Nosing is not taken into account when calculating initial stair
set-out, but added later.
The rise of a residential stair in the US is 8" and the run is
10" with a nose of 1". This means that the tread depth is 10", the
height from stair to stair is 8" and the tread sticks out 1" over
the the tread below. It is still 10" from front to back.
A commercial stair is 7" rise, 11" run, 1" nose.