Every stair calculation starts with two measurements: the total rise, from the finished floor below to the finished floor above, and the total run, the horizontal distance available for the stair. Everything else — the number of steps, the height of each riser, the depth of each tread, the angle of the stair, the length of the stringers — is derived from those two numbers and the rules that keep stairs safe and comfortable. This guide works through the derivation with a full example, states the code limits that govern real construction, and explains the layout of stringers, the part of the job where most errors are made.

The basic stair calculation, worked through

Measure the total rise first, from finished floor to finished floor — including the thickness of the finished flooring at both levels, because a stair built to subfloor measurements will be wrong by the flooring thickness at one end. Suppose the total rise is 105 inches (8 feet 9 inches). Choose a target riser height in the comfortable range, 7 to 7½ inches: 105 ÷ 7 = 15 exactly, so the stair has 15 risers of exactly 7 inches. If the rise had been 108 inches, 108 ÷ 7 = 15.43, which rounds to 15 risers of 7.2 inches, or 16 risers of 6.75 inches — either is legal and comfortable, and the choice depends on the available run.

Treads number one fewer than risers: 15 risers need 14 treads, because stepping onto the upper floor is the fifteenth rise. With a tread depth (going) of 11 inches, the total run is 14 × 11 = 154 inches (12 feet 10 inches). The stair angle is arctan(rise ÷ run) = arctan(105 ÷ 154) = arctan(0.682) ≈ 34.3 degrees — inside the comfortable 30° to 37° band for residential stairs. The stringer length is the hypotenuse: √(105² + 154²) = √(11,025 + 23,716) = √34,741 ≈ 186.4 inches, plus allowances for the top and bottom cuts. Every figure in the design follows from the two starting measurements and the chosen riser height; change the riser count and the run, angle, and stringer length all move together.

Comfort formulas: 2R + T and the angle

Two empirical formulas, developed from studies of gait, predict whether a stair feels comfortable. The first: two risers plus one tread should total 24 to 26 inches (610 to 660 mm) — the length of a natural stride on the flat, split between the vertical and horizontal components. A 7-inch riser with an 11-inch tread gives 25 inches, dead centre. A 7¾-inch riser with a 10-inch tread gives 25½ inches, also acceptable, but the steeper combination feels harder on the knees. The second: riser plus tread should total 17 to 18 inches (430 to 460 mm). Seven plus 11 is 18; 7¾ plus 10 is 17¾ — both pass.

Angle is the third check. Stairs below 30° feel shallow and consume excessive run; stairs above 37° feel ladder-like and are tiring and risky to descend. The comfortable band is 30° to 37°, and the 7/11 combination sits at about 32.5°. Ship’s ladders and alternating-tread devices run at 50° to 70° and are not stairs in the code sense — they are permitted only in narrow circumstances, and they demand handrails on both sides and a different gait. If your available run forces an angle above 37°, the honest options are a longer run, a landing with a turn, or a different stair type — not a steeper straight flight.

Code limits: risers, treads, headroom, and handrails

The widely adopted residential baseline (International Residential Code, subject to local amendments) sets: maximum riser height 7¾ inches; minimum tread depth 10 inches; maximum variation of ⅜ inch between the largest and smallest riser, and between the largest and smallest tread, within any flight; minimum headroom 6 feet 8 inches measured vertically from the nosing line; minimum stair width 36 inches; and handrails on at least one side where there are four or more risers, at 34 to 38 inches above the nosings, with a graspable profile. Guardrails are required on open sides where the drop exceeds 30 inches, with openings that will not pass a 4-inch sphere. Winder treads — the pie-shaped treads of a turning stair — have their own rules: at least 10 inches deep at the walk line (12 inches from the narrow side) and at least 6 inches at the narrow end.

Two code points are commonly missed. First, the variation limit applies to the finished stair, including flooring thickness: a stair whose risers are equal on the framing but differ after carpet is laid on the treads can violate it. Second, the nosing — the tread’s overhang past the riser — counts toward tread depth in some codes and not in others; where nosings are required, they project ¾ to 1¼ inches. Check the local amendment before building: some jurisdictions require 11-inch treads, some limit risers to 7 inches for certain occupancies, and commercial stairs follow the International Building Code, which differs in several figures.

