Most of the time when you're posting to Instagram you're probably uploading the photos that you took on your phone. The whole service is very much geared towards using it on phones, after all.
Sure, you'll have to decide which part of the picture you want to upload in the square dimensions and which filter to use (or not), but issues about resolution and image size are pretty much taken care of.
But there are times when you might want more control. Maybe you're editing the photo on your computer in Photoshop or Lightroom. Maybe you're applying sharpening and want to look it's best. Or, more commonly, maybe you're adding text or logos and want to make sure it's going to be clear and able to be read easily.
Whatever you're trying to do, below are the dimensions that Instagram accepts and displays through its web app. How they'll display through the phone apps is harder to pin down because of the many variations in screen sizes and display densities. Retina display iPhones, pre-Retina iPhones, Android phones, etc., all have different types of displays with different pixel-densities. So trying to pin down photo sizes on mobile displays is a case of chasing one's tail. And you're totally at the mercy of the combination of app and phone anyway. At least with the web app, there's some consistency you can work with.
Higher-resolution images. In mid-2015, Instagram started rolling out support for higher-resolution images. Instagram had always used square photos with sides of 640px. Now it displays squares with 1080px sides. Nothing will break if you still use smaller images, but using larger ones will make them look better. Up to now, they've been automatically stretched when you look at them at larger or high-resolution phone display, but now there are more pixels to provide sharper photos with more detail.
You can also upload larger if you like, but they'll be downsized to 1080px.
No Longer Only Square. Instagram has finally ditched the requirement that all images be square. See this post for details.
All of the measurements I use below are in the order of width by height, and all are in pixels.
What Size Photo Should You Upload to Instagram?
The photos you upload should be at least 1080px on the shortest side. You can crop it to a square (or shoot it as square to start with) before you upload or crop it in the Instagram app when you go to post. But Instagram now supports rectangular images as well.
If you're uploading photos you took on your phone, this is mostly a moot point. But it can be useful to know if you're resizing images elsewhere.
When you upload a photo to Instagram, it gets converted to an image with the longest side at 1080px. There is some JPG compression applied, but it doesn't appear to be as aggressive as that used on Facebook (which makes sense for a service based mainly on photos).
On smartphones, the images are displayed at a maximum of 1080px (automatically stretched if the original photo is smaller) for sharpest display.
For now, the web app still uses images of 640px and display them in a box 600px by 600px. But for optimum quality across devices, start with an image that is at least 1080px in both dimensions. You can upload one that's smaller, but it won't look as sharp. And larger images will also come in handy as more and more devices more to Retina and high-density displays.
Profile Page Header and Thumbnail Grid
Instagram had changed its layout and done away with the profile header that used to feature a tiled mosaic of your images at the top when someone viewed your account's home page.
The new layout is much cleaner and faster, with your profile information at the top and a grid of thumbnails, 3 across by 4 down, below. To see more than 12 thumbnails, users can click on the "load more" button at the bottom to start an infinite page with new thumbnails loaded as they scroll down.
The thumbnails are about 292px squares. I say "about" because the size is determined by a percentage, which, when at full size, measures to precisely 291.672px. For practical purposes it's 292px. But in reality, it's pulling in an image that's 640px by 640px and downscaling it for display. The result is that it automatically display crisply on Retina and high-density displays.
Large Photo Popup & Photo Pages
Using a desktop web browser, if you click on one of the thumbnails in the lower part of a profile page, you'll get a popup larger version of the photo.
The photo fits in a box 600px wide and 600px high (note, this is a shade smaller than the old 612px). A square image will fill the entire frame.
But you can also now use landscape or portrait images, and they'll be 600px in the longest dimension.
The popup is responsive, which means that on narrow browsers it will scale down proportionally. On narrow screens, the info and comment area is below the image.
Profile Picture / Phone App
In the phone app, your profile picture displays as a circle, so if you're using a logo, make sure that it's safely in the center of the image.
Profile Picture / Web App
In the web app, it displays as a square with a thin white border. It displays as a square with sides of 152px.
Changing Your Profile Picture
You can't change your profile in the web app. It can only be done in the phone app. In the Instagram phone app, click on the profile icon, which is the silhouette of a person at bottom right.
Then tap on the round profile picture at top left. You'll then get a choice of where to get the new profile picture from.
What is the Maximum Photo Size You Can Upload to Instagram?
I've seen in some places that the maximum image size it will accept is 2048px. That seems to be outdated. I've uploaded images over double that size without any issues. Which makes sense as the cameras in smartphones are getting better and bigger. So if there is an upper limit, it's much higher than 2048px and isn't a practical impediment in normal use.
Do the Photos All Have to be Square?
No, not anymore. See this post for details.
What About Display on iPads?
Ah, yes. Instagram and iPads. There's still (!!) no iPad-optimized app for Instagram. You can run the regular iPhone app on an iPad, but you either have to settle for using a tiny iPhone-sized portion of the screen or hit the 2x button at bottom right and get images looking pretty horrible. Wouldn't it be nice to be able to look at Instagram pictures on an iPad in full resolution glory?
Can My Photos Be Stolen?
Yes. Instagram uses some fancy programming to make it more difficult for people to just save your images to their hard drive, but that's by no means absolute security. While I'm not going to make it easy for anyone by spelling out here how to do it, it's still very possible for anyone to download any image you share publicly on Instagram (a truism for sharing on any public space on the web). By all means, add a watermark if you think that's going to help. But also know that any image on Instagram can be downloaded by anyone who can view it.
At the time of writing, this is what the terms say about copyright:
They also provide recommendations on reporting copyright violations:
Reporting Copyright and Other IP Violations
We respect other people's rights, and expect you to do the same.
We provide you with tools to help you protect your intellectual property rights. To learn more about how to report claims of intellectual property infringement, visit: https://help.instagram.com/customer/portal/articles/270501
If you repeatedly infringe other people's intellectual property rights, we will disable your account when appropriate.
Posting to Instagram from a Desktop or Laptop
Instagram is primarily designed to be used with mobile devices, but there are aways to post to Instagram from a computer.