DPI explained, Part 3: Calculations

When working with print, you will often run into these questions:

• What will the DPI be if I print my image at this size?
• What pixel resolution should my image be to print this big at 150 DPI?
• How large can I print my image without dropping below (say) 300 DPI?

In this article, I'll show you how to find the answers.

Jump ahead

Looking for something specific? Use these links:

• The magic formula — plus automatic calculator!
• Calculate DPI from pixel resolution and print size
• Calculate print size from pixel resolution and DPI
• Calculate pixel resolution from print size and DPI
• Using metric system to work with centimeters

The magic formula

Here is how the pixel resolution, print size and DPI come together in one simple formula:

resolution (pixels) / print size (inches) = DPI (pixels per inch)

In plain English: divide the number of pixels by the size of the print to get your DPI. If you find this hard to remember, focus just on the units:

pixels / inches = pixels per inch

That's easy enough! It's just like driving: if you drove 500km in 5 hours, you drove 500km per 5 hours, which is th same as 100 kilometers per 1 hour (500 km / 5 hrs = 100 km/h).

To make it even easier, I've made an "automagic" calculator for you. Simply enter two values and it will calculate the 3rd for you:

This calculator is super-handy and I recommend you bookmark this page for whenever you need it. That said, what if you want to do the calculations yourself? The rest of the article will show you how to do that for any of the three values. Lastly, we'll talk about how to use it with the metric system.

Case 1: Find the DPI (given resolution and print size)

Let's say you have an image 3000 pixels wide and you want to print it 10" (inches) wide. Here's the DPI you would end up with:

resolution / print size = DPI
3000 px / 20" = 300 DPI

If 300 DPI is sufficient, you are good to go! With the same formula, you can find out that you could print this image 20" wide at 150 DPI, or 5" at 600 DPI. If you're not sure why, try putting the numbers in the formula and see what comes out.

Case 2: Find the print size (given resolution and DPI)

Let's say you have an image 7500 pixels wide that you want to print on fabric at a minimum of 150 DPI. To find out the maximum size you could print the design, switch the print size and DPI around, like this:

resolution / print size = DPI
becomes
resolution / DPI = print size

Perfect, this formula turns our two known values into the one we are after! As you can see, you can print this 7500 pixel wide image up to 50 inches while staying above 150 DPI:

resolution / DPI = print size
7500 px / 150 DPI = 50"

Case 3: Find the needed resolution (given print size and DPI)

Lastly, let's take another common DPI question: you want to know the necessary resolution for a digital image, so you can print it at a certain size and DPI.

For this, we need to flip around the formula once more:

resolution / print size = DPI
becomes
print size × DPI = resolution

Different from the other cases, here we have to multiply to get our answer. Let's say you want to print a wallpaper covering a 100" tall wall at 100 DPI. It turns out you'll need a 10,000px tall image:

print size × DPI = resolution
100" × 100 DPI = 10,000 pixels

Calculating with DPI in the metric system

We started off with inches because it's a little simpler, as DPI itself is expressed in inches. While the USA works with inches and feet, most other countries rely on the metric system, so let's look at how that works.

For these examples we'll take our measurements in centimeters, but of course you can do the same for millimeters, meters, etc. To get from centimeters to inches, divide your desired print size by 2.54 (1 inch = 2.54 cm) before putting it into the equation.

Let's say you have a 3000 pixel wide image that you want to print at 40 centimeters wide. Here's how we find the resulting DPI:

centimeters / 2.54 = inches
40 / 2.54 = 15.75"

resolution / print size = DPI
3000 px / 15.75" = 190.5 DPI

What if you want to calculate the print size itself? Easy, do the calculation as described in case 2, then multiply by 2.54 to go from inches to centimeters:

resolution / DPI = print size
7500 px / 150 DPI = 50"

inches × 2.54 = centimeters
50" × 2.54 = 127cm

Lastly, if you want to find the resolution for a given print size and DPI, you can combine what we've learnt so far to make this calculation:

centimeters / 2.54 = inches
100 / 2.54 = 39.4"

print size × DPI = resolution
39.4" × 100 DPI = 3,940 pixels

In conclusion

Calculating with DPI isn't complicated, you just need to know the formulas to get the numbers you're after. Bookmark this page to easily find the formulas again when you need them!

Next time, we'll look at how to use DPI within the context of our pattern app Repper.