Formula
Risers in one flight are the flight rise divided by your maximum, rounded up. Every riser is then the flight rise divided by that count. Treads are one fewer than risers on each flight, because the landing or the upper floor is the last tread. Two flights split the total rise in half before that count.
risers per flight = ceil(flight rise ÷ max riser)
riser = flight rise ÷ risers per flight
treads = flights × (risers per flight − 1)
run = treads × tread
run with landings = run + (flights − 1) × 36 in
stringer = √(flight rise² + flight run²)
IRC R311.7.5.1 limits a riser to 7.75 inches. R311.7.5.2 wants a tread of at least 10 inches. R311.7.3 limits a flight to 151 inches of rise. R311.7.6 wants a straight landing at least 36 inches in the direction of travel. Headroom (R311.7.2, 6 ft 8 in) and width (R311.7.1, 36 in) are not drawn here. Twice the riser plus the tread is the comfort number; 24 to 25 inches is the usual band. The stringer calculator takes one flight and adds nosing and throat. Nosing is not included in this run.
Worked examples
108 in rise, 7.75 in maximum, 10 in tread, one flight. 14 risers at 7.714 in, 13 treads, 130 in of run. No landing. Stringer length 169.0 in. 2 × 7.714 + 10 = 25.43 in.
160 in rise in two flights. The page flags a landing because 160 is over 151. Each flight rises 80 in. The run grows by one 36 in landing.
A 36 in deck at a 7.5 in maximum and a 10.5 in tread. 5 risers at 7.2 in and 4 treads. 2 × 7.2 + 10.5 = 24.9 in.
Reference
One flight, 10 inch treads, 7.75 inch maximum riser.
| Total rise | Risers | Riser | Run |
|---|---|---|---|
| 36 in | 5 | 7.2 in | 40 in |
| 72 in | 10 | 7.2 in | 90 in |
| 108 in | 14 | 7.714 in | 130 in |
| 151 in | 20 | 7.55 in | 190 in |
Questions
How many risers is a 108 inch stair?
14 risers at 7.714 inches if the maximum is 7.75, and 13 treads. At a 10 inch tread the run is 130 inches. That is the same count the stringer calculator uses.
When do I need a landing?
IRC R311.7.3 limits one flight to 151 inches of rise, 12 feet 7 inches. This page flags a taller stair and, if you split it into two flights, adds one 36 inch landing to the run. R311.7.6 is the 36 inch minimum for a straight landing.
How is this different from the stringer calculator?
This page is the stair: rise, run, flights, and the code checks. The stringer calculator cuts one flight, including nosing and the throat of the 2×12. Use both. A landing between flights is not a stringer.
Sources
- IRC R311.7.5.1 maximum riser 7.75 in. R311.7.5.2 minimum tread depth 10 in. Variation between risers is a separate 3/8 in rule and is not checked, because this page makes them equal.
- IRC R311.7.3 maximum flight rise 151 in. R311.7.6 straight landing at least 36 in in the direction of travel. Local amendments govern.