Stair Calculator Explained

What a stair calculator does

A stair calculator takes three numbers — the total rise from finished floor to finished floor, the maximum riser height your code allows, and the tread depth you want — and returns everything else you need to cut timber and frame a flight: number of risers, the actual riser height, number of treads, total horizontal run, the diagonal stringer length, and the pitch angle. It is the difference between sketching a stair on the back of a builder’s merchant receipt and ordering the right length of stringer the first time. The stair calculator on this site runs the same arithmetic that sits behind the stair tables in UK Approved Document K1, the US International Residential Code, and the trade carpentry handbooks — but it shows the working rather than burying it in a lookup table.

Stairs are one of the few jobs where being slightly out is not a cosmetic problem. A 5 mm difference between the top and bottom riser is the most common cause of trips on a flight of domestic stairs, and a tread that is 20 mm too shallow makes the descent feel like falling. The whole point of the calculation is to spread the rise evenly across whole steps and check that the resulting rhythm matches the way humans actually climb. The math is school-level geometry; the consequences of getting it wrong are not.

How a stair calculator works

The geometry breaks into four small calculations chained together. The first one is the only one that requires rounding.

N = ceil(total_rise / max_riser_height)

N is the number of risers. The maximum riser height is a hard ceiling — you cannot legally exceed it — so any fractional remainder forces an extra step. If the total rise is 2,700 mm and the maximum riser height is 180 mm, 2,700 ÷ 180 = 15.0 exactly, so N = 15. If the maximum were 200 mm, 2,700 ÷ 200 = 13.5 and N rounds up to 14, because a partial step is impossible and the maximum is a cap.

actual_riser_height = total_rise / N

The actual riser height is always at or below the maximum and always equal across every step in the flight. That equality is non-negotiable — Approved Document K1 and the IRC both require the difference between the tallest and shortest riser in a flight to be under about 10 mm. Inconsistent steps are the single largest contributor to stair falls in the home, which is why building codes are unusually strict about this one number.

treads = N - 1 total_run = treads × tread_depth

The number of treads is one less than the number of risers because the upper landing replaces the top tread. If the stair has 15 risers, you cut 14 treads. The total horizontal run is just the tread depth multiplied by the number of treads — the stair takes up that much floor space on the lower level, plus a bit of nosing overhang at the front edge.

stringer_length = sqrt(total_rise² + total_run²) pitch_angle = arctan(total_rise / total_run)

The stringer is the long diagonal board that the treads and risers attach to, and its length is the hypotenuse of a right triangle whose legs are the total rise and the total run. Pythagoras solves it directly. The pitch angle is the same triangle’s elevation, found with arctan. Both of these are the numbers you actually need at the timber merchant — the stringer for material length, the pitch to confirm the stair will land where you planned on the lower floor.

Worked example: a 2.7-metre domestic flight

Take a UK domestic staircase with a floor-to-floor rise of 2,700 mm, a maximum riser height of 180 mm (comfortably below the K1 cap of 220 mm), and a tread depth — the K1 "going" — of 250 mm. Run the numbers in your head with the stair calculator open beside you to check each step.

• Risers — ⌈2,700 ÷ 180⌉ = 15. That is your step count.
• Actual riser height — 2,700 ÷ 15 = 180.0 mm. Every step is the same height to the millimetre.
• Treads — 15 − 1 = 14.
• Total run — 14 × 250 = 3,500 mm. The staircase takes 3.5 m of floor space.
• Stringer length — √(2,700² + 3,500²) = √19,540,000 ≈ 4,420 mm.
• Pitch angle — arctan(2,700 ÷ 3,500) ≈ 37.6°, inside the K1 maximum of 42°.
• Blondel 2R + G — 360 + 250 = 610 mm, squarely inside the 550–700 mm comfort window.

Now do the US equivalent. A 108-inch rise (2,743 mm), a 7¾-inch IRC maximum riser (196.85 mm), and a 10-inch IRC minimum tread (254 mm). Risers = ⌈2,743 ÷ 196.85⌉ = 14. Actual riser = 2,743 ÷ 14 = 195.9 mm. Treads = 13, total run = 13 × 254 = 3,302 mm. Stringer = √(2,743² + 3,302²) ≈ 4,293 mm. Pitch = arctan(2,743 ÷ 3,302) ≈ 39.7°. Blondel 2R + G = 392 + 254 = 646 mm — still inside the comfort window, but noticeably steeper than the UK equivalent because the IRC tolerates higher risers in exchange for shallower treads. Both stairs are legal; the UK version is the more comfortable to climb.

