Stair Stringer Calculator
Enter the total rise from finished floor to finished floor and this works out how many risers you need, how tall each one lands, the total run the stairs will take up, and the diagonal length of the stringer so you can buy the right stock. Riser height and tread depth are checked against the limits US residential code sets.
Results
How a stringer is laid out
Everything follows from one measurement: the total rise from the finished surface at the bottom to the finished surface at the top. Not subfloor to subfloor — if tile is going down at the bottom and hardwood at the top, those thicknesses change the rise and therefore every riser in the flight.
- Divide the total rise by a target riser height — around 7 to 7.5 inches is comfortable — and round to the nearest whole number. That is the riser count.
- Divide the total rise by that count to get the actual riser height. It will rarely be a round number, and that is fine; what matters is that every riser is identical.
- Treads are always one fewer than risers, because the top riser lands on the floor above rather than on a tread.
- Total run is the tread count times the tread run.
- Stringer length is the diagonal:
√(total rise² + total run²).
An 8-foot basement stair makes the arithmetic concrete. A 96 inch rise at a 7.5 inch target gives 12.8, which rounds to 13 risers at 96 ÷ 13 = 7.38 inches each. That leaves 12 treads, and at a 10 inch run the stairs eat 120 inches — 10 feet — of floor. The stringer is √(96² + 120²) = 153.7 inches, so a 14-foot 2×12 is the stock to buy.
The numbers code holds you to
| Dimension | Limit |
|---|---|
| Maximum riser height | 7 3/4 in |
| Minimum tread depth | 10 in |
| Maximum variation between risers in a flight | 3/8 in |
| Maximum variation between treads in a flight | 3/8 in |
| Minimum headroom | 6 ft 8 in |
| Minimum stair width | 36 in |
| Maximum vertical rise between landings | 12 ft 7 in |
The 3/8 inch variation rule is the one that catches people. It is why the rise is divided evenly rather than cut at a round 7 1/2 inches with whatever is left over at the bottom — a short bottom step is the classic trip hazard and it fails inspection. Local amendments exist and commercial stairs are stricter, so confirm before you cut.
The other rule worth knowing is the informal one: 2 × riser + tread should land between 24 and 25 inches. It comes from stride length rather than from code, and stairs that miss it feel wrong even when every code number checks out. A 7.38 inch riser with a 10 inch tread gives 24.77 — comfortable.
Dropping the stringer
This is the step that ruins first attempts. Once the stringer is cut, the bottom riser is taller than all the others by exactly the thickness of the tread material, because the treads sit on the horizontal cuts everywhere except at the bottom, where the stringer sits directly on the slab or footing.
The fix is to cut the bottom of the stringer down by one tread thickness before you install it — "dropping the stringer". With 1 inch nominal treads that is 3/4 inch off the bottom. Skip it and the bottom step is 3/4 inch taller than the rest, which is twice the 3/8 inch variation code allows.
The same logic runs at the top: if the top tread is the finished floor above, the top riser is already correct. If a tread is being fitted at the top, the framing has to account for it.
How many stringers, and what stock
- Two stringers carry a 36 inch stair only with 2× treads, which are stiff enough to span it. With 5/4 decking or 1× treads the middle bounces.
- Three stringers is the standard for a 36 inch residential stair, giving roughly 16 inch spacing — the same interval joists use, for the same reason.
- Four stringers for stairs 48 inches wide, for commercial traffic, or wherever the treads are thin.
- Stock is nearly always 2×12. After the notches are cut, what remains behind them must be at least 5 inches of solid wood, and a 2×10 does not leave that once a 7.5 inch riser and a 10 inch tread are cut out of it.
Buy the stock a size longer than the diagonal, not equal to it. The plumb cut at the top and the seat cut at the bottom both consume length, and a stringer that comes up an inch short is firewood.
Frequently asked questions
How do I calculate stair stringers?
Measure the total rise from finished floor to finished floor, divide it by a target riser height of about 7.5 inches, and round to the nearest whole number to get the riser count. Divide the total rise by that count for the exact riser height. Treads are always one fewer than risers, and the total run is the tread count times the tread depth. The stringer itself is the diagonal, √(rise² + run²).
What is the maximum riser height for stairs?
US residential code (IRC R311.7) caps the riser at 7 3/4 inches, and requires that no riser in a flight differs from another by more than 3/8 inch. Commercial and public stairs are held to tighter limits, and some local jurisdictions amend the residential figure, so confirm before cutting.
What is the minimum tread depth?
Ten inches, measured from the face of one riser to the face of the next — the nosing overhang does not count toward it. Nosing is separately required to project between 3/4 and 1 1/4 inches where the tread depth is less than 11 inches.
How long a board do I need for stair stringers?
Take the diagonal, √(total rise² + total run²), and buy the next stock length up. A 96 inch rise with a 120 inch run gives a 153.7 inch diagonal, which is 12 ft 9.7 in — so a 14 ft 2×12, not a 12 ft one. The plumb cut at the top and the seat cut at the bottom both use up length.
What does dropping the stringer mean?
It means cutting the bottom of the stringer down by one tread thickness before installing it. Treads sit on top of the horizontal cuts, so without the drop the bottom step ends up taller than every other one by exactly that thickness — usually 3/4 inch, which is twice the variation code permits.
How many stringers do I need?
Three for a standard 36 inch wide residential stair, which puts them about 16 inches apart. Two is only enough if the treads are 2× material stiff enough to span 36 inches without flexing. Go to four at 48 inches wide, for commercial traffic, or when the treads are thin.
Why are stair stringers cut from 2x12?
Because of what is left after the notches. Code requires at least 5 inches of solid wood behind the cuts, and taking a 7.5 inch riser and a 10 inch tread out of a 2×10 does not leave that much. A 2×12 does, which is why it is effectively the only stock used for cut stringers.