Don’t crop those photos when using for them for Facebook profile photos. Why would you want to if you don’t have to? It doesn’t show the full image in all its wonderful glory. That photo was picked because it’s one of your best works, or the model’s favorite photo, or the best portrait that person has, and so forth. Why not show it in its entirety? Don’t crop those photos!
Now let’s not get it twisted; I am not saying don't crop your photos. I personally do not apply square crop in my post-processing work; I don’t see why I should cut out the scene unless the photo was intentionally shot for that. However, I am not saying you shouldn’t. Let’s say you took a wonderful full-body shot of a subject, then decided to give it a square crop because the scenery wasn’t helping or it just flows better. That’s fine, but what if the subject wants to use it as their profile photo, or you decide to use it as your page’s profile photo and you or the subject want the profile to be a closeup of the face? Why crop the whole photo then when you don’t have to?
I am not sure about you, but I occasionally received a few request from models and clients asking if I could crop the image for Facebook for their profile. Sometimes, I even come across my work cropped to only a certain area of the image, which means they cropped out my watermark most of the time. Whatever your stance on watermarking your images, the bottom line is they are not the artist who created the piece and shouldn’t edit your work unless you have given permission. That’s a whole other topic for discussion.
Back to it: this method only works on desktop. I have tried a few times through mobile web and the iOS app; you do not get the same option. If you figure it out, please share with the rest of us. On desktop, when you’re resetting your profile photo on either the page or your profile, simply click on “Skip Cropping” to have your image be used in its full size. Next, you can crop the thumbnail view if you wanted to zoom in on the face or another part of the photo. Now, when people click on the profile photo, the full image will pop up, not just the cropped thumbnail. Next time someone asks or you want to set a new profile photo, jump online on your desktop and apply the full image instead.