american lumber doesn’t use standard imperial units. an “inch” isn’t the standard you’d expect on a so-called “nominally” 2 inch by 4 inch board. just attempting to use metric without accounting for the extra wackiness added by lumber ‘measurement’ on top of standard imperial silliness, you’d end up with a bunch of errors.

tl;dr: a 2" x 4" board actually measures something like 3.81cm x 7.62cm.