The design live load your stair must be built to carry under code, and the total that implies for the stair area.
Building codes set the minimum live load a stair must be designed to carry. Residential stairs use 40 psf (pounds per square foot) plus a 300 lb concentrated load; commercial and assembly stairs use 100 psf. This calculator gives that design load and the uniform total over the stair plan area. It does not tell you what a built stair will hold — that is capacity, which requires structural engineering.
Residential stairs are designed for 40 psf plus a 300 lb concentrated load under the IRC; commercial and assembly stairs for 100 psf under the IBC.
No. This is the design load the code requires, not the capacity of a built stair. Real capacity depends on materials, spans, and connections, and must be checked by an engineer.
A single point load (300 lb under the IRC) applied to the worst-case spot, representing a heavy individual or object, checked in addition to the uniform load.