Font size and column width (LaTeX)

Optimal column widths are claimed to be between 50-75 characters per line. So, if given a font-size in pt, what is an acceptable width of the text area?

This depends on the average character width, which in turn depends on the font, font-size, the text (more "i"s or "W"s?), and kerning. Given font and font-size, a rough measure of the character width is given by the alphabet length/26.

I am using the usepackage{lmodern} font in a 10pt size. The exact name of the text font is then lmroman10-regular, which you can see by viewing the pdf with Adobe Reader, then going to File -> Properties -> Fonts.

I created a test document with the line

abcdefghijklmnopqrstuvwxyz

I opened the pdf in Illustrator (after installing the missing font from here from C:\Program Files\MiKTeX 2.9\fonts\type1\public\lm) and measured the line to be 126pts long, or roughly 4.8pts/character. Assuming that the font width is directly proportional to font size, this works out to the dimensionless number

char_width = 0.48

The optimal line length can then be calculated as

 line_length = (75 characters)*char_width*font_size

We know that 1pt = (1/72) inch., so for 75 characters of 10pt sized text, the lines should be 127mm wide.

Or, the other way around, assuming a standard sized A4 paper (210mm * 297mm) with 35mm margins, the text area is 140mm * 227mm. We can rearrange the formula for the line length a bit and calculate

font_size = line_length/(75 characters * char_width)

This gives us an optimal font size of 11pt. Good to know.