Stringers: layout, cuts, and count

A cut stringer is laid out with a framing square: set one leg to the riser height and the other to the tread depth, clamp stair gauges at those marks, and step the square along the board, marking each riser and tread in turn. The critical adjustments are at the ends. The bottom riser is cut shorter by one tread thickness, because the first tread sits on top of the stringer’s lowest step and the finished first riser must equal the rest. The top of the stringer is cut to bear against the upper floor framing or to sit flush with the upper finished floor, depending on whether the stair is housed or open. A stringer laid out without the bottom adjustment produces a first step that is a full tread-thickness too tall — the most common cause of a first-step trip.

Stringer count: two stringers suffice for stairs up to about 36 inches wide in most residential construction, with a centre stringer added for wider stairs, for treads of thinner stock, or where deflection is a concern. Cut stringers remove material at every step, so the remaining section at the narrowest point — the throat — must be adequate: a 2×12 stringer leaves a throat of about 3½ inches after a 7-inch riser and 11-inch tread are cut, which is the minimum most codes and carpenters accept. Laminated or engineered stringers, and closed stringers with housed treads, carry more load and are worth considering for wide or heavily used stairs.

Landings, turns, and headroom

A flight should not run indefinitely: landings break long flights, provide rest, and allow direction changes. The code requires a landing at the top and bottom of each flight, at least as wide as the stair and at least 36 inches deep in the direction of travel. L-shaped and U-shaped stairs use landings to turn, and the landing counts as part of the run: a U-shaped stair returning on itself needs a landing as deep as the stair is wide, plus the width of both flights. Winder stairs turn without a landing, but their treads must meet the walk-line depth rule, and they are harder to navigate and to move furniture around — a landing turn is preferable wherever space allows.

Headroom is measured from a line through the tread nosings, vertically, to the ceiling or any obstruction above: the minimum is 6 feet 8 inches. Headroom failures happen where a stair passes under a floor edge or a beam, and they are expensive to fix after framing — check the headroom at the lowest point of the stair’s path, usually where it passes under the upper floor, before cutting anything. Spiral stairs have their own rules (minimum tread width 7½ inches at 12 inches from the narrow end, minimum diameter 5 feet for residential use in many codes) and are suitable only for limited access, not as a primary stair.

Frequently asked questions

How do I calculate the number of steps for a staircase?

Divide total rise by a comfortable riser height (7–7.5 inches) and round to a whole number of risers. Exact riser height = total rise ÷ riser count. Treads = risers − 1. Example: 105 inches ÷ 7 = 15 risers of 7 inches, 14 treads.

What is a comfortable riser height and tread depth?

Risers of 7 to 7.5 inches with treads of 10.5 to 11 inches suit most people. The comfort checks are 2R + T = 24–26 inches and R + T = 17–18 inches. Steeper combinations are legal to the code maxima but feel harder, especially descending.

What is the maximum riser height allowed by code?

7¾ inches under the International Residential Code baseline for residential stairs, with tread depth at least 10 inches and variation under ⅜ inch within a flight. Local amendments vary — confirm with your building department before constructing.

How long should a stair stringer be?

The stringer follows the hypotenuse: √(total rise² + total run²), plus end-cut allowances. For a 105-inch rise and 154-inch run, the sloped length is about 186 inches. Layout with a framing square, remembering to shorten the bottom riser by one tread thickness.

How much headroom do stairs need?

At least 6 feet 8 inches, measured vertically from the nosing line to the ceiling or obstruction above. Check the lowest point where the stair passes under the upper floor — headroom failures are costly to fix after framing.

Can I build stairs with different riser heights?

No — within a flight, riser heights must not vary by more than ⅜ inch under the code baseline, and comfort demands even tighter consistency. Uneven risers are a leading cause of stair falls, because the body calibrates its step to the first riser and trusts the rest to match.