The formula is simpler than the table looks
Going around one full bend, the extra distance an outer lane covers compared to the lane inside it is pi times the lane width, and that number does not depend on the track's radius at all, only on how wide the lane is. With a standard 1.22 m lane, that works out to about 3.83 meters of extra distance per lane, per bend. A 200m race has one bend in lanes, so its stagger uses that number once; a 400m race has two bends, so its stagger is roughly double.

