Stair calculator

Risers, tread depth, total run, and stringer length from one total rise — with the IRC compliance check, the 3/8 in uniformity rule, and the riser-vs-tread off-by-one most calculators leave out.

01 How the math works

A stair is a right triangle laid on its side. The total rise is the vertical leg, the total run is the horizontal leg, and the stringer is the slope you cut the steps into. Everything starts from the total rise — the height from the finished lower floor to the finished upper floor — because that number has to divide into equal risers with none left over.

Pick a target riser near 7 in (178 mm) and the calculator rounds the rise into that many equal risers, then reports the height each one actually lands at. The tread count is one less than the riser count — the top tread is the upper floor itself, so it does a tread's job without being cut as one. Multiply the treads by the tread depth for the total run, and the stringer is the hypotenuse of rise and run.

02 Worked example

Take a straight flight with a total rise of 108 in (2.74 m) — the common floor-to-floor for 8 ft ceilings plus the floor structure — a 10 in (254 mm) tread depth, and a target riser of 7 in (178 mm).

Round 108 ÷ 7 and you get 15 risers, each landing at 108 ÷ 15 = 7.2 in (183 mm). Fifteen risers means 14 treads; at the 10 in depth the total run is 14 × 10 = 140 in, or 11.67 ft (3.56 m). The stringer is √(108² + 140²) = 176.82 in — 14.73 ft (4.49 m) — at a stair angle of about 37.6°.

Both checks pass: the 7.2 in riser is under the 7-3/4 in maximum and the 10 in tread meets the 10 in minimum, so the flight is IRC-compliant. The stringer comes off a 16 ft (4.88 m) board, with stock to spare for the end cuts.

03 When this calculator is wrong

The layout above is geometry on paper. What trips a real flight is usually not the arithmetic but where the finished surfaces end up and which steps get counted.

• Finished flooring can break the uniformity rule. The IRC lets the tallest riser in a flight exceed the shortest by no more than 3/8 in (9.5 mm) (R311.7.5.1). Cut the stringers to bare subfloor, then lay 3/4 in (19 mm) of tile on the bottom landing and the first riser drops 3/4 in — twice the tolerance, and a failed inspection. The 3/8 in limit is thinner than the flooring that usually causes the problem. Measure total rise finished floor to finished floor.
• Risers and treads are not the same count. A flight has one more riser than it has treads (R311.7.5). Divide the rise by 15 when there are 15 risers, not by the 14 treads — off by one step and every riser height is wrong at once.
• Tread depth is measured nosing to nosing. It's the horizontal distance between the front edges of adjacent treads, not the board width. Where the tread depth is under 11 in (279 mm) the IRC requires a nosing of 3/4 in to 1-1/4 in (19 to 32 mm) (R311.7.5.3); the nosing overhangs the riser below and does not add to the run.
• This is a straight flight only. Winders, a mid-flight landing, or a switchback break the single-stringer math — each straight segment has its own rise, run, and stringer, and the landing eats part of the total run. Lay those out segment by segment.

04 What to do with the result

Cut one stringer, set it in the actual opening, and check every riser with a level against the finished floor heights before you cut the second. A test stringer costs one board; a miscut pair costs two boards and an afternoon. Once it sits right, use it as the pattern and trace the rest from it rather than laying out each one fresh.

Buy the stringer stock long and cut it short. The per-foot premium on 16 and 20 ft lengths runs under 15% over 8 and 10 ft, and a stringer is the one board you never splice — a joint in a stringer is a hinge. So the 14.73 ft stringer above comes off a 16 ft stick, not a spliced pair of shorts. The exception is transport: a 16 ft 2×12 rides in few pickups without an overhang flag, and a stair that runs past a 20 ft stringer wants an intermediate landing to break the run rather than a special-order board.

05 Common questions

How do you calculate the number of stairs from a total rise?

Divide the total rise by a target riser near 7 in (178 mm) and round to the nearest whole number — that's the riser count. Then divide the rise by that count for the actual riser height. A 108 in rise gives 15 risers at 7.2 in each.

How many treads are there for a given number of risers?

One fewer. A flight has one more riser than treads, because the top tread is the upper floor. Fifteen risers means 14 treads. Divide the rise by risers, never by treads.

What is the maximum riser height and minimum tread depth?

Under the IRC, the maximum riser height is 7-3/4 in (196 mm) and the minimum tread depth is 10 in (254 mm) (R311.7.5.1 and R311.7.5.2). Within one flight the tallest riser may exceed the shortest by no more than 3/8 in (9.5 mm). Subject to local code.

How long does a stair stringer need to be?

It's the hypotenuse of the total rise and total run: √(rise² + run²). For a 108 in rise and a 140 in run that's 176.82 in, or 14.73 ft (4.49 m). Round up to the next mill length — a 16 ft board — for the end cuts.

What size lumber is used for stair stringers?

Cut stringers are typically laid out on 2×12 (1.5 × 11.25 in / 38 × 286 mm actual), which leaves enough throat behind the notches. Stock comes in the standard mill lengths — 6, 8, 10, 12, 14, 16, 18, 20 ft. Buy one long enough to avoid a splice.