Nails & Numbers

Home › Structural › Stair Construction Calculator

Stair Construction Calculator

Source: IRC R311.7 · riser R311.7.5.1 · tread R311.7.5.2

Enter the floor-to-floor rise and this lays out the flight: how many risers, how tall each one is, the total run and the stringer length. Every result is checked against IRC R311.7 — and when a number fails, the page tells you which code section it fails and why.

Stair rise & run calculator

in
in
in
in

Checked against IRC R311.7: riser ≤ 7 3/4 in (R311.7.5.1), tread ≥ 10 in (R311.7.5.2), width ≥ 36 in (R311.7.1), flight rise ≤ 147 in (R311.7.3).

Worked example

A basement stair with 9 ft floor-to-floor — 108 in of total rise — and a 10½ in tread.

  1. Find the riser count. 108 ÷ 7.75 = 13.9, and you cannot round down without breaking the maximum, so it goes up to 14 risers.
  2. Divide the rise evenly. 108 ÷ 14 = 7.714 in, which is 7 11/16 in per riser. It has to be even: R311.7.5.1 allows only 3/8 in of variation across the whole flight.
  3. Count the treads. 14 risers give 13 treads — the top riser lands on the floor above, so there is always one fewer tread than riser.
  4. Total run. 13 × 10.5 = 11 ft 4.5 in. This is the number that decides whether the stair actually fits the room.
  5. Stringer. √(108² + 136.5²) = 14 ft 6.06 in along the slope, before you cut the notches or add a landing.

The check most people skip is the last one: 2 × 7.714 + 10.5 = 25.93 in, above the 24–25 in comfort range. The flight is code-legal but will feel long and shallow. Dropping the tread to 10 in brings it to 25.43 in and saves 6½ in of run.

The formula

Stairs are not a table lookup — the geometry is arithmetic, constrained at both ends by the code. The whole layout falls out of the total rise:

n = ⌈R / 7.75⌉    r = R / n    T = n − 1    Run = T × d    S = √(R² + Run²)
R
total rise, finished floor to finished floor, in
n
number of risers — always rounded up, never down
r
riser height, in — must be ≤ 7.75 and uniform within 3/8 in
T
number of treads = n − 1, because the top riser lands on the floor above
d
tread depth, in — must be ≥ 10
Run
total horizontal run, in — what has to fit the room
S
stringer length along the slope, in

The rounding direction is the part that trips people. Dividing by the 7.75 in maximum gives a fractional riser count, and rounding it down makes each riser taller than the code allows. Always round up: more risers, each one shorter.

The code limits this checks against

Every dimension above is tested against IRC Section R311.7, “Stairways.” These are the numbers, with the section that sets each one:

R311.7.5.1 Risers — riser height not more than 7¾ in, measured vertically between the leading edges of adjacent treads. The greatest riser in a flight may not exceed the smallest by more than ⅜ in. Risers must be vertical or sloped no more than 30° from vertical. At open risers, any opening more than 30 in above the floor or grade below must not pass a 4 in sphere.

R311.7.5.2 Treads — tread depth not less than 10 in, measured horizontally between the foremost projections of adjacent treads. Same ⅜ in uniformity limit. Winder treads must hold 10 in at the walkline (R311.7.5.2.1).

R311.7.5.3 Nosings — where risers are solid, a nosing of not less than ¾ in and not more than 1¼ in. No nosing is required where the tread is at least 11 in deep. Radius of curvature not more than 9/16 in, bevel not more than ½ in.

R311.7.1 Width — not less than 36 in clear above the handrail height and below the required headroom. With a handrail on one side the clear width at and below handrail height may be 31½ in, and 27 in with handrails on both sides.

R311.7.2 Headroom — not less than 6 ft 8 in, measured vertically from the sloped line joining the tread nosings.

R311.7.3 Vertical rise — a single flight may not rise more than 147 in between floors or landings. Past that, you need a landing.

R311.7.8 Handrails — required on at least one side of any continuous run with four or more risers, at a height of 34 in to 38 in above the sloped plane of the nosings (R311.7.8.1).

Stair stringer calculator — laying out the cut

The stringer length above is the straight-line distance along the slope, which is what you measure to buy the stock. It is not the cut length. Two adjustments come off it: the bottom of the stringer is dropped by the thickness of one tread so the first step ends up the same height as the rest, and the top is notched to hang off the header or ledger. Get the tread-thickness drop wrong and every riser in the flight is fine except the first and last, which is exactly the failure R311.7.5.1's ⅜ in uniformity rule is written to catch.

For a deck stair, the same arithmetic applies but the total rise is measured from the deck surface to the finished grade or landing pad — not to the dirt. A concrete pad poured later changes the rise and therefore every riser in the flight.

Why the tread count is one less than the riser count

A flight of 14 risers has 13 treads. The top riser brings you level with the floor above, and that floor is the last tread — you do not build a separate one. This is the single most common arithmetic error in stair layout, and it shows up as a stair whose total run is one tread longer than the room allows.

Frequently asked questions

What is the maximum stair riser height?
7¾ in for stairs in a dwelling, per IRC R311.7.5.1. It is measured vertically between the leading edges of adjacent treads, and no riser in a flight may differ from any other by more than ⅜ in. Some jurisdictions amend this number, so confirm locally.
What is the minimum tread depth?
10 in under IRC R311.7.5.2, measured between the foremost projections of adjacent treads. At 11 in or more you no longer need a nosing projection.
How many stairs do I need for 9 feet?
108 in of rise needs 14 risers at 7 11/16 in each, giving 13 treads. Fourteen is the smallest number that keeps every riser under the 7¾ in maximum — 13 risers would need 8.3 in each, which fails.
How do I calculate stringer length?
It is the hypotenuse: √(total rise² + total run²). For 108 in of rise and 136.5 in of run that is 174.06 in, or 14 ft 6 in. Buy longer stock than that — the notching and the bottom drop eat into it.
Do I need a handrail?
Yes on at least one side of any continuous run with four or more risers (R311.7.8), mounted 34 in to 38 in above the sloped plane joining the nosings (R311.7.8.1). A guard is a separate requirement — see the deck railing page.
Is there a limit on how tall a flight can be?
Yes. R311.7.3 caps a single flight at 147 in of vertical rise between floors or landings. Anything taller has to be broken with a landing.
What is the 2R + T rule?
A carpenters' comfort check, not code: twice the riser plus the tread should land between 24 and 25 in. A stair can pass every code limit and still feel wrong; this is the number that predicts it.

Check these numbers yourself

Figures on this page last checked against the source documents on 2026-09-05. Codes are amended locally; confirm against the edition your jurisdiction enforces.

Related calculators

Estimates only. This calculator applies the prescriptive limits in IRC R311.7 for planning purposes. It is not a construction document and does not replace your local building department. Many jurisdictions amend riser and tread dimensions — Rapid City, for one, amends R311.7.5 outright — and stairs are the most common source of injury in a home. Confirm every dimension against the code edition and local amendments your building department enforces before you cut a stringer.