Stair Calculator

How to use the stair calculator

Everything starts with one measurement, and it is the one most often taken wrongly. Total rise is finished floor to finished floor: from the surface you will walk on downstairs to the surface you will walk on upstairs. If either floor covering is not down yet, add its thickness now rather than discovering it later.

That number is not negotiable, and it is why the calculator solves for risers rather than letting you choose the riser height directly. A flight has to arrive exactly at the upper floor, so the rise divides into a whole number of equal risers and the riser height is whatever that division produces.

The target riser height nudges the division rather than setting the answer. Ask for 7 1/2 inches on a 108 inch rise and you get 14 risers at 7.714 inches, because 14.4 rounds to 14. Ask for 7 inches and you get 15 risers at 7.2 inches instead. The rise never changed; only how finely you sliced it.

Tread depth is the other half of the geometry and it behaves quite differently, because it is a free choice within limits rather than a division. Deeper treads make an easier stair and a longer one. At 10 inch treads that 108 inch rise consumes 130 inches of floor; at 11 inch treads it consumes 143.

Note that treads always come out one fewer than risers. The upper floor itself is the last tread, so a 14 riser flight has 13 treads. Getting that backwards is the classic way to end up with a stair one full step too long for the opening it has to fit.

The stringer length is straight Pythagoras on the total rise and the total run, and it is what you take to the lumber yard. A 108 inch rise with a 130 inch run gives 169 inches, a little over 14 feet, so the stock has to be longer than that before you have cut anything or allowed for how the stringer meets the floor at either end.

The IRC limits, and who they actually bind

Two figures do most of the work in residential stair code. Under IRC R311.7.5.1 the maximum riser height is 7 3/4 inches, and under R311.7.5.2 the minimum tread depth is 10 inches. Between them they set how steep a stair in a dwelling is allowed to be.

A third rule in R311.7.5.1 is the one that catches real builds. The greatest riser height within a flight may not exceed the smallest by more than 3/8 inch. That is a uniformity requirement, and it is why this calculator divides the rise into equal risers instead of letting you pick a round riser height and stuff the remainder into the last step.

The important caveat is that the IRC is a model code, and what binds you is whatever your jurisdiction has adopted and amended. The differences are not cosmetic: Michigan Administrative Code R 408.30519 permits a maximum riser of 8 1/4 inches and a minimum tread depth of 9 inches, which is a materially steeper stair than the model code allows.

So treat the pass and fail flags here as a first filter. A flight that fails the model limits is very unlikely to pass anywhere. A flight that passes them still has to satisfy the code your building department enforces, along with the separate requirements for stairway width, headroom, handrails, guards and landings that this page does not attempt to quote.

The rules of thumb that are not code

Two old carpentry formulas circulate alongside the code figures and are regularly mistaken for them. One says rise plus run should land near 17 to 18 inches. The other says twice the rise plus the run should land near 24 to 25 inches. Neither appears in the IRC, and neither is enforceable.

They are still useful, because they encode something the code limits do not: comfort. A stair can satisfy every dimensional requirement and still feel wrong to climb, usually because the tread is generous while the riser is short, or the reverse. The rules of thumb are a rough measure of whether the two are in proportion.

Where the rules of thumb earn their keep is on the stairs the code barely governs. A steep utility stair to a basement or a shallow flight of exterior steps can meet the dimensional limits and still be unpleasant, and running the two sums is a fast way to notice that before the stringers are cut.

The formula, worked line by line

A stair is a division problem with one hard constraint: the flight must arrive exactly at the upper floor. That is why you cannot simply choose a riser height. You choose a target, the rise divides into the nearest whole number of risers, and the actual riser height is whatever that division gives back.

Doing it that way makes the risers equal by construction, which is not a nicety. IRC R311.7.5.1 caps the spread between the tallest and shortest riser in a flight at 3/8 inch, and equal risers are the only way to be certain of clearing that with room to spare.

The rest follows. Treads are one fewer than risers, because the upper floor is the final tread. Multiply the treads by the tread depth for the total run, and the stringer is the hypotenuse of the triangle formed by the total rise and the total run.

risers = total rise ÷ target riser height, rounded to the NEAREST whole number
riser height = total rise ÷ risers   [exact, no remainder]
treads = risers − 1
total run = treads × tread depth
stringer length = √(total rise² + total run²)
code check: riser height ≤ 7.75 in  AND  tread depth ≥ 10 in

Rounding to the nearest whole riser rather than always up is the right call, and it can go either way. On a 108 inch rise a 7 1/2 inch target rounds down to 14 risers and produces a slightly taller riser than you asked for. Ask for 7 inches on the same rise and it rounds down to 15, giving 7.2 inches.

That is why the tool also reports the fewest risers that keep the flight legal. On a 108 inch rise that is 14, because 108 divided by 7.75 is 13.94 and you cannot have a fraction of a riser. Push the same target onto a 130 inch rise and the legal floor rises to 17.

Finally, remember what this page deliberately does not do. It checks two dimensions against two model code limits. Stairway width, headroom, handrail height and graspability, guard heights, landing sizes and nosing projection are all separate requirements in the same part of the code, and they are the reason a stair passes or fails an inspection just as often as rise and run.

Questions people ask