The stair formula
Designing a flight of stairs means splitting a fixed total rise into equal risers, then sharing the total run across the treads.
risers = round( total rise ÷ target riser )
riser height = total rise ÷ risers
treads = risers − 1
tread depth = total run ÷ treads
Every flight has one more riser than tread, because the upper floor serves as the last step. Rounding the riser count to a whole number keeps every step exactly equal — uneven steps are a trip hazard.
Worked example
A staircase with 108 in total rise, 120 in total run, target riser 7 in:
Risers: 108 ÷ 7 = 15.43 → round to 15.
Riser height: 108 ÷ 15 = 7.20 in.
Treads: 15 − 1 = 14.
Tread depth: 120 ÷ 14 = 8.57 in.
Check the comfort rule: 2 × riser + tread ≈ 24-25 in for a natural stride. Here 2 × 7.20 + 8.57 = 22.97 in — slightly tight on tread, so a longer run would feel more comfortable.
Building code limits
Typical US residential code (the IRC) caps the riser at about 7.75 inches and sets a minimum tread depth around 10 inches, with all steps in a flight kept uniform within a small tolerance. These limits keep stairs safe to climb and descend. Local jurisdictions can differ, so always confirm with your building department before cutting stringers.