Re-sizing for prints

[Natural_Disaster]

I found a few threads on here about this but im still kind of confused.
I know 300 dpi is needed for best quality (right?)
Do you devide that into the number of pixels you have to get the size of the image you can print?

If i have an image thats 4288x2848 does that mean the larges picture i can print at 300 dpi is a 14x9? How crappy would it look to print that as a 10x13?

If best quality for a 10x13 is 3000x3900 at 300 dpi.....but my image is now cropped to 3291x2561 and i use 300 dpi, best quality will be printed as a 10x8.5 (right?)
Is there any way to get a 10x13 out of it and it still be frame-able quality?

What is the lowest pixels and dpi combination i can use to get a frame-able quality 10x13?

Sorry, i know thats a lot of questions. I thought i had it all figured out until i uploaded pics to be printed and some say the quality wont be good and others say there will be a white border unless i allow them to crop and cropping will take out the border i added to the pictures on the top and bottom but not the sides! Ugggg

 

[KmH]

Don't use the term dpi (dots per inch) unless you are describing printer resolutions. Digital photo's are made from pixels, so its ppi (pixels per inch).

Back in the early days of digital when top-of-the-line pro cameras had all of 4 or 5 mega pixels and we wanted a print that had density approaching what we could get with mainstream print film, we used the standard of 300 ppi.

Today it's different.

How big a photo can be printed at depends on the photo and how the print will be made.

There are 2 main ways prints get made today.

The first is known as chromogenic printing (C-print or a continuous tone print) and the second is inkjet printing (using dots, more on that below).

A chromogenic print is made using light sensitive paper that is exposed with your image using red, green, and blue light, and then immersed in a couple of different chemicals to develope the photo (the RA-4 process).

Viewing distance also has a direct bearing on what ppi will work.

You want a 10x13 out of a photo that has a resolution of 3291x2561.

So 3291 pixels divided by 13 inches = 253 pixels per inch, and 2561 divided by 10 = 256 ppi.

You should wind up with a beautiful print using a 3291 pixel by 2561 pixel photop printed at 253 ppi.

BEWARE your cropped photo has a 1.285 aspect ratio while the 10x13 is exactly a aspect ratio of 1.3 so the print will be slightly less than 10 inches at 253 ppi or slightly more than 13 inches at 256 ppi.

Edit; Oops! Forgot to discuss inkjet printing.

Inkjet prints are made by the print head propelling variable-sized droplets of ink on to paper. (dots)
Each image pixel is rendered by multiple droplets of ink. Some inkjet printer heads today have as many as 175 nozzels in each print head.
Giclée, a fine art term, has come to be associated with inkjet printsmade using fade-resistant, archival inks (pigment based, as well as newer solvent based inks), archival substrates, and the inkjet printers that use them.

Inkjet prints cost more to make than C-prints.

 

[Big Mike]

Print as large as you can imagine...just remember that you have to stand back further as the size gets bigger.