Stair Calculator

The method, in the order you actually do it

Stairs are laid out from the total rise and nothing else. You do not choose the riser height; you choose a target and then let the arithmetic land on the real number.

1. Measure the total rise — finished floor to finished floor. This is where most errors start, because people measure subfloor to subfloor and then someone lays ¾ in of hardwood at the top and ⅜ in of tile at the bottom, and every riser is now wrong. 2. Divide by your target riser, usually 7 inches. 108 ÷ 7 = 15.43. 3. Round to a whole number of risers. 15. You cannot have four tenths of a step. 4. Divide the total rise by that whole number to get the actual riser height. 108 ÷ 15 = 7.2 inches. That is your riser, and every single one is cut to it. 5. Treads = risers − 1. 6. Total run = treads × tread depth. 7. Stringer length = √(total rise² + total run²) — it is just the hypotenuse.

A worked example

A 108 in floor-to-floor rise with 10½ in treads.

• Risers: 108 ÷ 7 = 15.43, round to 15
• Riser height: 108 ÷ 15 = 7.2 in
• Treads: 15 − 1 = 14
• Total run: 14 × 10.5 = 147 in, or 12 ft 3 in of floor space
• Stringer: √(108² + 147²) = √(11,664 + 21,609) = √33,273 = 182.4 in, about 15 ft 3 in
• Angle: arctan(108 ÷ 147) = 36.3°

Check it: riser 7.2 in is under 7¾, tread 10.5 in is over 10, 2R + T = 24.9 in which sits inside the 24–25 band. This flight is legal and it walks well. Note the total run — 12 ft 3 in is a lot of floor, and it is the number that most often forces a redesign or a landing.

Why the treads are always one fewer than the risers

This trips up almost everyone the first time, and it is worth seeing clearly.

Every step up is a riser. The last riser lands you on the upper floor — and the upper floor is the surface you step onto, so it is not a tread you have to build. Fifteen risers means fourteen treads plus the floor at the top.

If your flight lands on a landing rather than a floor, the same rule holds: the landing is the last surface, so it counts as a tread you do not cut. And a stair with a landing part-way is two flights, each calculated separately — but both must use the same riser height, which means you work out the riser off the total rise first and then decide where the landing falls.

Equal risers, within ⅜ of an inch

This is the rule inspectors check first, and it is the one that matters most for safety.

Across an entire flight, the difference between the tallest and shortest riser must not exceed ⅜ inch, and the same tolerance applies to tread depths. Not ⅜ in from the average — ⅜ in between the largest and the smallest.

The reason is how people use stairs. After two or three steps your body stops looking and starts predicting: it has learned the rhythm and it swings your foot to where the next tread ought to be. A riser that is half an inch off breaks that prediction, and the foot arrives early or late. That is the mechanism behind a large share of household stair falls, and it is why an otherwise well-built stair with one odd step at the bottom is genuinely dangerous.

The classic way to create one is to forget the finish floor, or to forget the tread thickness cut at the bottom of the stringer. When you notch a stringer, the bottom riser ends up one tread thickness too tall unless you trim the stringer's foot by exactly that amount. Cut it, check it, and measure every riser once the treads are down.

The comfort rules

Three old rules of thumb, all describing the same relationship between how far your foot travels forward and how far it travels up:

• 2 × riser + tread = 24 to 25 in. The most widely used, and the one that fits normal walking stride.
• Riser + tread = 17 to 18 in.
• Riser × tread = 71 to 75.

A stair that satisfies all three feels effortless. One that satisfies the code but violates all three — say a 7¾ in riser with a 10 in tread, giving 25.5 — is legal and tiring. Comfortable flights land between about 30 and 37 degrees.

Headroom and the rest of the assembly

Headroom is measured plumb from the nosing line to whatever is above it, and the minimum is 80 inches for the whole length of the flight. It is the constraint that most often kills a basement stair layout, because the floor opening above is fixed and lengthening the run to reduce the angle also moves the nosing line forward under the header.

Beyond the geometry: handrail height is typically 34 to 38 inches above the nosing line, guards on open sides are 36 inches residential, and the 4-inch sphere rule governs baluster spacing. Cut one stringer, dry-fit it against the actual rise before you use it as a pattern, and measure your risers after the treads go on rather than before.