How many steps do I need?

How stair math works

Every stair starts with one number: the total rise, the height from finished floor to finished floor. Divide it by the tallest riser you are allowed, round up, and you have the number of risers. A 108-inch rise divided by 7¾ is 13.9, so you build 14 risers of 7.71 inches each. Every riser must be the same height — the code allows only ⅜ in of difference between the tallest and shortest — because a single odd step is what trips people.

Treads are always one fewer than risers, since the top step is the upper floor. Fourteen risers means thirteen treads, and at 10½ inches each the stair runs 136.5 inches, about 11 feet 4 inches. Make sure you have that much floor in front of the bottom step before you commit.

Stringer length and boards

The stringer is the hypotenuse of the rise and the run: the square root of 108² plus 136.5², or about 14.5 feet. Stringers are cut from 2x12 lumber, and you need a board longer than the stringer to leave room for the plumb and level cuts at each end, so this calculator adds a foot and rounds up to the next stock length — 16 feet here.

The comfort rule

Builders check a layout with one more formula: two risers plus one tread should land between 24 and 25 inches. At 7.71 and 10.5 that is 25.9 — slightly steep but within code. If there is room, a 7¼-inch riser with an 11-inch tread feels noticeably easier to climb.

A worked example: deck stairs

A deck 30 inches above a patio is a common job. At a 7¾-inch maximum riser, 30 ÷ 7.75 = 3.9, so you build 4 risers of 7.50 inches and 3 treads. At 10½ inches each the stair runs 31.5 inches, about 2.6 feet, and each stringer is about 3.6 feet long, so an 8-foot 2x12 is plenty.

For a 36-inch-wide stair with stringers 18 inches apart, you need three stringers. If you go wider, add one stringer for every 16 to 18 inches. Treads for deck stairs are often two 2x6 boards side by side (11 inches), or the same decking as the deck itself.

The bottom of the stair needs a solid landing: a concrete pad or compacted gravel at least as wide as the stair, so the stringers do not sit on soil and rot.

The basic code numbers

These are the common residential limits from the International Residential Code (IRC), which most US jurisdictions use. Your local code is what counts, so check it before building.

Mistakes that make stairs dangerous

• Measuring the rise from the wrong place. Measure from the finished surface at the bottom to the finished surface at the top. Adding flooring or a pad later changes the first or last step and breaks the ⅜-inch rule.
• Forgetting the tread thickness at the bottom. When you cut a stringer, the bottom riser has to be shortened by the thickness of one tread, or the first step ends up taller than the rest.
• Undersized stringers. A notched 2x12 leaves only a few inches of wood. Keep at least 3½ to 5 inches of solid material below the notches, depending on your code.
• Skipping the handrail. Four risers or more usually require one, and it is the cheapest safety item on the job.