How To Scale An Image for Monitor Display or Printing

While I believe it is very useful to understand the math and concepts presented on this page, many imaging programs and scanner and printer software control applications will do most of the scaling and sizing math transparently by allowing the user to just 'plug in' numbers for image, scan or print size. Understanding the math behind digital imaging will insure that you will have the knowledge necessary to produce images that are suitable for a wide variety of different output needs.

It is important to know what you intend to use your image for before you scan it or take the picture. As we mentioned previously, you will need higher pixel resolution files for printing than you will need for web or email attachment use. In digital image creation and workflow pixel resolution (dimensions in pixels) is the first and most important decision. 'What pixel resolution do we need to print to 8X10 inches at 300 ppi output resolution?' -- ' What is the scanning dpi necessary to get 2400X3000 pixels from my 35mm film?' -- 'What pixel resolution does it take to fill up half my monitor display when it is running 1024X768 resolution?' We will adjust the DPI of the scanner or the resolution setting of the digital camera or resize the image in our editing program to scale the digital image to the pixel resolution that is required for a specified print size or for display on a computer monitor.

Pixel resolution and assigned PPI (print or output resolution) are independent of each other but the ratio between the pixel dimensions of your digital image and the PPI selected for printing is what determines the printed size of your photograph. Or, in the case of scanning, the selected scanning DPI in relation to the size of your original scanned media is what determines the pixel resolution (dimensions) of your scanned image.

It is important to understand that DPI is a user assigned number for scaling media to a required pixel resolution during scanning. PPI is used to scale existing digital images to a required size for printing (output resolution). After you have scanned your media or taken a digital photo at your selected pixel resolution you can then change the assigned PPI number to scale the image's pixels to print at any size on paper. Just remember that 240-360ppi is the threshold for photo quality. Changing the assigned PPI after a digital image is created does not change it's pixel resolution. Changing the assigned PPI of an existing digital image only changes print size that would be created when printing that digital image.

For printing purposes each pixel in your digital image is going to be converted into ONE DOT of color information on your print. This matrix of 'dots' when viewed at normal viewing distances give the viewer the illusion of a continuous tone photograph.  As mentioned above, printed output generated at 240-360 PPI is considered by most to be a safe threshold for seeing digital prints as a continuous tone photograph.

You don't need to be concerned about your home printer's native output resolution. If your printer is capable of 1440X2800 dpi output the printer will do the necessary math and interpolation behind the scenes to make the 8X10 at 300 ppi image you have scaled in your image printing program. The 240-360 ppi threshold we have given is an 'equivalent' standard. In other words, if you have enough pixels to print to required size at 240 ppi or higher output resolution, you will get photo quality prints from any of the current batch of home printers. Some of the higher end commercial printing machines like Fuji's Frontier system, LightJet, and Chromira do a little better with 300 ppi and above.

There are 4 related variables involved that can be arranged in simple math equations that will allow to you solve all of your digital image resolution and scaling requirements. The four variables are as follows: PIXEL RESOLUTION - DPI/PPI - ORIGINAL MEDIA SIZE - PRINTED OUTPUT SIZE.

Some Formulas For Scaling DPI/PPI For Scanning Or Printing

1. Determining the necessary pixel resolution for printing to a required print size or for computer monitor display:

FOR PRINTING: Multiply the length and the width of your intended print size (in inches) by 300 (printing at the equivalent of 300 PPI is universally accepted as generating photo quality output) This formula will give you the pixel resolution (length and width in pixels) that you need to have to print to your required size with photo quality. Actually, some printing systems will work with quite nicely with 240 or 360 PPI. 300 is a safe minimum when you don't know the actual requirements of your printer.
FOR MONITOR DISPLAY: Decide the approximate fractional area of the monitor you'd like your image to cover and divide that into the current monitor resolution.
PRINTING EXAMPLE: You want to print a digital file to 16X20 inches. Multiply 16 times 300 and get 4800 and 20 times 300 to get 6000. Your digital file will need to have a pixel resolution of 4800X6000 pixels to print to 16X20 with a print output resolution of 300 PPI.

MONITOR EXAMPLE: Filing up 1/2 the monitor's side to side viewing area with an image when running 1024X768 pixel monitor resolution. Divide 1024 by 1/2  and we get 512 pixels necessary to cover half the monitor's 1024 pixel side to side viewing area. 

2. Determining the pixel resolution (pixel dimensions) of a document or photo to be scanned:

The scanned media's length and the width dimension (in inches) multiplied times scanning DPI equals the length and width pixel resolution of the resulting digital image.

EXAMPLE: Scanning a 4X6 inch photograph at 300 dpi will yield a 1200X1800 pixel digital image. 300 times 4 = 1200 and 300 times 6 = 1800. The resolution of this image is 1200X1800 pixels
3. Determining the proper DPI setting for scanning to a required pixel resolution (pixel dimensions):

Length or width of the required pixel resolution divided by the length or width of the media to be scanned gives you the required scanning DPI.

EXAMPLE: You want a 300 pixel wide image for computer screen placement from a scan of a 4X6 inch print. 6 is the width of the print so divide 300 by 6 and you get 50 as your setting for scanning dpi.
4. Determining the required printing resolution for a given print size and existing digital image:

pixel resolution (length or width dimension) divided by the corresponding dimension (in inches) of the required print size equals printing resolution in PPI.
EXAMPLE: A 2400X3000 pixel file that you wanted to print at 16X20 inches would require a print output resolution of 150 ppi since 2400 divided by 16 equals 150.
5. Determining print size for an existing digital image for any given printing resolution

pixel resolution (length or width dimension) divided by printing DPI equals print dimension.
EXAMPLE: You want to see what the print size of a 2400X3000 pixel image would be when printed at 400 dpi. Divide 2400 by 400 PPI equals 6 and 3000 divided by 400 PPI equals 7.5. Printing this file at 400 PPI would produce a 6 by 7.5 inch print.

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