The codes — and where they disagree

Three regulatory regimes cover the vast majority of stairs built in English-speaking countries. The differences are small, but they bite when you ship a design across borders.

UK Approved Document K1

Domestic stairs (general access in a dwelling): maximum riser 220 mm, minimum going 220 mm, maximum pitch 42°, the 2R + G comfort range 550–700 mm. Common (shared) stairs are tighter still: maximum riser 190 mm, minimum going 250 mm. Headroom is 2,000 mm clear. Read the current edition of Approved Document K on gov.uk; the 2013 edition with 2025 amendments is the version in force at the time of writing.

US IRC R311.7

Residential stairs under the International Residential Code: maximum riser 7¾ in (196.85 mm), minimum tread 10 in (254 mm), minimum headroom 6 ft 8 in (2,032 mm), maximum riser-to-riser variation 3⁄8 in (9.53 mm). The IRC does not formalise a 2R + G comfort rule, but the riser/tread minima produce a comfort window that overlaps the Blondel range for most domestic flights.

US IBC 1011

Commercial stairs under the International Building Code: maximum riser 7 in (177.8 mm), minimum tread 11 in (279.4 mm). The IBC is stricter than the IRC because commercial stairs see higher traffic, more people unfamiliar with the layout, and a legal duty of accessibility under the Americans with Disabilities Act. ADA stairs add nosing-profile, handrail, and contrast-marking requirements that are outside the geometry scope of this calculator.

Factors that change the calculation

Where you measure the rise

The total rise is always from finished floor to finished floor — not floor to the top of the upper joist, and not floor to the underside of the upper subfloor. Forgetting this is the single most common amateur error and produces a stair that misses the upper landing by 18–25 mm, the thickness of the finished floor. If the upper floor finish has not been laid yet, measure to the planned finished height and double-check before cutting the stringer.

Subfloor depth and the joist hanger

The stringer top is usually housed into a joist hanger or bolted to the trimmer joist below the upper landing. That connection has its own dimensions: the stringer is cut to land against the face of the joist, not against the top of the floor, and the top tread is the upper finished floor itself. The calculator assumes the connection is dimensionally clean. On a real frame you will need to add 25–50 mm of working length to the stringer to allow for the connection geometry.

Nosing overhang

A nosing is the front edge of the tread that overhangs the riser below it, typically 19–25 mm. The nosing does not change the tread depth used in the calculation (the going is measured nose-to-nose), but it does extend the visible front edge of the stair by the nosing depth times the number of treads. Under UK K1 the nosing depth is part of the "going" and is permitted up to 25 mm; under IRC R311.7.5 the nosing must project between 3⁄4 in (19 mm) and 1¼ in (32 mm).

Winders, half-landings and quarter-turns

The calculator handles a straight flight. A staircase with a winder (the triangular treads at a turn) or a half-landing does not change the riser geometry — every step in the flight still has the same height — but the run calculation is no longer the simple product of treads and going. Each landing adds its own depth, and winder treads are dimensioned separately under K1 and the IRC. Design the flights either side of the landing as separate stairs and add the landings afterwards.

How to design a stair that actually feels right

• Aim for the Blondel sweet spot. 2R + G between 580 and 640 mm is where the rhythm is most comfortable for the largest range of users. Below 580 the stair feels shallow and stretches the stride; above 640 it feels tight and forces a short step. The stair calculator reports 2R + G alongside the geometry so you can adjust before ordering timber.
• Target a riser well below the code cap. The UK K1 maximum of 220 mm is legal but uncomfortable on a long flight. 175–200 mm is the trade comfort range; 180 mm is the most common spec on a UK domestic stair. The US IRC cap of 7¾ in is similarly an upper bound rather than a target — most US residential stairs land between 7 and 7½ in (178 and 191 mm).
• Prefer a deeper tread than the minimum. A 250 mm going (UK) or 11 in tread (US) is noticeably more comfortable on the descent than the legal minimum. The descent is where most stair falls happen, because the eye tracks the leading foot and a short tread offers less margin for error.
• Confirm the upper landing fits the stringer. Calculate the total run before framing the opening above the stair. A 14-tread flight at 250 mm going takes 3,500 mm of floor space below the upper landing; the trimmer joists above need to be positioned to clear that run plus the nosing.
• Order timber 10–15 % longer than the calculator number. The stringer length is the diagonal between two points. You will lose 50–100 mm at the bottom for the newel housing, 50–100 mm at the top for the joist connection, and a plumb cut or two along the way. Better to cut off than to splice on.
• Draw the cuts on the actual stock. Before committing the saw to the stringer board, mark out the housings on the timber itself. The "throat" — the narrowest point of the board after the housing cut — needs to be at least 130 mm for a typical domestic stringer; if your marked-up cuts leave less, step up to deeper stock.

