Size the notched board that carries your steps: cut length, throat depth behind each notch, and the right board (2x10 vs 2x12).
The stringer is the sloped board the steps are cut from. Its length is the hypotenuse of the rise and run; the throat is the sound wood remaining behind each notch, which must stay at least 3.5 inches for a cut stringer. This calculator gives both, recommends a board size, and rounds up to a standard purchase length.
A cut stringer must keep at least 3.5 inches of sound wood behind each notch. Most residential step geometry needs a 2x12; a 2x10 only works for shallow steps.
At least the diagonal length (square root of rise squared plus run squared), plus 6 to 12 inches for the top and bottom cuts. Buy the next standard board length up.
The perpendicular distance of sound wood behind a notch. It equals the board depth minus the notch triangle perpendicular height (riser times tread divided by the notch hypotenuse).