How many steps, and how long a stringer?

How do I calculate stairs?

Measure the total rise from the ground or lower floor to the top of the deck or upper floor. Divide it by the tallest riser allowed — 7¾ inches under the IRC — and round up to get the number of risers; then divide the rise by that number for the exact riser height. For a 36 inch rise: 36 ÷ 7.75 = 4.6, so 5 risers of 7.2 inches (about 7 3/16).

How many treads do I need?

One fewer than the risers, because the deck or upper floor is the top step. Five risers need four treads; at 10½ inches each, the stairs run 42 inches out from the deck.

How long should a stair stringer be?

The stringer runs along the slope: the square root of rise² + run². For a 36 inch rise and a 42 inch run, that is √(36² + 42²) = 55.3 inches, so a 2 × 12 cut from an 8 ft board, with length to spare for the top and bottom cuts.

What are the code requirements for stairs?

The International Residential Code, used by most US towns, limits risers to 7¾ inches and asks for treads at least 10 inches deep, with all risers in a flight within ⅜ inch of each other. Local codes can differ, so check with your building department.

How do I lay out a stringer?

Set a framing square on the 2 × 12 with the riser height on one arm and the tread depth on the other, trace, and slide it along for each step. The table in the result gives the height and run of every step from the bottom, so you can check each mark with a tape.

How do I figure the stairs for a deck that is 8 feet above the ground?

The rise is 96 inches. 96 ÷ 7.75 = 12.39, which rounds up to 13 risers, each 7.38 inches high. There are 12 treads, and with 10 inch treads the stairs run 120 inches (10.0 feet) out from the deck at an angle of 38.7°.

Why do the steps not come out at exactly 7¾ inches?

Because the number of risers must be a whole number. The rise is divided evenly among them, so the riser is always at or below the limit you enter. Rounding the riser to a neat number on the saw and leaving the last one to absorb the difference would break the rule that risers in a flight are within ⅜ inch of each other.

How the numbers are worked out

The number of risers is the total rise divided by the tallest riser you allow, rounded up. The riser height is the rise divided by that number, so every riser is the same. The top step is the deck or floor itself, so there is one tread fewer than risers. The total run is the number of treads times the tread depth. The stringer, the board that carries the steps, follows the hypotenuse of the triangle formed by the total rise and the total run, and the angle is the arctangent of rise ÷ run. The length is measured along the long edge, so the board you buy must be longer than the figure to leave room for the cuts at the top and bottom.

Worked example: 8 feet of rise

With a 96 inch rise, a 7¾ inch maximum riser and a 10 inch tread, the stairs have 13 risers of 7.38 inches and 12 treads. The run is 120 inches, the stringer is √(96² + 120²) = 153.7 inches (12.8 feet) and the angle is 38.7°. That means a 2 × 12 board of 14 feet, since the cuts at the top and bottom use up part of the length. With an 11 inch tread the run grows to 11.0 feet and the angle falls to 36.0°, a gentler stair that needs more room in the yard. A shorter case, a 36 inch rise with 10½ inch treads, gives 5 risers of 7.20 inches and a 42 inch run.

Other code points to check

The riser and tread limits are only part of the stair provisions in the International Residential Code, section R311.7. The same section asks for a minimum clear width of 36 inches, a minimum headroom of 6 feet 8 inches, and a handrail on stairs with four or more risers. Landings, guards at open sides and the treatment of the top riser vary with the code edition and your local amendments, so use this calculator for the geometry and your building department for the requirements.

Common mistakes

Measuring the rise to the wrong surface is the most common error. The rise runs from the finished surface at the bottom to the finished surface at the top, and the thickness of treads and decking changes the first and last risers, so cut the first and the last riser to allow for it, keeping every riser within ⅜ inch of the others. The second is counting treads equal to risers; the top step is the floor. Third, soft ground: set the bottom of the stair on a firm, level pad rather than directly on soil, so the first riser stays the height you cut it.

Sources: 2021 International Residential Code, section R311.7 (stairways), including R311.7.5 (riser height at most 7¾ inches, tread depth at least 10 inches, ⅜ inch variation in a flight); geometry as in the Pythagorean theorem. Related: slope calculator, Pythagorean theorem calculator and deck calculator.