Formulas and Hints

Formulas

From image resolution to banding, file sizes to color formulas; these formulas and hints are a collection of often-needed reference material.

(1) What resolution should I use for scanning an image?

Example: Image to scan is 5w x 3.5h inches. Desired print size of image is 2w x 1.4h inches. Screen ruling (lines per inch) will be 150 lpi.
1.4 / 3.5 x 150 x 1.5 = 90 spi

(2) How can I determine the effective resolution of an image in a document?

Example: Image placed in document is 300 ppi. Scale percentage (its reduction or enlargement percentage) is 140%.
300 x 100 / 140 = 214 ppi

(3) How many colors can be displayed in an image that is n-bit?

Example: In a 16-bit image there are:
2^16 = 65536 colors

(4) What is the maximum lines per inch (lpi) that I can get from my printer and maintain 256 shading levels?

Example: On a 600 dpi printer, what is the maximum lpi I can use and still have full tonal levels?
600 / 15.97 = 37.57

(5) How many shades of gray can I produce using a particular lpi - dpi combination? For PostScript Language Level 1, reduce the resulting number to the limit of 256 if necessary.

Example: I am printing on a 600 dpi laser printer using 85 lpi. How may shades of gray can it (theoretically) produce?
(600 / 85)² + 1 = 50.83

(6) How large will the file be (in MB) for a scanned image? Channels: Use 1=grayscale, 3=RGB, and 4=CMYK.

Example: I want to scan a 8w x 10h inch photograph at 300 ppi and create a CMYK (four channels) TIF file. How many MB will the file be?
10 x 8 x 300² x 4 / 1000000 = 28.8 MB

(7) How wide will each tint (band) of a gradient be?
You will need to use formula (5) above for determing how many shades of gray a particular lpi - dpi combination can produce. Knowing this, you can determine the width of 'bands' in a gradient by taking the width or height of the gradient (use the one that travels in the same direction as the gradient) by the number of shades of gray possible. This is assuming a 0% to 100% gradient fill.
If you are using different start and end values for your gradient, you will have to multiply the percentage difference by the total number of grays. (10% to 90% is an 80% change overall, so you multiply 0.8 by the total number of grays.)
Using your results:
Banding width 1 point or less: not visible
Banding width 1 to 2 points: acceptable for most circumstances
Banding width 2 or more points: noticable, use visual discretion
Example 1: I have a gradient that is 4w x 2h inches. The gradient is 0% to 100% from left to right (along width). I am printing at 150 lpi and 2400 dpi. How wide will each band of the gradient be?
Step 1: (2400 / 150)² + 1 = 257 grays
Step 2: 4 / 257 = 0.016 inches (multiply by 72 for points) or 1.12 points: acceptable
Example 2: I have a gradient that is 1w x 8h inches. The gradient is 15% to 85% from bottom to top (along height). I am printing at 133 lpi and 2400 dpi. How tall will each band of the gradient be?
Step 1: (2400 / 133)² + 1 = 327 grays (round results to nearest integer)
Step 2: (85 - 15) = 70 (percent overall change)
Step 3: 327 x 0.7 = 229 (new number of grays or tints actually available)
Step 4: 8 / 229 = 0.035 inches (multiply by 72 for points) or 2.52 points: noticable
Keep in mind:
...that printing process color gradients will reduce noticable banding because of the four inks being involved.
...that large band sizes in lighter colors will be less noticable than large band sizes in darker colors.

Fixes for banding gradients:
1. Increase resolution (dpi).
2. Lower screen (lpi).
3. Increase difference between start and end points of gradient.
4. Shorten the gradient.
5. In all cases, adjusting settings such that there are more than 256 levels of gray is usually pointless.

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Helpful Hints

Avoid specifying colors based on the way they appear on your monitor. For the most reliable results, choose colors from a color-matching system.

Never copy and paste images into your layout program. Use the place or get image commands so that there will be an established link to the full image file.

For a deeper, richer black on four-color process work, use rich black or 'superblack' instead, which is made with percentages of the other process colors.

Neutral rich black = 100% K + 20% C + 20% M + 20% Y

Cool rich black = 100% K + 20% C

Warm rich black = 100% K + 20% M

Avoid saving raster images as EPS unless they are duotone or require vector data.

Generally, images obtained from web pages are compressed, low-resolution, indexed color mode, or combinations of these. Unless printed very small, they typically do not produce desirable results in offset printing. If possible try to contact the web designer to see if a high-resolution TIF or original image can be obtained instead.

If you are experiencing 'jaggy' fonts, check that: (see our font section for more information)

You have both the screen and printer version if you are using a PostScript font.

Your printer is capable of processing and printing PostScript data.

Your computer is correctly set up to utilize PostScript fonts. (eg. Adobe Type Manager is installed and functioning properly.)

The TrueType font you are using is not damaged.

Remove unnecessary items:

Provide documents that do not have items in the pasteboard (the area outside of the actual document). This can create links and font requirements that are not necessary for the job.

Provide only the fonts and images that are required by the document. Supplying additional fonts and images can lead to mislinked images, font conflicts, and make the job more confusing.

Check that raster images are not overscanned. Images that are scanned at unnecessarily high resolutions will take more disk space, longer times to print, and will not yield higher quality printing. Use formulas (1) and (2), and our Images and Scanning page to help determine correct resolutions for your images.

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