There are several (at least) formulas for stairs. But as In the cases of the French and English examples they give almost
the same result. There is, or at least was ,a big difference between rules used by architects and country tradesmen. Audels Carpentry books in the earlier editions, defined "cottage stair" as one with a tread of only nine inches.
I agree the stairs used by the house help and coal shovelers are better than they once were.