Common mistakes

Measuring rise to the subfloor. The total rise must be finished floor to finished floor. Measuring to a bare subfloor and forgetting to add the planned finish thickness produces a top step that is 18–25 mm shallower than every other step in the flight, which is illegal under both K1 and the IRC and is the classic "trip on the top step" stair.

Using the maximum riser as the target. The 220 mm K1 cap and the 7¾ in IRC cap are upper bounds, not design values. A stair built to the cap is legal but uncomfortable, especially for older users and small children. Drop the maximum on the calculator to a comfort target — 180 mm for UK domestic, 7¼ in for US residential — and accept the extra step.

Forgetting the tread is one less than the riser. Treating the flight as if it has the same number of treads as risers produces a stringer that is 250 mm too long and a stair that overshoots the upper landing. The top step is the landing itself, not a tread you cut.

Ignoring the Blondel check. It is possible to build a flight where every single dimension meets code — riser below the cap, tread above the minimum, pitch below 42° — but the rhythm feels wrong because 2R + G falls outside 550–700 mm. Two-up-one-back climbs at the gym deliberately work this out-of-rhythm sensation; you do not want that feeling on the stair to your bedroom.

When to seek professional advice

For any structural stair — anything that is not a free-standing flight in an outbuilding, anything subject to building control sign-off, anything wider than 1,200 mm, or anything in a commercial setting — have the design checked by a competent person before you cut timber. A structural engineer or building inspector will check stringer throat depth, joist hanger spec, headroom, handrail mounting, and balustrade fixings. The cost of a half-hour consultation is a small fraction of the cost of rebuilding a stair that fails building control. For domestic stairs in England and Wales, notify Building Control under the building regulations approval process on gov.uk before starting work.

Frequently asked questions

What inputs does the stair calculator need?

Three numbers: the total rise from finished floor to finished floor in millimetres, the maximum riser height your code allows (or your chosen comfort target, whichever is lower), and the tread depth or "going" in millimetres. The stair calculator returns risers, actual riser height, treads, total run, stringer length, pitch angle, and a Blondel comfort check.

How accurate are the calculator’s outputs?

The arithmetic is exact to the precision of the inputs. A 2,700 mm rise with a 180 mm target maximum produces 15 risers of exactly 180.0 mm. The stringer length is the exact Pythagorean diagonal; in practice you will order timber 10–15 % longer to allow for the housing cuts and connections at either end. The pitch angle is exact to within rounding.

Why does the calculator round risers up but not the stringer?

Risers round up because a partial step is impossible and the maximum riser height is a hard code limit — exceeding it is not negotiable. The stringer is a continuous timber length, so the calculator reports the exact geometric diagonal and lets you add a working margin on the timber order. Rounding the stringer would lose information you might want.

Can I use the calculator for a spiral or curved stair?

No. The calculator handles straight flights only. Spiral stairs follow a helical geometry where the going varies across the width of each tread, and curved stairs need a per-tread layout. Both are specialist designs — use a stair manufacturer or a structural engineer who specialises in helical timber framing.

What is the difference between the going and the tread?

The going is the horizontal distance from the front of one riser to the front of the next, measured along the pitch line. The tread is the visible top surface of the step, which includes the going plus the nosing overhang. UK K1 specifies the going; US IRC R311.7 specifies the tread depth measured nose-to-nose, which is the same dimension. The calculator uses whichever you enter — the nosing is cosmetic on the geometry.

How wide should the staircase be?

UK K1 sets a minimum clear width of 600 mm for a domestic stair serving a single room, and 800 mm for the main stair to a dwelling. US IRC R311.7.1 sets a minimum of 36 in (914 mm) above the handrail and 31½ in (800 mm) below the handrail. The calculator reports geometry only and does not check width — confirm the clear width on the framing plan before ordering stringer stock.

Related calculators and reading

• Stair calculator — run the numbers above with your own rise and tread inputs.
• Square footage calculator — area for the floor and wall finishes around a stair.
• Concrete calculator — volume and bag count for a stair footing or landing pad.
• Brick calculator — bricks and cost for a wall alongside a flight.
• Carpet calculator — carpet run length including stair treads and risers.
• Drywall calculator — plasterboard sheets for the stair void and soffit.
• Concrete calculator explained — companion article on volume, wastage, and bag yields.
• Square footage calculator explained — area math for irregular rooms.