Canon 5D Mark III - Printing at 40 x 30 inches help

Preference for PPI will vary based on what it is and how close people will be to it looking at it. For looking up close at a photo the most you should need is 300ppi but it can definitely still look good at lower. The size you can print while maintaining a certain ppi is based on the size of the sensor in your camera. Your sensor is 5760 x 3840 pixels so you divide that by the amount of pixels per inch you want in your print. If you print at 200ppi then 5760/200=28.8 and 3840/200=19.2. So the largest you can print and keep around 200ppi is about 30x20. If you print at 40x30 you will be closer to around 130ppi and that might be ok depending on what you are doing with it, but it likely won't look very crisp up close at that size.

You also have to take into account if you cropped the photo any. When you do that you remove pixels from the image so in those situations you would start with less than 5760 and 3840 to calculate it and maintaining the same ppi would mean a smaller print.

The main factor in how large you can print is the same as it has always been; it is the size of the negative (36x24mm) and the image quality (IQ) of the negative (raw file) in terms of detail/sharpness/grain(noise).

If the image looks good on your monitor at 100% zoom, then simply divide the sensor resolution (5760) by your monitor resolution to determine the maximum print size. For instance, the monitor of my MBPR is running at 102PPI; so 5760/102 would equal a 56.5" wide print that will look just as good.

But the chances are good that it will not look "crisp" at 100% zoom due to a lack of IQ. So if looks acceptable at 50% zoom, then divide the sensor resolution by 2x the monitor resolution, e.g. 5760/204=28.25". But that is not large enough to meet your requirement, so then you would have to attempt to upsample and sharpen the image to an acceptable degree.

Also note that your sensor's aspect ratio is 3:2 and you are wanting to print at a 2.66:2 ratio, so the image will have to be cropped some from the sides. That is going to reduce the sensor resolution remaining (it will be less than 5760 on the long edge).

Edit: an easier answer is to just enlarge the image on your screen so that it equals the desired print size. E.g. 25% of the image occupies ~10"(25% of the desired print size) on your monitor. If it looks good on your monitor to you, then it will look good printed (because photo printers output at a higher resolution than any computer monitor does).

I agree there mostly. There is variation in what the answer would be depending on the situation. But at the same time your options for who can print it are sometimes limited. I have to give my preferred resolution where I print from. But even though there is a routine way to calculate it you can still improve that sometimes with software or get the same results at lower than expected ppi. If you've never printed before its likely you won't be satisfied with the first attempt for one reason or another and it may have nothing to do with size. Ive tossed prints in the trash that looked great on my monitor but turned out to be not bright enough once I sent them in to print and I was no longer viewing the printed version on a backlit screen. Its something to learn the basics of and then do a little bit of trial and error just like with learning to take those pictures that are worthy of the prints.