How to calculate image size for printing?

Question

Raster graphics

For example, given a photo from a phone: 3264 × 2448 px, 72ppi
How to understand what size (in centimeters) this image will have at a resolution of 300ppi?

Answer 1

When printing, the term dpi ( dot per inch ) is used, and for monitors, it is customary to consider ppi ( pixel per inch ) resolution. The resolution of the monitor on the size when printing is irrelevant, so no one needs your 72 ppi. And I don't know where you even managed to find such a device.
The size of the image on the screen also does not depend on the resolution of the monitor - only the total number of pixels matters. Therefore, when they say “screen resolution”, they mean exactly the number of pixels used by the OS in width and height.
If we talk about printing from a computer, then the printer, format (if it allows), paper orientation is selected in the print dialog box. And then it depends on which document and with what styles the image is located - the printer driver will adjust the document to the printed width.
In fact, for you, the dpi of a printer is only the quality of the printed document.
But for typographic needs, when preparing images, dpi is necessary, since different values ​​\u200b\u200bare used for different media, types of printing, and depending on many other factors. However, if the words “prepress” mean nothing, then you don’t need to delve into this. Yes, and the pictures are taken for 300 dpi, using professional equipment, not a mobile phone.
Well, if you still persuade to print your picture on a device that allows you to output 300 dpi, then the size is considered simply:
1 inch ≈ 2.54 cm
300 dpi ≈ 118.11 dpcm (a kind of liberty - dot per cantimeter) The
total photo would be 27.64 × 20.73 centimeters.

Answer 2

The comments on the first answer are good. I can add that you can calculate the size without calculators and a piece of paper with pencils - you can use Photoshop.
Open the image, then: Menu Image > Image size.
In the dialog box, uncheck the Resample Image checkbox and in the Resolution field, substitute the resolution of the printer or printing machine, which is necessary for maximum print quality. For a multi-color photo inkjet, this is 400-450 dpi, for offset printing - 300, for a photo lab with Noritsu - 150, etc. For permission to print for other processes, ask the technologist of the organization that will print.
Accordingly, the Width and Height fields will contain dimensions in millimeters that the picture will take at the specified resolution.
That is, if you need to print on A3 offset, the picture at 300 dpi will turn out, based on the dimensions in the question, 27 by 20 centimeters. Size A3 42 * 30 cm, so the picture will be stretched twice. And if you print on A4 30 * 21 cm, then you get just the maximum quality.
It should be borne in mind that the real resolution of smartphone photos is 4 times less than the physical resolution of the matrix, because the picture quality is greatly reduced by noise from an extremely small matrix and the quality of poor plastic optics of a lens the size of a fingernail.