 X-height

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]