How do inkjet printer DPI and image PPI relate when estimating maximum print size?

Question

I’m trying to estimate the largest size I can print a digital image while still having it look good at a given viewing distance. On a screen, I can compare pixel pitch to human visual acuity fairly directly. For printing, I’m confused because the printer’s advertised DPI refers to ink drops, not image pixels.

For example, if a printer is specified as 9600 × 2400 dpi, how does that translate into meaningful image resolution? Is there a fixed conversion from image pixels (PPI) to printed ink dots, or a known number of dots needed to represent one pixel? I’ve heard people mention a printer’s “native” resolution such as 300 or 600 ppi—does that mean something like 2400 dpi / 300 ppi = 8 dots per pixel in one dimension?

In short: how should printer DPI, image PPI, halftoning/dithering, and viewing distance be related when estimating print size?

user37321 · Accepted Answer

I have written a more elaborate post in Spanish here, which Google translate can probably help you read.

A simplified version.

There is a unit for offset commercial printing called lpi. This is defined by the real resolution of a laser printing on a negative film or plate.

Let us say the laser plate printer gives you 2400 dpi. If you need 256 tones of gray then you need a 16x16 square.

(this next image is only using an 8x8 square to simplify)

So the linear resolution is given by 2400/16=150; 150 lpi. On a 2400 dpi printer you can have 256 levels of gray resulting in 150 lpi.

The relation of ppi to dpi is given traditionally by this conversion: ppi = 2*lpi (to have good interpolation). So 150 lpi is like 300 ppi.

Ink jet printers work differently.

The dots are random, the minimum size of this ones determines only whether you see the ink dot or not.

But what determines the file resolution is the real pixels you can actually see.

As this is a Photo forum think of the printer dot size as the grain of a photo, and the resolution as the sharpness of a lens. The 2 are not that related in modern inkjet printers.

This randomness is not given pixel by pixel, but... random. Each pixel can have a different number of ink dots, so the dots do not directly define the pixel size you can see.

Yes you can assume that you need a similar number of dots to form some shades of color. But using 300 ppi is a waste on a digital printer. Go for 200ppi or 150ppi, regardless of the printer model.

It is more important for the paper to have a small dot.

So, what data really matter?

Contrary to popular belief you do not need a 300 ppi image for print on a digital media. 200 ppi is enough. It has more information than a normal magazine that only holds 150 ppi.

100ppi you can hardly see pixels on a print at, say, 50cm. So as a backup you use 200ppi.

If you double that viewing distance you need only half the ppi.

So here is a diagram (It is old and has an error: It should say ppi and not dpi)

This resolution can be adjusted by 2 factors. The real level of detail you need and other elements like text on the image.

You need more detail on an art gallery than on a billboard on a bus stop. And the text on the image, because a low resolution print with text is more noticeable than on a photo.

This graph is labeled mts. on the bottom for viewing distance of the printed material vs. ppi (not dots).