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I think you're a bit confused here. It's the height of the capital M, not the width of the lowercase em, that is generally 1em.



"In olden days, an 'em' was the width of an 'M', but this is no longer true; ems are simply arbitrary units that come with a font" - the TeXbook, p60


Yeah, it's the height now, but the name derives from the width of an "m", half an em is an "en" (as in em-dash or en-dash)




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