin of its own is the reliable fix: it keeps the grid inside the printable area, so nothing has to be scaled away. Note too that A4 is 210 × 297 mm while US Letter is 216 × 279 mm — Letter is wider and shorter — so a file built for one and printed on the other will be scaled or cropped no matter what you choose.
Line weight is the other thing to test before printing fifty sheets. Very fine lines that look correct on screen can vanish on an inkjet or turn muddy on a low-toner laser, while lines heavy enough to be safe can overpower pencil work. A vector PDF helps here because every line is drawn as real geometry and rendered at the printer's own resolution — commonly 600 dpi or more — rather than being scaled up from a screen-resolution image, so a hairline stays a crisp hairline instead of a grey smear. A light paper tint or a mid-grey line colour usually reads better under pencil than pure black.