How to calculate stair stringers
The measurements a stringer needs, in the order you work them out: riser count, riser height, tread depth, total run, and the stringer length, each held to IRC R311.7. Worked from one real total rise.
Updated
Skip the arithmetic
The stair stringer calculator does every step below from a single total-rise measurement and checks it against code.
Watch the method in under a minute
The short version
To calculate a stair stringer, measure the total rise floor to floor, divide it by a comfortable riser height of about 7 to 7-1/2 inches to get the riser count, then divide the rise by that count for the exact riser height. The treads are one fewer than the risers. Multiply the treads by the tread depth (10 inches is the code minimum) for the total run, and the stringer length is the diagonal: the square root of the rise squared plus the run squared.
Step by step, worked from a 9 ft rise
A 108 in total rise, floor to floor. Every number below is computed by the same code the app runs, not typed in.
- 01
Measure the total rise
Measure straight up from the lower finished floor to the upper finished floor. That is your total rise. Here it is 108 in. Get this wrong and every riser is wrong, so measure it, do not assume the framing.
- 02
Find the riser count
Divide the total rise by a comfortable riser height, around 7-1/2 in, and round to a whole number. 108 divided by 7.5 is 14.4, which rounds to 14 risers. Then check the code cap: if that count would leave any riser over 7-3/4 in, add one more riser to bring it back under. Here 14 risers is 7-11/16 in each, already under, so it stands.
- 03
Get the exact riser height
Divide the total rise by the riser count for the real riser height. It rarely lands on a clean fraction, and every riser has to be within 3/8 in of the others (R311.7.5.1), which is why you carry the exact number, not a rounded one.
- 04
Set the tread depth and total run
Tread depth is 10 in minimum (R311.7.5.2). The number of treads is one fewer than the risers, because the top riser lands on the floor above, not on a tread. Treads times depth is the total run, the horizontal distance the stair covers.
- 05
Get the stringer length
The stringer is the diagonal of the rise-and-run triangle: the square root of the total rise squared plus the total run squared. That is the board length before you notch it, plus a little for the cuts.
For a 108 in rise
| Risers | 14 |
| Riser height | 7-11/16 in |
| Treads | 13 |
| Tread depth | 10 in |
| Total run | 10 ft 10 in |
| Stringer length | 14 ft 1 in |
The code the numbers answer to
IRC R311.7 sets the limits this math stays inside: risers no taller than 7-3/4 in, treads no shallower than 10 in, and no more than 3/8 in of variation between the tallest and shortest riser or the deepest and shallowest tread. The 3/8 in rule is the one that trips people, because it means you cannot fudge a riser to make the layout come out even.
Common questions
- How many stringers does a stair need?
- Two at the sides carry a normal residential stair, with a third down the middle once the treads span more than about 36 in or the treads are thin. Cut one stringer, check its fit, then use it as the template for the rest so every notch lines up.
- Why is there one fewer tread than risers?
- Because the top riser brings you level with the upper floor, and you step onto the floor itself, not onto a tread. A 14-riser stair has 13 treads. Miscounting this is the most common stringer layout mistake.
- What is the 7-11 rule for stairs?
- A rule of thumb for a comfortable stair: a riser near 7 in and a tread near 11 in. It is a target, not the code limit. The code caps the riser at 7-3/4 in and floors the tread at 10 in, and this math keeps you inside both.
- How do I lay the stringer out on the board?
- Set a framing square to the riser height on the tongue and the tread depth on the blade, and step it down the board, marking each notch. The app prints the same layout with a running dimension to each step so you are not re-measuring a square every time.
Cut it from a plan, not a guess
The app derives the whole stair from one rise, checks it against IRC R311.7, and prints the stringer drawn on the board with every notch dimensioned.
See also