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I am submitting a photo for an exhibit. They require a jpeg to be evaluated and then a print, if accepted. The rules indicate "Entries must be in JPEG format sized at 300 dpi on a CD (4” width of image 1,200 pixels at 300 dpi is the largest dimension please)." The final submission will be a maximum of 36" x 36". I don't see any of this in the photo's properties. What exactly are they looking for?

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What it means is that whoever wrote the rules probably doesn't have a clue how JPEGs are rendered using most current image viewing applications. DPI (dots per inch) is a term that, when used properly, refers to printer hardware. PPI (pixels per inch) is the way we refer to how many pixels of a digital image should be rendered per inch when the image is embedded in a document such as would be produced by a page setting program. See this answer to How do I generate high quality prints with an ink jet printer? for a very thorough explanation of the relationship of ppi to dpi. PPI is pretty much irrelevant for viewing and printing full page photos with most current applications. I guess it is possible they want to import multiple submissions into a page setting application before viewing them and want all of the entries to be the same size in the maximum dimension.

Having said that, it is pretty easy to set the DPI at 300 and the large dimension at 1200 pixels. For best results, do it when converting and saving your RAW files (you are shooting RAW, aren't you?). Then save and convert a full resolution version for the print at 300dpi and whatever dimension you want (up to 36", which would be 10800 pixels wide or about 78MP at a 3:2 ratio!)

See also How to get the best results with resizing an image?

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Assuming the photo is square (from the 36" x 36" max) It sounds like the largest photo they want is a 1200 x 1200 pixel image. You will need to compress your photo down to under 1200 x 1200 pixels and save it as a JPEG. The Dots Per Inch (DPI) is a way of telling the image viewing program the scale of each pixel. Some software programs allow you to view an image at actual size. The program would then take the resolution of your image, divided by the DPI, and represent the resulting scaled image on the screen. If your image were the same resolution, but a higher DPI, the image would should up smaller on the screen, even though it's resolution is the same.

They are most likely requesting a 300 DPI, 1200 pixel image so that they won't have to do any image conversion when they print them out on 4 inch paper to review the submitted photos.

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