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PPI (Pixels Per Inch / Pixel per Inch) denotes a resolution according to points / pixels and should be used in connection with scanners, monitors and electronically stored images. The American length measure of inch, which corresponds to about 2.54 cm, serves as a reference. So 254ppi is the same as 100 dots (or pixels) per cm.

DPI (Dots Per Inch) denotes the number of print points / drops and is an important measure for laser printers and inkjet printers, for example.

LPI (Lines Per Inch) is a measure of the screen width [i.e. the distance between the screen cells (see below)] in (offset) printing, i.e. the normal printing process for magazines and others.

The difference between these terms:

To a pure Black and white image In most printing processes, black paint is applied point by point to the white paper.
For Grayscale images (and therefore also for color images), this method is actually unsuitable, as there is no gray color (s) available.
In order to still be able to produce gray tones, several drops / points are combined. A field of 16 by 16 points, for example, can be printed entirely, not at all, or only partially. A total of 16x16 (= 256) combinations / gray tones are then possible.
One such field is one Gridcell, the image is rasterized for printing.
At the Offset printing (Printing processes for magazines etc.) there are usually 150 of these grid cells per inch. And 150 rows of these grid cell rows fit on one inch of printing height. One then speaks of 150 LPI (lines per inch).
If you convert this to cm, you can see that 150dpi corresponds to the 60 grid standard in Germany with 60 rows of grid cells per cm. For Color in print in principle the same applies.
The impression of many colors is achieved by overprinting 3 colors (cyan, magenta, and yellow (CMY) and black (K) with a grid of 16 by 16 points. 256x256x256 then results in 16777216 different color tones.
The black is not included in this calculation, as it only serves to create the black, which cannot be 100% realized by mixing the three colors. With black you can also create a gray in the picture cheaper and better than if you wanted to create it from the three bright colors.

The Quality factor
Since it can lead to problems if the scan resolution (PPI) adheres exactly to the value of the print resolution (LPI), one scans with a quality factor of 1.5 to 2, that is, for example, with a Scan resolution of up to 300ppi works for offset printing, although only 150dpi is printed there. [If an image consists of thin lines (= graphics), the higher scan resolution is required.]

What about laser printers and inkjet printers? Laser printer With 600 DPI (dots per inch) create (if you're lucky) 600 black dots per inch. In order to be able to print grayscale with it, the printer has to put together raster cells from these points. To be able to print 256 shades of gray, you need 16 dots per cell in width (and in height).
So 600 dpi become 600/16, i.e. approx. 35 LPI. In terms of resolution in gray levels, the 600 dpi laser printer is about as good as a rather poor (black and white) daily newspaper print.

(Color)Inkjet can set points of different sizes, and the grid cells can be flexible (frequency-modulated grid). This makes the grid more inconspicuous, the image looks more even, rounder. Nevertheless, these devices also have to raster and can only partially put the high DPI values ​​on paper (i.e. convert them to LPI).

The image resolutions (which should actually be given in PPI) can therefore be significantly smaller than the DPI values ​​of the inkjet or laser printer suggest. An older 720dpi inkjet printer hardly shows any improvement with color images beyond 180ppi. With the newer models, which have a resolution of 720 x1440 dpi, approx. 250 PPI scan resolution should be sufficient for 1: 1 printing. And more than 400 ppi are not necessary even with very finely resolved image details.
[For the sake of simplicity, calculate with 254 ppi, which is then converted to cm (1 inch = 2.54 cm) 100 pixels per cm. For a picture in 10x15 you need 1000x1500 pixels.]

A scan with 1440 PPI does not bring any advantages for 1: 1 printing (printing in the same size as the original) but only makes the "handling" more inconvenient due to the immense file size. A double PPI number leads to four times the file size.

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It looks different if the print should be larger than the original. If a 10x15 picture (postcard format) is to be enlarged to 20x30cm, you need 2000x3000pixels for the final picture (based on the simple 100pixel per cm (254ppi) formula).
The original 10x15cm image must then be scanned with 200 pixels per cm, i.e. 508 pixels per inch.

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