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Is there an agreement on the optimum mathematical proportion of line height and the size of a text? And if there is, is it the same for print and web?

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Short answer: "No."

Long answer: There are four factors involved in deciding the leading (nowadays meaning the distance from one baseline to the next, also called line height): the x-height of the characters, the measure (length of the line), the weight of the strokes of the characters themselves and the size of the type. In this answer, for simplicity, I'm going to use "leading" and "line height" interchangeably.

Of these, the one that dominates is the measure, followed by x-height and point size.

The wider the measure, in general, the more open the line height must be to maintain readability. If your measure is longer than about 70 characters of your chosen typeface and point size, you'll need to increase the line height so the reader doesn't skip or accidentally repeat a line while reading.

The size of the characters is never the same as the point size, which in the days of metal type was taken to be the total measurement from the bottom of the lowest descender (e.g., the tail of the lowercase "y") to the top of the highest ascender (such as the vertical stroke of the lowercase "h"). The height of the lowercase "x," from which "x-height" derives, might be tall (Arial) or very short (Bernhard Modern) in relation to the point size. Type set so that the line height is the same as the point size is "set solid" -- no extra lead between the lines. Arial or Helvetica look horrible set solid. Bernhard Modern doesn't.

To maintain readability, typefaces with a large x-height in relation to the cap and ascender height (e.g., Century Schoolbook or Helvetica) need more line height, relative to point size, than Garamond or Futura, which have smaller x-heights.

Sans serifs tend to have much thicker strokes, relative to their size, than serif typefaces. Setting them too tightly (small line height) makes paragraphs and pages look very heavy and dark, and can make them very hard to read. Opening up the leading, and sometimes the character spacing, improves the look of the text considerably. An serif face with a relatively small x-height, like Garamond, can be set with much less line height.

All of these considerations are modified by how the designer wants the page to look. Some subjects are enhanced by a more airy look to the page (e.g., romantic poetry, unicorn stories), calling for a delicate typeface and open leading. Others need more authority (textbooks, say) and benefit from a darker "type color."

Now let me dispense with the Golden Ratio (phi) idea. It would be wrong in almost all cases. Mathematics has nothing to do with it. Appearance does.

Contrary to what you might think, large text such as headlines requires tighter leading than paragraph text. Headlines are often set with "negative leading" -- the line height is less than the point size. This is especially true for headlines in all caps, which always require reduced leading. (Because of ascenders and descenders, it is common for multi-line headlines to have different leading on each line in order to make the line spacing look even.) Conversely, small sizes, such as for captions or footnotes, need more leading or they become hard to read. Type looks "looser" as it gets larger and "tighter" as it gets smaller, which requires adjustments to letterspacing below 8 pt and above about 24 pt for most typefaces.

You would go seriously astray if you tried to use phi (or any fixed ratio) to calculate line height, because you would be right only by accident.

For the web, use typefaces designed for low-resolution devices for at least the next few years, until moderate-resolution screens (250 - 400 ppi) become commonplace. Not all "web fonts" from providers such as Google, Extensis or Typekit are usable at text sizes on most displays. Web text tends to read better when spaced a little more openly than on a printed page, because of the coarse dot grid and OS manipulations that blur strokes and distort character shapes.

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Very short-measure text with few lines like floating labels or block quotes sometimes benefit from negative (less than point size) leading as well, so long as the point size isn't too low. I think of it as a little like setting the rhythm of the text (although now I try to put that analogy into words, I realise it probably only makes sense in my head...) –  user568458 Aug 28 '12 at 8:41
    
You're right. And "rhythm of the text" communicates the concept perfectly, I think. :) –  Alan Gilbertson Aug 29 '12 at 1:19
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Edit Ok, so, maybe "cant go wrong" wasn't the best choice of words. Of course there is no universal optimum, but the golden ratio really does look good in a lot of cases. Check out this phi based layout calculator. http://www.pearsonified.com/typography/

And here is a great article explaining the programmer's reasoning http://www.pearsonified.com/2011/12/golden-ratio-typography.php


You cant go wrong with the golden ratio.

Line Height = text height x 1.62

Great question, by the way.

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You can also use em to size your fonts. On the web it can go down to .01em which is 1/2 a pixel. –  Julian Aug 26 '12 at 22:15
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This answer is not good advice. It runs contrary to centuries of typographic practice. No typesetter would use a fixed ratio for all text, and almost never one as large as phi. –  Alan Gilbertson Aug 27 '12 at 6:04
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Of course you can go wrong with the golden ratio. It's a ratio that makes sense in ancient monumental architecture, but isn't necessarily appropriate for everything else. –  DA01 Aug 27 '12 at 6:27
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This answer pretty much ignores all conventional wisdom and is entirely arbitrary - it does not reflect typographical practice and it is not really a good idea. It also fails to take into account factors such as the design of the typeface (probably the biggest factor), the context, the type size, the column width and margins, and others. –  thomasrutter Aug 27 '12 at 8:33
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This golden ratio typography phenomenon appears to have no solid typographical grounding and is basically a gimmick or fad that just "sounds geeky, so it must be cool". That article is almost cult-like in its insistence that the golden ratio is going to solve all our typographical problems. –  thomasrutter Aug 28 '12 at 7:31
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