Why your printer shrinks your graph paper
You wanted 5 mm graph paper, but your printer made squares that are 4.7 mm. Nothing is broken. Your print dialog did exactly what it was configured to do, and that is the problem. Here's how to make sure that your printer behaves and prints what you want it to print. If you want to skip ahead, the printer calibration sheet tells you in one page what your printer is doing.
The one setting that causes almost all of it
Every major print dialog ships with "page scaling" switched on by default. It is called Fit to page, Shrink oversized pages, Fit to printable area, or just Scale: Fit, depending on which app you are printing from. When it is on, the printer driver measures the page it was given, measures the area it can physically put ink on, and shrinks the first to fit inside the second. For a US Letter page going to a US Letter printer, that is a reduction of roughly 4–6%. Your 5 mm squares will land somewhere between 4.7 and 4.8 mm: every square on the sheet is equally wrong, and nothing anywhere tells you that it happened.
Why the printable area is smaller than the page
The reason the driver thinks it needs to shrink anything is that almost no consumer printer can print to the edge of a sheet. The paper is gripped by rollers as it feeds, and the area under the grip cannot receive ink. Reserved margins vary by machine and by edge, commonly between 2 and 8 mm, and the trailing edge is usually the widest because that is where the rollers release the sheet. Laser printers are typically around 4 mm on all four sides. So a 216 × 279 mm Letter sheet has a printable area of roughly 210 × 271 mm. A PDF sized to the full sheet does not fit inside that, and the driver, trying to be helpful, scales the whole page down until it does. When it does that, your perfect grid becomes collateral damage.
What to set, in each dialog
The fix is the same everywhere, but it is buried in a different place in each app. Adobe Acrobat and Reader: in the print dialog, under Page Sizing & Handling, choose Actual size, not Fit, not Shrink oversized pages. Chrome and Edge: expand More settings and set Scale to Custom: 100. The default, confusingly labeled Default, is actually the fit-to-page setting. Firefox: under More settings, set Scale to 100% rather than Fit to page width. macOS Preview: select Scale: 100% rather than Scale to Fit. Windows Photos or Paint: avoid these for grids entirely, because several versions offer no true-size option at all.
Set the paper size to match the file, too
Scaling is the common failure, but there is a second one that produces the same symptom. If you print an A4 PDF on a printer whose default paper size is US Letter, the printer driver needs to negotiate two differently-sized sheets of paper. A4 is 297 mm tall and Letter is 279 mm, so fitting one inside the other means 279 divided by 297, or about 94%. Even with scaling nominally off, many drivers will quietly apply exactly that, which is almost exactly the number you get from fit-to-page, so the two failures are indistinguishable by measurement alone. If you are outside North America and printing US-origin grids and templates, or in North America and printing European ones, check the paper size selector before you blame the scale setting.
How to prove it, rather than assume it
All of the above is advice. Verification is better. Print the calibration page. It carries a ruler drawn at known true size, plus a 100 mm and a 4 inch reference bar. Print it, lay a real ruler along the printed one, and read off what your printer actually did. If the printed 100 mm bar measures 94 mm, your driver is scaling to 94% and you now know exactly where to make a printer dialog adjustment. If it measures 100 mm, then your setup is correct and you can stop worrying about it for every subsequent sheet from the same machine. This takes one sheet of paper, once.
When the page is right and the grid is still wrong
Two smaller causes account for most of the remainder of these printer mismatches. The first is a printer whose hardware calibration has drifted. This shows up as a page that is correct on one axis and off on the other. When this happens, you may see a stretched or squashed grid rather than a uniformly small one. This is a paper-feed problem, and on most machines it is adjustable in the maintenance menu. The second can happen with paper that has absorbed moisture and physically changed size. The change may be well under a percent and only worth thinking about if you are working to tolerances where that matters. If your grid is off by 5%, it is probably the print dialog. It is nearly always the print dialog!
Why this matters more for grids than for anything else
A 6% reduction on a page of text is invisible and harmless. On a grid it is neither, because the entire purpose of the sheet is that the measurement is trustworthy. A quilter cutting to a printed pattern, an engineer sketching to scale, a gardener laying out beds on a square-foot grid, someone drafting a sewing pattern, all of them are relying on the printed distance being the stated distance. They, like you, are relying on accuracy. Every sheet on this website is built to exact physical dimensions for that reason, and you can adjust the spacing to whatever your work actually needs.