Your blog may be a labor of love, but if your painstakingly crafted images get resized and lose quality once you upload them to Tumblr, it's enough to make the most loving person in the world scream in frustration. The issue is that Tumblr has very strict image size guidelines -- adhering to them is the only way to keep your images from being resized.
Maximum Image Sizes
Whether an image is resized or not after being uploaded to Tumblr is based on the width of the dashboard's content area and depends on how many images you place in each row. As of the October 30, 2014, update, this width is 540 pixels, with no margins on either side; this is also the maximum possible width for an image placed in a row of its own. If you place two images in a row, they can be no wider than 268 pixels each and will be displayed with a four-pixel space between them. Similarly, three images placed in a single row may be no wider than 177 pixels each; they will have four pixels of space separating them, plus a one-pixel margin on the right-hand side that you can't remove.
What Happens Otherwise
If you upload images wider than the dashboard allows for, Tumblr will automatically create a resized version to display on the dashboard. Although your readers will still be able to click on the images and see the full-size version whether they're viewing your blog through the dashboard or by visiting its page directly, the resized images often look decidedly worse than the originals. Still images can lose sharpness and appear blurry as a result of the resizing, while animated GIFs may lose their animation altogether and be displayed as still images instead.
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Uploading Large Images
The only time you may not care whether your images get resized on the dashboard is if you are uploading large still images and want your readers to view them at full size anyway. In this case, you should treat the dashboard image as a preview outside of your control and focus on keeping the quality of the full-size image as high as possible. As far as still images are concerned, Tumblr allows for a maximum width of 1280 pixels and a maximum height of 1920 pixels; images that exceed either or both dimensions will get resized.
As of November 19, 2014, one important exception to the pixel size rules remains. Uploading 540-pixel-wide images in the JPG or PNG format works as you would expect -- they appear on the dashboard exactly as you uploaded them, without being resized. Images in the GIF format, however, are currently bugged -- if you upload one that is 540 pixels wide, it will get resized down to the old maximum width of 500 pixels and then visually stretched to cover the full 540 pixels. Until this bug is fixed, you are better off creating your GIF images 500 pixels wide. They will still get stretched on the dashboard, but you retain full control over their quality and you don't run the risk of animated GIFs being turned into stills.