Rich1939 Loc: Pike County Penna.

What is a "reasonable sized print" ?

Tim Hoover

A 24MP image with no up or downsampling printed at 240 dpi is roughly 15x23".
A 45MP image with no up or downsampling printed at 240 dpi is roughly 23x34".

These are reasonably large for most people.

Good upsampling algorithms support somewhere around a factor of 3 without (very) noticeable loss of quality. The larger the print, the larger the viewing distance (in general) so the differences become moot.

Rich1939 Loc: Pike County Penna.

I've been struggling with this and quite frankly I don't understand how you came up with those dimensions. As an exercise I wanted to change the DPI to 360, couldn't work it out. Maybe I need more coffee.

Tim Hoover

A standard sensor has an aspect ratio of 3:2
For a 45 MP sensor that is roughly 8216x5477 pixels (5612x3742 for 21 MP).

Divide those numbers by the printer's DPI and you get 34.2x22.8" for 45 MP and 23.4x15.6" for 21MP at 240DPI, (22.8x15.2" and 15,6x10.4" respectively) at 360DPI.

Rich1939 Loc: Pike County Penna.

Had another cup of coffee and the lights came on.
So, for a 24mp image you believe something approaching 11.1 X 16.7 would be about the right size for a reasonable sized print. Are you also implying that a larger size would degrade the image?

Tim Hoover

At that size one pixel on the sensor maps to one dot on the print (under ideal conditions where the printer puts out square dots of perfectly aligned ink). That is all the information available in the file.
If you print bigger, then an algorithm is employed to extrapolate the data to the larger size (effectively inventing data). As I mentioned previously, there are some very good algorithms available for doing this. So, would you NOTICE a degradation? I doubt it if you don't push the extrapolation too far.

Remember though, this thread started out in basically the opposite direction. That is, how many pixels are really needed for a given sized print? Many people seem to think that more is better. It's not. Any time you print SMALLER than the native resolution an algorithm is employed to throw away data so you gain nothing, and in fact risk degradation due to the algorithm employed to downsample.

Now, just on the unlikely chance that someone else has followed the thread to this point, let me emphasize that these resolution questions are all theoretical. Will you actually NOTICE a difference if you print a bit larger or small than optimal? Very likely not. Oh, and one last (technical) point, the term 'resolution' does NOT refer to the number of pixels in a sensor. However, everyone I've ever read on this forum treats them the same (including me) so I will continue with that sloppy practice unless someone call me out on it.

Rich1939 Loc: Pike County Penna.

I don’t know that resolution has ever been quantified. At least not in a way Joe Six Pack can make use of it.
In another vain I do know for my purposes I would rather have the pixels to throw away than need to fake them when wanting to go larger. With stitching and using normal or medium telephoto lenses my 24MP camera can give me a .dng file equivalent to a 36MP camera or larger. I also like the additional control that stitching allows over aspect and/or capture angles while diminishing distortion. My lens of choice is either a 50mm or an 85mm. Both used in the vertical position, not a whole lot of native distortion to deal with with those. While I have been blessed with a good eye for level when looking through the view finder, plumb (fore and aft) is problematic. Keystone correction fortunately is not a big deal in Photoshop.
FWIW I have printed pictures almost 2X what your formula would indicate is optimal and have been pleased with the prints

Gene51 Loc: Yonkers, NY, now in LSD (LowerSlowerDelaware)

A stitched pano is a lot like a fine art painting of a landscape. The point of view and longer focal lengths possible with stitched images resembles what the painter used - his/her eyes and the muscles in the neck to rotate the head (and eyes) for a wider view. If you go to a museum, NONE of the classic landscapes "look" like they were viewed through an ultrawide lens. Ultrawides have a very nasty extension distortion and volume deformation at the edges. An interesting effect but it's something that has become passé since so many photographers have access to lower cost ultrawide lenses.

For the record - you can make a billboard sized image from an iPhone shot.

But the stitched pano does have the advantages of higher resolution, which can be used to reduce noise by downsampling.

This will tell you what image resolution you will need for specific viewing distances.

http://www.photokaboom.com/photography/learn/printing/resolution/1_which_resolution_print_size_viewing_distance.htm

Gene51 Loc: Yonkers, NY, now in LSD (LowerSlowerDelaware)

A print will show the difference. And if you crop you will still have more than enough pixels with the D850, more so than the D7500. And if you shoot in low light and high ISO, I think you will like the results from the D850 over the D7500. I like the D7500, but it is definitely not a D850 for so many reasons.