Pieces from a Stock Length (with Saw Kerf)

Saw blades remove wood. A carbide blade takes about 1/8 in, a thin-kerf blade about 3/32 in, a metal chop saw around 2 mm, a bandsaw much less. Ignore that and your cut list comes up one piece short at the worst possible moment. Each interior cut costs a kerf, but the last piece needs no trailing cut, which is exactly why the formula is $(L_s + k)/(L_p + k)$ rather than the naive $L_s/L_p$.

An 8 ft stick cut into 15 in pieces with a 1/8 in blade gives 6.36, so six good pieces and a 5$\ frac{3}{8}$ in drop. Round down here, not up: the fractional piece is offcut, not product. That reverses the usual jobsite instinct, and it is the reason this compute returns the raw number instead of deciding for you.

Run backwards, the formula sizes a kerf allowance for a known cut list. Four 597 mm pieces out of a 2400 mm stick leave exactly 4 mm of blade per cut, which is a neat way to see why cabinet shops draw their cutting diagrams before touching the saw.