16 x 20 too pixelated

[CCericola]

Ok, I put in the dimensions into photoshop. 4288x2848 will be 16x24.9 at 178ppi. If your printer only wants 300ppi then you can print up to a 9.493 x 14.293 without resampling the image.

 

[KmH]

I just pulled up the image info in PS, when viewed at 100% those are the dimensions. 4288 x 2848 was the original when I pulled the exif data.

At some point your photo got resampled to be 7227 x 4800 pixels then.

What ever application was used to do that made up pixels that the camera never recorded. That can have an undesireable effect on image quality.
There are a number of different algorithms that get used to resample an image, and each makes up pixels in slightly different ways. Algorithms like: Nearest Neighbor, Bilinear, Bicubic, Bicubic Smoother, and Bicubic Sharper.

Image pixel side dimension x the pixels-per-inch (PPI) assigned = print size - Like Christina demonstrated. By doing some basic algebra, the forgoing equation can be re-written to solve for each equation term.
So - Print size ÷ Pixels-per-inch (PPI) = the image pixel dimensions needed for a specific print size.
Image pixel dimension ÷ print size = PPI (pixels-per-inch)

You wanted a 16x24. With original image pixel dimensions of 4288 x 2848 we find that: 4288 px ÷ 24 inches = 178.6 PPI which is usually sufficient for viewing a 2 foot wide wall print since people would stand back from the print to view it.

Note that because 2848 px ÷ 16 inches = 178 inches exactly we know that 4288 x 2848 pixels is not an exact 3:2 aspect ratio, so a sliver of the image will be lost when printing at a 3:2 aspect ratio.
However, since the print will be made 'full bleed', or all the way to the edge of the paper, the printing machine will print the photo about 2% oversize to allow for slight variances in the accuracy of postioning the paper in the printing machine a sliver of the photo will be lost from each side.

Here is a group of short tutorials that you may find useful, if you haven't already seen them: Tutorials on Color Management & Printing

 

[DiskoJoe]

you probably need to increase the pixel ratio. To print images of larger size you need to bump it to 300-400. The photoshop default is only 240 PSI. This is fine for the web but not printing.

Also you will need to crop a 16x20 out of the original image since dslr's only shoot in 3x2 or 16x9 aspect ratios.

 

[KmH]

The pixels-per-inch (PPI) value is meaningless for web or other electronic display.
For the web and electronic display the pixel dimensions are the only numbers that any have meaning.

DiskoJoe has it exactly backwards. Making the pixels-per-inch value larger makes the print smaller.

For example: A 3000 x 2000 pixel image set to 100 PPI will be a print 30 inches x 20 inches. The same 3000 x 2000 pixel image set to 300 PPI will be a print 10 inches x 6.67 inches.
3000 px divided by 100 PPI = 30 inches