300 DPI, explained: pixels, print size, and why the shop said no

The photo looks perfect on the screen. The print shop, or the visa portal, or the person laying out the brochure, says it is “only 72 dpi” and needs to be 300. So you open it in something, type 300 into a box labelled resolution, save, and send it back. It is accepted, or it is rejected again, and either way you have learned nothing, because that box did not change a single pixel.

Here is what is actually going on, and the one piece of arithmetic that settles every version of this argument.

An image does not have a DPI

A digital image is a grid of pixels. That is the whole of it. A photo from a phone might be 4032 pixels wide and 3024 tall — about 12 million of them — and that number is fixed the moment the shutter closes.

DPI, dots per inch, is not a property of that grid. It is an instruction about how big to make the grid when it lands on paper. The same 4032 × 3024 photo is 13.4 inches wide at 300 dpi, 40 inches wide at 100 dpi, and 4 inches wide at 1000. Nothing about the file changes between those three sentences. Only the intended physical size does.

That is why the box marked “resolution” is so misleading. In most software it writes a number into a tag — the JFIF density field, or the EXIF XResolution and YResolution pair — and the tag is a note for whoever prints the file. It is genuinely useful in a print workflow, where a layout program reads it to decide how big to drop the photo onto the page. It adds no detail. A blurry 500-pixel image tagged 300 dpi is still a blurry 500-pixel image; it has simply been relabelled as a 1.7-inch print.

There are only two operations that change what is in a file: cropping, which throws pixels away, and resampling, which invents or discards them by interpolation. Anything else is bookkeeping.

The formula

Everything below comes from one line:

pixels = inches × dpi

And because most of the world specifies documents in millimetres, the companion:

inches = millimetres ÷ 25.4

An inch is exactly 25.4 mm — that has been the international definition since 1959, so this is not a rounding you need to worry about.

Run it in the direction you need. To find out whether a file is good enough for a print you already know the size of, divide instead:

actual dpi = pixel width ÷ print width in inches

A 3000-pixel-wide photo printed 10 inches wide is 300 dpi. The same photo printed across an A3 poster, 16.5 inches, is 182 dpi. Neither number is in the file. Both are decisions.

The numbers you will actually need

Print sizes at 300 dpi, which is the default assumption almost everywhere:

Print size	Pixels needed at 300 dpi
4 × 6 in (10 × 15 cm)	1200 × 1800
5 × 7 in	1500 × 2100
8 × 10 in	2400 × 3000
A6 (105 × 148 mm)	1240 × 1748
A5 (148 × 210 mm)	1748 × 2480
A4 (210 × 297 mm)	2480 × 3508
A3 (297 × 420 mm)	3508 × 4961
Business card (85 × 55 mm)	1004 × 650

And the two identity-document sizes that generate most of the questions:

Document	Physical	At 300 dpi	At 600 dpi
Most passport photos	35 × 45 mm	413 × 532	827 × 1063
US passport / visa	2 × 2 in	600 × 600	1200 × 1200

That 827 × 1063 figure is worth memorising if you deal with European, Indian or Central Asian paperwork, because it is the number a great many application systems check for directly. The passport photo tool outputs at the size and resolution each country publishes, so the arithmetic is done for you — but it is the same arithmetic.

Where 300 came from, and when it is wrong

Three hundred is not a law of physics. It is a comfortable answer to a question about eyesight.

A person with normal vision resolves detail about one arcminute apart. Turn that into a rule and you get a required resolution of roughly 3438 ÷ viewing distance in inches. At the 12 inches you hold a photograph, that is 286 dpi — which is where 300 comes from, with a little headroom. The moment the viewing distance changes, so does the honest answer:

Viewed from	Resolution that is genuinely enough
12 in — a photo in your hands	~290 dpi
2 ft — a magazine spread on a desk	~145 dpi
3 ft — a poster on a wall you walk past	~95 dpi
10 ft — an exhibition banner	~30 dpi

This is why billboards are printed at resolutions that would look catastrophic on a postcard, and why a photographer who insists on 300 dpi for a two-metre banner is asking you for twenty times the pixels the job needs. If someone specifies 300 dpi for something viewed across a room, they have copied a rule rather than applied one.

DPI, PPI, and the inkjet that claims 4800

Two different measurements share the abbreviation, which is most of the confusion.

PPI — pixels per inch — describes your image: how many of its pixels land in each inch of paper. That is the number every table above is really about.

DPI — dots per inch — describes a printer: how many droplets of ink it can place. A printer has maybe six inks and cannot mix a continuous tone, so it simulates one by clustering many tiny dots into a halftone cell. It takes a great many printer dots to render one image pixel convincingly. That is why an inkjet advertising 4800 dpi is not asking for a 4800 ppi image, and never was.

For commercial offset work the number that matters is the halftone screen, in lines per inch. The long-standing rule of thumb is image ppi ≈ 2 × lpi, so a 150 lpi magazine wants around 300 ppi. The familiar figure again, arrived at from a completely different direction.

What to do when you do not have enough pixels

Check first. Divide the pixel dimensions by the print size in inches and see what you actually have. If the answer is 220 for a photo print, print it anyway — the difference between 220 and 300 dpi in the hand is far smaller than the difference between a sharp photo and a soft one.

If the number is genuinely too low, your options, in order of how well they work:

1. Crop less. People often crop to taste first and discover the resolution problem afterwards. Going back to the original frame is free pixels. If you are cropping for a fixed shape, the crop tool shows the resulting pixel dimensions as you drag, so you can watch the budget while you work rather than after.
2. Print smaller. A 5 × 7 that is sharp beats an 8 × 10 that is soft.
3. Reshoot or rescan. For a document, rescanning at 600 dpi takes a minute and solves it permanently.
4. Upscale, knowing what it is. Resampling upwards cannot recover detail that was never recorded — modern methods hide the softness better than old ones, but nothing invents the texture of fabric that the sensor did not see. Use it as a last resort, and never more than about double.

Going the other way — a 48-megapixel photo destined for a 4 × 6 print, or for an email — resampling down is genuinely lossless in every way that matters, and it is the single biggest saving available on file size. The resize tool takes exact pixel dimensions, so you can paste in 1200 × 1800 from the table above and be done.

The 72 dpi myth

You will still be told that images for the web should be 72 dpi. They should not, because the number is meaningless there. A screen displays your pixels in its own pixels; the density tag is not consulted at all. Seventy-two is a leftover from the original Macintosh, whose display happened to show 72 pixels per inch so that a typographic point on screen matched a point on paper.

For anything shown on a screen, specify pixels: 1200 wide, 1920 wide, 2048 on the long edge. The only number that has any effect is the one measured in pixels.

The short version

• Pixels are real; DPI is a label attached to them.
• pixels = inches × dpi, and inches = mm ÷ 25.4. Everything else is a lookup table.
• To judge a file, divide its pixels by the print size you want and read off the answer.
• 300 dpi is right for things held in the hand and wasteful for things seen from across a room.
• Never type a new number into a resolution box and expect the image to have improved.