Formula
Count the risers by dividing the total rise by the maximum you will accept, then round up. Divide the rise back by that count so every riser is the same. One less tread than risers, because the upper floor is the last tread.
risers = ceil(total rise ÷ max riser)
riser = total rise ÷ risers
treads = risers − 1
run = treads × tread depth
stringer = √(rise² + run²)
throat = stock width − (cut riser × tread) / √(cut riser² + tread²)
The cut riser is the finished riser minus the tread thickness, so the finished step still equals the riser you checked against the code. The angle is arctan(riser / tread). Twice the riser plus the tread is the comfort number. IRC R311.7.5 is the riser and tread limit this page flags. Local codes and amendments govern. For the whole stair, including a landing when the rise passes 151 inches, use the stair calculator. This page is the stringer cut.
Worked examples
108 in rise, 7¾ in maximum, 10 in tread. 14 risers at 7.714 in, 13 treads, 130 in of run, stringer 169.0 in (14 ft 1 in).
Same stair with a 1 in tread. The finished riser stays 7.714 in. The plumb cut on the stringer is 6.714 in, so the throat gets deeper. The overall stringer length does not change.
A 36 in deck rise at 7½ in maximum. 5 risers at 7.2 in and 4 treads. 2 × 7.2 + 10.5 = 24.9 in, inside the comfort band, if the tread is 10½ in.
Reference
108 in total rise, 10 in treads, no tread thickness. IRC maximum riser is 7.75 in.
| Max riser | Risers | Actual | Run | Stringer |
|---|---|---|---|---|
| 7 in | 16 | 6.75 in | 150 in | 184.8 in |
| 7.25 in | 15 | 7.2 in | 140 in | 176.8 in |
| 7.5 in | 15 | 7.2 in | 140 in | 176.8 in |
| 7.75 in | 14 | 7.714 in | 130 in | 169 in |
Questions
How many risers does a 9 foot stair need?
108 inches divided by a 7¾ inch maximum is 13.94, so the next whole number is 14 risers. 108 ÷ 14 is 7.714 inches. There are 13 treads, because the top riser lands on the upper floor. The run is 130 inches and the stringer is about 169.0 inches.
What does IRC R311.7 allow?
R311.7.5.1 limits the riser to 7¾ inches. R311.7.5.2 requires at least 10 inches of tread depth. Riser and tread variation in one flight is capped at ⅜ inch. R311.7.2 asks for 6 ft 8 in of headroom, and R311.7.1 asks for 36 inches of width. Those last two are not measured from the rise and run. Local amendments govern.
What is the 2R + T rule?
Twice the riser plus the tread is a comfort check, not a code section. A result around 24 to 25 inches is the usual target. The 108 inch example is 2 × 7.714 + 10 = 25.43 inches, a little over that band.
Does nosing change the run?
No. Total run is treads times tread depth. Nosing overhangs the riser. It is shown so you can order the tread stock, and it is not added to the stringer length.
Sources
- IRC R311.7.5.1 (max riser 7¾ in), R311.7.5.2 (min tread 10 in), ⅜ in variation, R311.7.2 headroom 6 ft 8 in, R311.7.1 width 36 in. Local amendments govern.
- Stringer length is the hypotenuse of total rise and total run. Throat is the stock width minus the perpendicular depth of one notch.