It ain't necessarily so!

The spindle of a cottered crank extends fully to the outside of the arm, whereas cotterless spindles end roughly 3/8" or so short of the outer face.

Also, the cottered crank is probably of a low or no offset design (straight crank) and so would take a longer spindle than most relatively modern cotterless cranks with curved arms to bring the center in closer (for a stiffer shorter spindle). That too, would mean a shorter spindle.

Unfortunately, there's no real formula for translating spindle length to chain line because cranks have such variance in the chainline offset.

However, most cranks specify a suggested spindle length, and this is the best guide (though not 100% reliable). Most experienced mechanics can eyeball a crank and roughly predict the spindle they'll need, and/or have an off the bike for gauging the offset, so they don't have ti install, then replace BBs (too often).