Stair calculator

Laying out a flight is two divisions and one decision. The divisions are easy: every riser in a flight has to be the same height, so you take the fewest risers that keep each one inside the legal maximum, divide the total rise by that, and divide the run you have by one fewer treads. The decision is which maximum, and that is where a stair calculator can quietly mislead you, because there is no universal figure. A riser may be 7 3/4 inches in a house built to the International Residential Code, 220 mm in an English house under Approved Document K, 9.5 inches on a workplace stair under OSHA and 7 inches on an escape route under the ADA Standards. Give this tool a 2.6 m floor-to-floor and those four documents answer fourteen, twelve, eleven and fifteen risers. So pick the one that governs your building, and treat the answer as a starting point for the person who signs it off, not as approval.

How it is calculated

risers = ceil(total rise ÷ maximum riser), riser = total rise ÷ risers, tread = run ÷ (risers − 1)

The ceiling is doing the work. You cannot have a fractional riser and you cannot mix heights, so the count has to be a whole number and the first whole number that brings every riser under the limit is the one that gives the shallowest flight fitting in the space. Treads are one fewer than risers on a straight flight, because the last riser lands you on the floor above and that floor is not a tread. The pitch is then the arctangent of riser over tread, which is the figure Approved Document K caps at 42° for a private stair and OSHA brackets between 30° and 50° for a workplace one.

Source: The number of risers is the smallest whole number that keeps every riser inside the published maximum, because every riser in a flight has to be the same height

Questions people ask

Which code applies to me?

The one your building control body or inspector enforces, which this page cannot know. The International Residential Code is a model code published by the International Code Council; it carries no force by itself and applies where a state, county or city adopts it, usually with local amendments. Approved Document K is statutory guidance for England, and Scotland, Wales and Northern Ireland publish their own. OSHA 1910.25 is United States federal law for workplaces under general industry rules, not for homes. The ADA Standards apply to stairs on a required means of egress in places the Americans with Disabilities Act covers. Pick the one you are actually being judged against, and check the edition your jurisdiction adopted.

Why does the tool sometimes say the tread is too deep?

Because Approved Document K puts a ceiling on the going as well as a floor: 300 mm for a private stair, 400 mm for a utility or general access one. A run of 3.6 m against a 2.6 m rise gives a 327 mm going, which is past that ceiling, and the same layout also breaks the 2R + G rule the table sets out — "twice the rise plus the going (2R + G) equals between 550mm and 700mm" — at 761 mm. A flight that gentle is comfortable to walk but it is not what the guidance describes, and on a stair that long the going stops matching a normal stride.

Can I use the maximum rise and the minimum going together?

Not on an English private stair, and the tool will tell you so. Take 220 mm of rise with 220 mm of going, both exactly at the limits in Table 1.1, and the pitch is 45° — past the 42° that note [1] to that table sets for a private stair. The rise and going limits are not independent permissions you can combine freely; the pitch cap and the 2R + G window sit on top of them. This is the case most calculators get wrong, because checking a rise against one column and a going against another never surfaces it.

What are treads and risers, exactly?

The riser is the vertical face between two treads and the going, or tread depth, is the horizontal depth of the step you put your foot on. The codes measure them slightly differently: Approved Document K measures the going nosing to nosing, so any overlap between treads is excluded, while the IRC measures tread depth "horizontally between the vertical planes of the foremost projection of adjacent treads". Both come to the same thing on a stair with a consistent nosing, but it means the depth of the timber you cut is not the number the code is talking about.

Why does the run divide by one fewer than the risers?

Because a straight flight always has one more riser than tread. Climb three risers and you stand on two treads and then on the landing; the landing is floor, not a step. It is the single arithmetic mistake that shows up most often in a homemade layout, and it makes every tread come out a little too shallow. If your flight turns or has an intermediate landing, split it into straight sections and run each one through separately.

Does the tool check everything the code says?

No, and nothing that fits on one page could. It checks the rise, the going, the pitch and the 2R + G window where the document you picked publishes them. It does not check headroom, stair width, handrails, guards, nosing profile, the maximum number of risers in a flight, landing sizes or the vertical rise allowed between landings — all of which are in the same documents and any of which can fail an inspection on a flight whose arithmetic is perfect.

Where do the limits on this page come from?

Four documents, each readable in full. The IRC riser and tread figures are quoted verbatim in the City of Boise Building Division handout #437 of February 2022, at https://www.cityofboise.org/media/14405/437-treads-risers_march-2022.pdf. Approved Document K, 2013 edition for use in England, is at https://assets.publishing.service.gov.uk/media/60d5bdcde90e07716f516cfd/Approved_Document_K.pdf, and Table 1.1 in it carries the rise, going, pitch and 2R + G figures. The workplace limits are OSHA 29 CFR 1910.25(c), at https://www.osha.gov/laws-regs/regulations/standardnumber/1910/1910.25. The egress limits come from the U.S. Access Board technical guide to the ADA Standards for stairways, at https://www.access-board.gov/files/ada/guides/stairs.pdf. Where a document prints both inches and millimetres, this tool works from the inch figure, because the metric one beside it is a rounded conversion — the IRC prints 196 mm next to 7 3/4 inches, which is 196.85 mm.

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