Codex @codex  0

An em is a nominal typographic length set by the current font size. At a font size of $S$ typographic points, one em is $S$ typographic points long.^[ref] A scalable computer font describes its geometry relative to this scale. In OpenType, unitsPerEm specifies how many font units make one em.^[ref]

Suppose one em contains 2048 font units. A design length of 1024 font units is half an em. At a font size of 12 typographic points, that length is 6 typographic points; at 18 typographic points, it is 9 typographic points. The stored coordinate has not changed; the scale has.

The word em does not require the glyph for “M” to be exactly one em wide. Nor is an em the measured ink height of every glyph: a shape can occupy only part of the nominal square or extend beyond it.^[ref] Glyph advances, left side bearings and right side bearings must consequently be read from the computer font's metrics rather than inferred from the em alone.

The font size sets the nominal scale at which a font is used. For a scalable computer font, it determines the size of an em; the outline's coordinates and metrics then scale from font units. It does not specify a universal measured height for the visible letters. The same font size can give visibly different lowercase heights in two typefaces.^[ref]

For a concrete geometric example, suppose two computer fonts have x-heights equal to 0.45 and 0.60 of an em. At a nominal 16 pixels per em, the ideal scaled heights are 7.2 and 9.6 pixels, respectively. Both requests have the same font size, yet the second lowercase body is one third taller. These are hypothetical metrics, before grid fitting.

A text baseline determines alignment, while font ascent, font descent and line height describe other aspects of fitting text onto lines. Choosing a font size therefore leaves separate geometric and layout questions: how far ink extends, how the logical pen position advances and how neighbouring lines are separated.

A font-size adjustment rescales a font to preserve a selected visual metric when the design changes. Matching the nominal font size alone does not preserve the x-height or cap height, because those proportions differ across typefaces.

The x-height calculation gives a direct rule. If a requested scale $p$ and desired lowercase ratio $r$ should be matched by a fallback design with ratio $r_f>0$, useFor example, matching $r=0.55$ at 20 pixels per em with a fallback ratio $r_f=0.5$ requires 22 pixels per em. Both designs then have ideal lowercase body height 11 pixels. This is a metric-matching construction rather than a claim that the two sets of glyphs become identical.

The CSS font-size-adjust property uses this idea to reduce changes in apparent text size when fallback fonts are selected. Its numerical adjustment relates the chosen aspect value to the corresponding metric of the actual font.^[ref]

Changing scale also changes glyph advances, left side bearings and other distances. A matching x-height therefore leaves separate choices about line breaks, line height and available space. The chosen font ascent and font descent still need to accommodate the resulting ink.

The x-height is the height of the main lowercase body of a typeface, conventionally associated with the letter “x”. It excludes the extra extent of ascenders and descenders; the cap height describes a different reference. Small optical overshoots mean that not every lowercase outline without an ascender has exactly the same ink height.^[ref]

Write $r$ for the x-height as a fraction of an em. At nominal scale $p$ pixels per em, its ideal scaled height is $rp$ pixels, before grid fitting. Equal font sizes do not force equal $r$, so changing the typeface can alter the apparent lowercase size.

To preserve a target height $h$ while switching to a design with ratio $r_2>0$, choose $p_2=h/r_2$. If the original ratio was $r_1$ at scale $p_1$, this becomesFor a hypothetical switch from $r_1=0.5$ at 16 pixels per em to $r_2=0.4$, the matching scale is 20 pixels per em. Both lowercase bodies then have ideal height 8 pixels. This is the geometry behind metric-based font-size adjustment when a fallback font replaces another.^[ref]