What is DPI?

Dots per inch counts how many samples land in each inch of physical output. Strictly, DPI describes an output device laying down dots of ink, while PPI — pixels per inch — describes the sampling density of the image itself; in everyday document work the two terms are used interchangeably, and the arithmetic is the same either way. What matters is that the number is a quotient: divide the pixel dimension by the inches it will occupy.

Inside a PDF this gives us effective DPI, which is the only resolution figure worth acting on. Effective DPI equals the image’s pixel width divided by the width in inches at which it is actually placed on the page. A 3000-pixel-wide photograph dropped into a two-inch-wide box on your page is being reproduced at 1500 effective DPI. No printer in your office resolves anything close to that, no screen comes near it, and every one of those surplus pixels is being stored, transmitted and discarded at render time. That single calculation explains most bloated documents.

The same arithmetic works in reverse and is how you should plan images. Decide the placed width first, multiply by the DPI the destination needs, and you have the pixel width to aim for. A picture that will sit six inches wide on a printed page at 300 DPI needs around 1800 pixels across. Supplying 6000 wastes bytes; supplying 600 will look soft no matter what quality setting you use, because the information is not there to begin with.

Screens sit around 72 to 96 DPI in the traditional reckoning, which is why on-screen-only documents rarely benefit from image data far beyond that — though high-density displays and the fact that readers zoom mean a modest margin above it is sensible rather than wasteful. For ordinary print work, 300 DPI is the long-established target for continuous-tone images: enough that individual samples are not resolvable at normal reading distance, and the point beyond which most eyes stop noticing improvement.

Line art and archival scanning are the case for going higher, commonly 600 DPI. The reason is not that ink resolves finer detail but that hard black-and-white edges are exactly where insufficient sampling shows: a diagonal hairline rule or a small serif rendered at 300 DPI can look ragged in a way a photograph never would. Bilevel content is also extremely cheap to store at high resolution, so the extra pixels cost far less than the same increase would on a colour photograph.

Whole-page figures follow from the same ratio. An A4 page measures roughly 8.27 by 11.69 inches, so scanning or rendering it at 150 DPI gives approximately 1240 by 1754 pixels, and at 300 DPI approximately 2480 by 3508 pixels. Those two numbers are worth internalising, because they tell you instantly whether a page image you have been handed is a screen-grade render or a print-grade scan — and therefore whether it can be printed acceptably at all.

PDFs do not measure pages in pixels. The default user-space unit is the point, defined as 1/72 of an inch, inherited from typographic tradition by way of PostScript. So 72 points equal one inch, 720 points equal ten inches, and a page’s size in the file is expressed in this unit rather than in millimetres or pixels. Every coordinate in a content stream — where a glyph sits, where a line begins, how large an image box is — is ultimately in these units.

This is why page sizes appear as the numbers they do: A4 is 595 by 842 points, US Letter 612 by 792. It is also why the 72-per-inch coincidence with traditional screen resolution is so convenient and so confusing at once. A PDF rendered at 72 DPI produces a bitmap whose pixel dimensions match the page’s point dimensions exactly, one pixel per point. Render the same page at 150 DPI and every point becomes just over two pixels.

The practical upshot is a conversion you can do in your head. To find what pixel dimensions a page render will produce, divide the point size by 72 to get inches, then multiply by your chosen DPI. To find the effective DPI of an image already placed in a document, take its pixel width and divide by the width of its box in points divided by 72. Neither calculation needs a tool — though a tool that reports both figures side by side saves the trouble of measuring the box.