Instagram has started storing images at 1080 x 1080 pixels (as opposed to the standard 640 x 640) and the hi-res versions can be found in the source code. The app still displays the lower resolution, but for more recently uploaded images, you can find better versions by digging around in the code on your computer.

Here's how:  Look up the page's source code. If you don't know how to do that, here is a list of commands for different browsers.  Use the Find command (hit Ctrl/Cmd+F) to search for '.jpg'  The first result is the direct URL to the big version. Easy!

These larger versions will make for better prints, and will probably be part of an improved viewing experience in a future version of the app.

Cover image: Instagram