What the Staircase Calculator does
This calculator designs a straight flight of stairs from the height between floors and the space available: how many risers, how tall each one is, how deep each tread is, the stringer length and the pitch. It then checks the design against the limits of the rules you choose - the US International Residential Code, the UK Approved Document K for private stairs, or your own - and shows which pass and which fail, including headroom under the stairwell opening.
A side-view diagram shows the flight to scale, with the pitch line through the nosings.
How to use it
- Choose millimetres or inches and the rules to check against. The limits fill in automatically; open Limits to see them or set your own.
- Measure the total rise from finished floor to finished floor, including floor coverings - an extra 20 mm of tile at the top changes the last step.
- Enter the horizontal run available for the flight, or leave it empty and give the tread depth you want instead.
- Enter the nosing projection (the overhang of each tread), which the IRC requires when treads are shallower than 11 inches.
- For a headroom check, enter the length of the opening in the floor above and that floor's thickness.
Reading the results
The number of risers is the smallest that keeps every riser within the maximum; all risers are equal, which the codes require within a small tolerance. Treads are always one fewer than risers because the top floor is the last step.
2 x rise + going is a comfort rule: people walk most naturally at about 600-640 mm (24-25 in). Approved Document K requires 550-700 mm; the IRC does not use it, so it is shown for information.
Headroom is measured vertically from the pitch line through the nosings to the underside of the floor above at the edge of the opening, which is where people hit their heads.
Worked example: a UK house stair
The floors are 2,600 mm apart and 2,750 mm of run is available. Approved Document K allows risers up to 220 mm, so 2,600 / 220 = 11.8 rounds up to 12 risers of 216.7 mm.
Twelve risers need 11 treads: 2,750 / 11 = 250 mm each. The pitch is atan(216.7 / 250) = 40.9 degrees, under the 42 degree limit, and 2 x 216.7 + 250 = 683 mm, within 550-700 mm. The stringer diagonal is √(2,600² + 2,750²) = 3,785 mm.
The opening above is 2,500 mm long and the floor 250 mm thick, so the ceiling is 2,350 mm up. The opening edge is 250 mm from the first riser, where the pitch line is 216.7 + 216.7 = 433 mm high, leaving 1,917 mm of headroom - short of the 2,000 mm required. Lengthening the opening by about 100 mm, or moving the stair, fixes it.
Formulas and scoring rules
- Risers
risers = ceil(total rise / maximum riser); riser = total rise / risers- Treads
treads = risers - 1; tread = run / treads (or as entered); run = tread x treads- Pitch and stringer
pitch = atan(riser / tread); stringer = √(total rise² + run²)- Comfort rule
2 x riser + tread (going)- Headroom
headroom = (total rise - floor thickness) - (riser + riser / tread x (run - opening length))- Presets
IRC R311.7: riser ≤ 7¾ in, tread ≥ 10 in, headroom ≥ 6 ft 8 in, nosing ¾-1¼ in when tread < 11 in. UK Part K private stair: rise ≤ 220 mm, going ≥ 220 mm, pitch ≤ 42°, 2R + G 550-700 mm, headroom ≥ 2.0 m
Limitations: what the result does not prove
- It checks only the listed limits. Handrails, guards and balusters, landings, winders, stair width, fire escape rules and local amendments also apply; your building-control body or inspector decides compliance.
- Straight flights only. Turns, landings and winders change the arithmetic and have their own rules.
- The stringer length is the diagonal of rise and run; the board you buy must be longer to allow for the cuts at the top and bottom and the plumb and level seats.
- Local codes differ from these presets and change over time. Check the edition your jurisdiction has adopted.
Privacy: where your data goes
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Standards and sources
- International Residential Code R311.7 - stairways - checked 19 Sep 2026
- UK Government - Approved Document K: Protection from falling, collision and impact
Frequently asked questions
How do I calculate the number of stairs?
Divide the total rise between finished floors by the maximum riser height your code allows and round up; that is the number of risers. The number of treads is one fewer. For a 2,700 mm rise under the IRC (7¾ in = 196.85 mm), 2,700 / 196.85 = 13.7, so 14 risers and 13 treads.
What is the maximum riser height for stairs?
Under the US International Residential Code it is 7¾ inches (196.85 mm). Under the UK Approved Document K a private stair may have risers up to 220 mm. Commercial and public stairs are stricter in both. Always check the edition adopted where you build.
What is the 2R + G rule?
Twice the riser height plus the going (tread depth) approximates a comfortable stride. Around 600-640 mm feels natural. The UK requires 550-700 mm for private stairs; other codes may not state it, but it is a good test of whether a stair will feel steep or awkward.
How much headroom do stairs need?
The IRC requires 6 ft 8 in (2,032 mm) measured vertically from the sloped line through the tread nosings. UK Approved Document K requires 2.0 m, with some relaxation for loft conversions. The calculator checks it at the edge of the stairwell opening, the lowest point.
How long should a stair stringer be?
At least the diagonal of the total rise and total run, which the calculator gives. Buy a longer board to allow for the cuts at each end and any extension to meet the floor or a landing.
What is a stair nosing?
It is the front edge of a tread that projects past the riser below. The IRC requires ¾ to 1¼ inches of nosing when treads are shallower than 11 inches, to give the foot more to land on. The calculator checks it only for the IRC preset.
Last reviewed by the A2Z.Tools team against the sources listed above.
