How it is worked out
A solid poured staircase is a stack of rectangular blocks: the cross-section area is rise × run × n(n+1)/2 for n steps, and the volume is that area times the stair width. Seven-inch rises with eleven-inch runs are a comfortable, code-typical stair.
That volume - 16.04 ft³ - is divided by 27 to give 0.59 cubic yards, and by each bag's yield to give the bag count. An 80 lb bag of premix yields about 0.60 cubic feet, so this job takes 27 of them; bag counts always round up, because you cannot buy part of a bag.
Ordering ready-mix instead? Suppliers sell by the cubic yard (or cubic metre) and usually have a minimum load and a short-load surcharge - worth a call before you choose between bags and a truck.