Stair Calculator

How stairs are sized

Stairs are built around two numbers: how far up you have to go, and how far forward you can afford to take it. The first is the total rise, measured from the top of the finished lower floor to the top of the finished upper floor. The second is the run, the horizontal distance the treads occupy.

The arithmetic is short. Divide the total rise by the riser height you want, round to a whole number, and that is how many risers you need. Divide the rise by that whole number again and you get the exact riser height, which will not be a round number. The number of treads is one fewer than the number of risers, because the upper floor serves as the top step. Multiply treads by tread depth to get the run.

Two rules keep a stair comfortable. The first is 2 x riser + tread = 24 to 25 inches, which balances a tall step against a short one. The second is consistency: every riser in a flight has to be the same height within 3/8 inch, because a single tall step is a trip hazard.

Worked example: an 8-foot 9-inch total rise

An addition with an 8-foot 9-inch floor-to-floor height, so the total rise is 105 inches.

• Risers: 105 divided by 7.5 = 14, exactly
• Riser height: 105 divided by 14 = 7.5 inches
• Treads: 14 minus 1 = 13 treads
• Run: 13 x 10 = 130 inches, or 10 feet 10 inches
• Stringer: the square root of 105 squared plus 130 squared = 167.1 inches, about 13 feet 11 inches
• Angle: 38.9 degrees

The comfort check passes, since 2 x 7.5 + 10 is 25 inches, right at the top of the range. The code checks pass too, with a 7.5-inch riser under the 7.75-inch maximum and a 10-inch tread sitting at the minimum.

Buy 16-foot stringer material rather than 14-foot. The calculation gives the length along the slope, but you also need extra at the top to notch into the rim and extra at the bottom for the bearing cut, so add 12 to 18 inches to whatever the formula returns.

Worked example: fitting stairs into a short run

Now the same 105-inch rise, but the space allows only 120 inches of horizontal run. Does a straight stair fit?

The shortest code-compliant straight stair is set by the maximum riser height of 7.75 inches. 105 divided by 7.75 is 13.55, so you need at least 14 risers. Fourteen risers means 13 treads, and at the minimum 10-inch tread that is a run of 130 inches.

130 inches does not fit in 120 inches. The gap is 10 inches, and there is no legal way to close it by shrinking the treads. Two options remain.

• Lower the rise. Dropping the upper floor by 10 inches is rarely possible, but a smaller change sometimes is.
• Turn the stair. Split the 14 risers into two flights of 7 with a 36-inch landing between them. Each flight has 6 treads at 10 inches, so each leg needs 60 inches of run plus the landing, and the whole stair fits an L-shaped footprint about 96 inches on each side.

The turn is the usual answer, and it is why so many basement and attic stairs are L-shaped. It costs a landing and a little extra framing, and it turns an impossible run into a comfortable one.

Code limits at a glance

These are the residential limits from the International Residential Code, which most US jurisdictions adopt. Commercial buildings follow the International Building Code, which is stricter in several places, and local amendments vary from town to town.

Two of these catch people out. Headroom is measured from the nosing of the tread, not from the floor, and it runs to the ceiling or the underside of the framing above. And the 3/8-inch riser rule applies across the whole flight, so a repair that replaces one tread with a thicker board can push a stair out of compliance on its own.

Stringer length, headroom and landings

The stringer is the sloped board the treads sit on, and its length is the diagonal of the rise and the run: the square root of rise squared plus run squared. For the 105-inch rise and 130-inch run above, that is 167 inches. Add 12 to 18 inches for the top and bottom cuts before you buy.

Use 2x12 stock for stringers at these dimensions. A 2x10 does not leave enough wood under the notch once you cut a 7.5-inch riser and a 10-inch tread out of it, and the board can split at the narrow point.

Headroom is the measurement people forget until the stair is built. You need 6 feet 8 inches from the nosing of any tread to the ceiling or the underside of the floor framing above it. On a basement stair that usually means the stair has to start further from the wall, or the floor opening has to be longer.

Landings go at the top and bottom of every stair, and they must be at least as wide as the stair itself. A single flight can rise up to 12 feet 7 inches before a landing is required in the middle, which is why most two-story houses get away with one straight run.

Lumber: how much you need

Here is the shopping list for the 105-inch rise stair, 36 inches wide, with 14 risers and 13 treads.

Three stringers for a 36-inch-wide stair, two for anything up to 30 inches. Treads at 36 inches each come out of 10-foot 2x10s with almost no waste, so buy four 10-foot boards or three 12-foot boards and keep the offcuts for blocking.

Two details save a rebuild. Cut the treads to length first and use one as a template for the notches, so every notch is identical. And shorten the bottom riser by the thickness of the tread material, because the first tread sits on top of that cut and the step would otherwise come out one tread thickness taller than the rest.

Common mistakes and how to avoid them

Six mistakes account for most stair problems.

• Measuring from the subfloor. The total rise is finished floor to finished floor. Hardwood, tile or a thick underlayment can add an inch or more, and that changes the riser height for every step.
• Forgetting the bottom riser adjustment. The first step lands on top of the tread material, so the bottom riser cut has to be shorter by the tread thickness. Skip it and the first step is short and the whole stair feels wrong.
• Letting the risers vary. The code allows 3/8 inch of variation across a flight, and that is the outside limit. A 1-inch difference is a trip hazard and the most common reason an inspector fails a stair.
• Ignoring headroom until the framing is up. Check it on paper, from the nosing to the underside of the floor above, before you cut anything.
• Cutting treads below 10 inches. Narrow treads are the usual way people try to squeeze a stair into a short run, and they are not allowed.
• Assuming the national code applies. Local amendments change limits, and some jurisdictions are stricter than the model code. Call the building department before you buy lumber.

Run the numbers through the calculator, then check them against the code your town enforces. The International Code Council publishes the model codes, the OSHA stairway standard covers stairs in workplaces and is a useful second reference, and the US Access Board sets the accessibility rules that apply to any stair the public uses.