STAIR CALCULATOR
How it works
A total rise of 9 ft 0 in — 108 inches — with 10-inch treads.
- Divide by the 7-inch carpentry target: 108 ÷ 7 = 15.4, which rounds to 15 risers.
- Riser height: 108 ÷ 15 = 7.2 inches, shown as 7-3/16" to the nearest sixteenth.
- Treads are always one fewer than risers: 15 − 1 = 14 treads.
- Total run: 14 × 10 in = 140 in = 11 ft 8 in.
- Stringer: √(108² + 140²) = 176.8 in = 14 ft 8-13/16".
15 risers at 7-3/16", 14 treads at 10" — an 11 ft 8 in run and a 14 ft 8-13/16" stringer. Passes IRC 2021.
Constants
| Constant | Value |
|---|---|
| Maximum riser height | 7-3/4" |
| Minimum tread depth | 10" |
| Minimum headroom | 6' 8" |
| Maximum variation in a flight | 3/8" |
| Comfort rule (2R + T) | 24" to 25" |
SOURCE — IRC 2021 §R311.7.5.1: maximum riser height 7-3/4". Local amendments override (MI and PA UCC allow 8-1/4").
SOURCE — IRC 2021 §R311.7.5.2: minimum tread depth 10" nosing-to-nosing (11" with no nosing). Local amendments override (MI and PA UCC allow 9").
SOURCE — IRC 2021 §R311.7.5: minimum headroom 6' 8".
SOURCE — IRC 2021 §R311.7.5: maximum riser and tread variation within a flight 3/8".
SOURCE — carpentry comfort rule: 2 × riser + tread should fall between 24" and 25". Not a code requirement.
Quick answers
A 9-foot rise takes 15 risers at 7-3/16 inches each, with 14 treads — a total run of 11 ft 8 in and a stringer of 14 ft 8-13/16 in.
There is always one fewer tread than riser, because the top landing is the last riser's destination and not a tread.
The IRC 2021 maximum riser is 7-3/4 inches and the minimum tread is 10 inches, but Michigan and Pennsylvania amend both — check your local code before cutting stringers.
Riser count is total rise divided by roughly 7 inches, rounded to a whole number. Divide the rise by that count to get the actual riser height, which is almost never a round number.
The comfort rule is 2 × riser + tread between 24 and 25 inches. A 7-3/16 inch riser with a 10-inch tread gives 24-3/8 inches, comfortably inside it.
FAQ
How do I calculate riser height?
Divide the total rise by about 7 inches to get a whole number of risers, then divide the total rise by that count. A 108-inch rise gives 15 risers at 7.2 inches each. Every riser in a flight must match within 3/8 inch.
How many stairs for an 8-foot ceiling?
An 8-foot floor-to-floor rise is usually 96 inches plus the floor structure, so 105 to 110 inches in practice. At 105 inches that is 15 risers of exactly 7 inches; at 108 inches it is 15 risers of 7-3/16 inches.
What is the maximum riser height by code?
7-3/4 inches under IRC 2021 §R311.7.5.1. Michigan and Pennsylvania allow 8-1/4 inches. A riser exactly at the maximum is legal but leaves no room for finish flooring, which is worth knowing before you cut.
How do I calculate stringer length?
It is the hypotenuse of the total rise and the total run: √(rise² + run²). For a 108-inch rise and a 140-inch run that is 176.8 inches, or 14 ft 8-13/16 in. Order the next standard length up.
What is the minimum tread depth?
10 inches nosing-to-nosing under IRC 2021, or 11 inches where there is no nosing. Michigan and Pennsylvania allow 9 inches. Deeper treads are always safer, and the trade-off is a longer total run.
What is the 2R+T rule?
A carpentry comfort check, not a code requirement: twice the riser plus the tread should land between 24 and 25 inches. Stairs that satisfy code but fail this rule tend to feel steep or stretched underfoot.