Figure 45 shows a set of stairs forming a right triangle. The stairs use the floor frame as the top step. Only one-half the stairs are shown. The Pythagorean theorem (Rise^2 + run^2 = Stringer Length^2) is used to calculate the hypotenuses or the lengths of the stringers. To determine the length of the stringer in figure 45, use the desired unit rise of 175 mm and unit run of 250 mm. The stairs have 11 risers and 11 treads. The 12th riser and tread is part of the floor frame. The rise used in the Pythagorean theorem to calculate the stringer length will be 175 mm times 11 = 1925 mm (the total rise shown in figure 45, not the true total rise of 2100 mm). The run used is 250 mm times 11 = 2750 mm. The square root of 1925 mm squared plus 2750 mm squared = 3357 mm. 3357 mm is the length of the stringer.

                                                                                           Figure 45  The Top Step Is The Floor Frame