Wednesday 5th February 2014

Really it is, and yet I see so many people get confused about the concept. In a way it’s understandable, given the amount of misinformation out there, so here’s my attempt to explain it as simply as possible.

DPI is about physical size

This is the essential detail. Everything else stems from this, the concept of physical dimensions. It’s part of the name: dots per inch. A digital image can’t have its dimensions measured in inches or millimetres, since it’s literally just a list of numbers. How many inches wide is a 16 megapixel image? The question makes no sense in isolation – it depends entirely on how it’s displayed/printed.

DPI (dots per inch) and PPI (pixels per inch)

These two terms are not technically interchangeable, as printers often use multiple dots to form a single pixel, so to avoid adding further confusion I’ll use the more correct PPI from now on.

Some examples

I usually learn best from examples, as discussing things in abstract doesn’t really help as much as seeing how something works in reality.

So, let’s start simple, with a square image, 300 × 300 pixels. If we print it so it’s 1 inch wide, that means we’re putting all 300 pixels across into a space 1 inch across. Sorry if this sounds patronising, but I want to make absolutely clear what’s going on. We have just created a picture with a resolution of 300 PPI, which is a common target because it’s the point at which any further increases become very hard to detect in colour photos.

Realise that it is only the physical print that has a resolution of 300 PPI. The digital image has not changed in any way. It’s still 300 pixels across and 300 pixels tall.

Now let’s make things a little more complex. Imagine we now have a digital image of 1500 × 1000 pixels. As you might have noticed, this is in the very common 3:2 ratio a lot of large-sensor digital cameras shoot.

What happens when it’s printed at 300 PPI? We can calculate exactly how wide the printed image will be:

1500 pixels ÷ 300 PPI = 5 inches across

Easy, right? Pixels ÷ resoltion = physical size.

And of course it works the other way around. If we want a picture 5 inches across, and we want to print it at 300 PPI, we can work out how many pixels we need:

5 inches across × 300 PPI = 1500 pixels

With that in mind, let’s take our aforementioned 16 megapixel image, in this example one produced by a Fuji X-E1 (since I have one myself), as before in a 3:2 aspect ratio, producing images of 4896 × 3264 pixels.

A common question is how big a given camera’s images can be printed, without compromising quality. So, assuming 300 PPI still:

4896 pixels ÷ 300 PPI = 16.32 inches across.

That’s pretty big! What if we wanted a smaller print, though? Perhaps you only have access to a basic desktop A4-sized printer, or maybe you want to print at 8 × 10 inches to fit in a standard portrait photo frame.

8 inches across × 300 PPI = 2400 pixels
10 inches high × 300 PPI = 3000 pixels

That’s 7.2 megapixels, in case you were wondering. So, since you have more pixels than necessary, the obvious thing to do is just print it at a higher resolution:

3264 pixels across ÷ 8 inches across = 408 PPI

If your printer doesn’t actually go that high, it’ll automatically resample the image, so you don’t even need to worry about it.

A derived figure

You don’t need to do these calculations manually then set the PPI figure yourself. All you need to do when printing is say how big you want the print (in inches, millimetres, or whatever), and let the computer work out the PPI value. The only reason you even need to pay attention to it is to make sure it’s not too low.

Too low? Let’s take another scenario: printing the same 16 megapixel photo at 30 inches across:

4896 pixels across ÷ 30 inches across = 163 PPI

Almost half the number of pixels per inch! At this point, it’ll be noticeably lower in detail if you look closely, but therein lies an important point: people don’t usually look as closely at 30-inch-wide prints as they do at, say, 6-inch-wide ones, because the former are usually hanging on a wall, not held in the hand.

In other words, while 300 PPI is a good target, it’s not really an absolute minimum, as the apparent detail of an image depends on viewing distance as well as resolution. It’s the same reason why Apple calls its 13-inch MacBook Pro’s display ‘Retina’ despite being only 227 PPI, compared to the iPhone 4’s 326 PPI – laptops are generally viewed from further away than phone screens, so the apparent detail is mostly similar. For a more extreme example, take a close look at a billboard: according to this Stack Exchange question, a 6 metre (~19.7 feet, or ~236 inches) wide billboard typically requires only 15 PPI. Fifteen!

236 inches × 15 PPI = 3540 pixels wide

You have plenty of pixels

Hopefully this (longer than expected) post has done two things: first, helped you understand what DPI/PPI means, and second, helped you to stop worrying about it; your camera probably produces images with easily enough pixels for most uses.