Stair Calculator

Stair Calculator: Risers, Treads and Stringer Length

Climb a staircase that was laid out by eye and you will feel the mistake in your knees. One riser a quarter of an inch taller than the rest breaks your stride on every single step — and that is the whole problem this calculator solves. Enter the one measurement that matters, the total rise from floor to floor, and it divides that height into risers that are exactly equal, then works out the treads, the total run, the stringer length and the stair angle. No uneven steps, no guesswork, no cutting a stringer twice.

Use it in inches or millimetres. The defaults suit a typical 8 ft floor-to-floor height, but any staircase works the same way: indoor stairs, basement stairs, garage steps and outdoor deck stairs all follow the same maths, because gravity does not care where the stairs are.

Check the verdict lines under your results. The comfort check tells you whether the stair will feel right underfoot, and the code check flags risers or treads that fall outside the standard US and UK limits — before you cut any timber.

The rules that keep stairs safe

In the United States, the International Residential Code (IRC) sets three hard limits for stairs. Risers may be at most 7¾ in tall. Treads must be at least 10 in deep. And every riser in a flight must sit within ⅜ in of every other — the code's way of demanding that all risers be equal. A stair with identical risers passes that rule automatically; a stair where the last step was fudged to absorb the leftover usually fails it.

In the United Kingdom, Approved Document Part K frames the same idea in millimetres: the rise of each step should be between 150 and 220 mm, and the going between 220 and 300 mm. It also applies the comfort formula 2R + G — twice the rise plus the going — which should land between 550 and 700 mm. A staircase inside all three ranges is both legal and comfortable to walk.

Under the legal rules sits a rule of thumb that stair builders have used for generations: twice the riser height plus the tread depth should come out near 24–25 in (about 600–635 mm). Inside that band a stair feels natural, because your foot lands where your stride expects it. Below it the stair feels steep and tiring; above it the stair feels flat and awkward. The calculator checks your numbers against this band and gives you a plain verdict.

How the maths works

The calculator does the one thing you cannot do with a tape measure alone: it divides the total rise into equal parts. Suppose your floor-to-floor height is 96 in and you aim for a 7.5 in riser. 96 ÷ 7.5 is 12.8, which is not a whole number of steps — so the tool rounds to 13 risers and divides the real height by 13. Each riser is then 96 ÷ 13 = 7.38 in. Every step is identical, the ⅜ in rule is satisfied automatically, and you never have to shave a short step in at the top or bottom.

Once the risers are fixed, the treads follow — and here is the part that confuses people: the number of treads is one fewer than the number of risers. Each tread is a surface you stand on, but the last "step" up is the upper floor itself, so the landing counts as your final tread. Thirteen risers need twelve treads, and the total run is twelve treads times your tread depth.

The stringer is simply the hypotenuse of a right triangle: one leg is the total rise, the other is the total run. The calculator applies Pythagoras — stringer = √(rise² + run²) — and the stair angle comes from the same triangle, as the arctangent of riser ÷ tread expressed in degrees. That angle tells you how steep the stair feels: most comfortable stairs land between about 30 and 37 degrees.

Deck stairs: the same maths, measured from the ground

Outdoor stairs obey exactly the same formulas, but the measurement that goes wrong is the rise. Indoors you measure finished floor to finished floor; outdoors you measure from the finished grade — the ground, the patio slab or the footing the bottom step lands on — up to the deck surface. Measure to soil you plan to excavate later and every riser comes out wrong.

Deck stairs also live in the weather, so the lumber choice matters: pressure-treated 2×12 is the standard stringer stock, and the notches must never be cut deeper than the layout requires. If you are planning the whole deck around the stairs, run the frame through the Deck Calculator first, so the framing, the stair opening and the stringers all agree before you buy timber.

What to calculate next

Three tools pair naturally with this one: the Deck Calculator if your stairs serve a deck; the Board Foot Calculator to price the 2×12 lumber your stringers are cut from — stringer stock is lumber, and it is sold by the board foot; and the Square Footage Calculator if you are costing the stairwell opening or the landing.

Stair guides

Practical guides that go with this calculator:

• How to Measure Stair Stringers — Total rise, equal risers, the framing-square layout and the first-step drop — with a deck-stairs example.

Frequently asked questions

Estimates only — stair dimensions are regulated; check your local building code before cutting stringers.