How to calculate stairs

1. The five words you need: rise, run, riser, tread, stringer

The total rise is the vertical distance from one finished floor to the next — not just the height of the wall, but floor surface to floor surface, including the thickness of the upper floor. The total run is how far the flight reaches horizontally. A riser is the vertical face of a single step and its height is the most important comfort dimension; a tread (its depth is called the going) is the horizontal part you stand on. The stringer is the sawtooth-cut board running up each side that carries the treads and risers. Because the rise is vertical and the run is horizontal, the stringer is the hypotenuse of a right triangle, which is why the whole calculation comes down to division and the Pythagorean theorem.

2. Step one — turn your rise into equal risers

Stairs must use equal risers — your foot learns the rhythm of the first step and expects every step after it to match, so an odd riser at the top or bottom is a genuine trip hazard. To find how many risers you need, divide the total rise by a comfortable target riser height and round to the nearest whole number. Around 7 inches (175 mm) is the sweet spot for most homes. For a typical 9-foot floor-to-floor height that is 108 ÷ 7 ≈ 15.4, which rounds to 15 risers.

Now reverse it: divide the total rise by that whole number of risers to get the actual riser height. 108 ÷ 15 = 7.2 inches. Every riser in the flight is built to that figure, so they all match exactly. If the result feels too steep, add one riser and recompute (108 ÷ 16 = 6.75 inches) for a gentler climb; if it feels too shallow, drop one. This single rounding choice is the most consequential decision in the whole layout.

3. Step two — set the run from the tread depth

A flight that lands flush on the upper floor always has one fewer tread than it has risers, because the top “step” is the finished floor itself. So 15 risers means 14 treads. The total run is simply the number of treads multiplied by the tread depth (going). With a generous 11-inch tread, 14 treads give a run of 14 × 11 = 154 inches — just under 13 feet of floor space, which is exactly why a comfortable staircase needs a surprising amount of room. If the run does not fit, a steeper flight with a deeper riser and a shallower tread shortens it, at the cost of comfort.

Tread depth is a comfort and safety dimension in its own right: too shallow and the ball of your foot overhangs the edge on the way down. A small overhang called the nosing lets the effective tread be a little deeper than the run each step consumes, but for laying out the stringer it is the going — the horizontal distance from one riser face to the next — that sets the run.

4. Step three — stringer length and stair angle

Once you have the total rise and the total run, the sloped stringer length is the hypotenuse: length = √(rise² + run²). For our 108-inch rise and 154-inch run that is √(108² + 154²) = √(11,664 + 23,716) = √35,380 ≈ 188 inches, or about 15 feet 8 inches of board before you account for the notch cuts, the bottom plumb cut and any connection at the top. The stair angle from horizontal is the arctangent of rise over run: arctan(108 ÷ 154) = arctan(0.701) ≈ 35°. Most comfortable domestic stairs land between roughly 30° and 37°, so 35° is normal; much above 37° starts to feel like a ladder, and much below 30° eats floor space.

This is the same rise-over-run triangle that governs roof slope — if you have ever worked out a roof, the maths will feel familiar. You can see it in action on the roof pitch calculator, which uses the identical √(rise² + run²) relationship to find rafter length.

5. The comfort rules: 17-inch, the 27 rule and the product rule

Carpenters have used a small family of comfort rules for centuries to check that a riser-and-tread pairing matches the natural human stride. The simplest is the 17-inch rule: one riser plus one tread should total about 17–18 inches. The 27 rule — a relaxed version of the seventeenth-century Blondel formula — says two risers plus one tread should fall in the 24–27 inch range (24–25 inches is the classic target). The product rule adds a third check: riser × tread should be roughly 72–75 square inches.

A 7-inch riser with an 11-inch tread comfortably passes the two stride rules — 7 + 11 = 18 and 2 × 7 + 11 = 25 — and sits just over the product range at 7 × 11 = 77, which tells you the tread is on the generous side rather than cramped. The calculator above shows your 2-riser + tread and your riser + tread so you can see at a glance which way to nudge the design. These are ergonomic rules of thumb, not the law — the enforceable maximum riser height and minimum tread depth come from your building code, covered next.

6. Reference table — common floor heights as a flight

Each common floor-to-floor rise worked into a flight using a 7 in target riser and an 11 in tread. Pure geometry — round to the calculator for an exact figure on your own rise.

For a rise that is not in the table, the stair calculator gives the exact riser count, height, run, stringer and angle in metric or imperial.

7. Headroom, landings, handrails and the building code

A safe staircase is more than rise and run. You need adequate headroom — the clear vertical height measured from the nosing line up to the ceiling or floor above — so taller people do not duck. Long flights need a landing to break the climb. Handrails, guards on open sides, and consistent nosings all matter for safety, and the maximum riser height, minimum tread depth, minimum headroom and minimum width are set by your local building codeand are real, enforceable numbers that vary by country and by whether the stair is in a home or a commercial building. This guide and the calculator help you lay out and check a flight geometrically and against the long-standing comfort rules; they do not replace the building code or a building inspector's sign-off. Confirm the required dimensions for your jurisdiction and occupancy before you cut a stringer. If you are weighing up whether to take it on at all, our guidance on carpentry tools and guides collects the related calculators in one place.

Common questions

How do I calculate how many stairs I need?

Divide your total floor-to-floor rise by a comfortable target riser height of about 7 in (175 mm) and round to the nearest whole number — that count is the number of risers. The actual riser height is then the total rise divided by that count, so the risers come out equal. A standard flight has one fewer tread than risers. For a 108-inch rise: 108 ÷ 7 ≈ 15.4 → 15 risers at 7.2 in each, with 14 treads.

What is the 27 rule for stairs?

The 27 rule is a comfort guideline that two riser heights plus one tread depth should fall within roughly 24–27 inches, matching an average adult stride. It is a relaxed form of Blondel's classic 24–25 inch rule. A 7-inch riser with an 11-inch tread gives 2 × 7 + 11 = 25 inches, comfortably inside the band.

What is the 17 inch rule for stairs?

The 17-inch rule says a single riser height plus a single tread depth should add up to about 17–18 inches. It is the quickest comfort check there is: a 7-inch riser with an 11-inch tread totals 18 inches, while a 7.5-inch riser with a 10-inch tread totals 17.5. Stairs that stray far from this range feel either cramped and steep or stretched and shallow.

How many stairs to get up 10 feet?

Ten feet is 120 inches. Using a 7-inch target riser, 120 ÷ 7 ≈ 17.1, so you would build 17 risers at an actual height of about 7.06 inches each, with 16 treads. Keep every riser equal — even a small variation between steps is a recognised trip hazard.