Methodology: How the Calculations Work and Are Tested

Measurement conventions

• Total rise: lower finished floor (or landing) to upper finished floor, measured where the stair stands.
• Riser height: total rise ÷ number of risers. All risers are equal. This equals the code measurement between leading edges of adjacent treads on a uniform stair.
• Going: horizontal distance nosing to nosing (equivalently riser face to riser face). It excludes the nosing overhang.
• Top of stair: "upper floor is the top step" gives treads = risers − 1; "extra tread level with the floor" gives treads = risers. The chosen convention is printed next to every result.
• Total run: treads × going, bottom riser face to top riser face. The bottom tread's nosing and any landings are extra.
• Pitch: atan(riser ÷ going), the angle of the line through the nosings.
• Pitch-line length: risers × √(riser² + going²). A geometric reference, never presented as a cut length.
• Stringer: treads rest directly on seat cuts; the first riser cut is riser − tread thickness (+ any floor finish added at the bottom later); the top ends in a plumb cut at the face of the top riser. Throat is board width − riser × going ÷ √(riser² + going²). The shortest board is the length of the stringer outline projected onto the board's axis.
• Deck stairs: for each riser count the landing point is treads × going from the deck face; the rise there is deck height + ground slope × landing distance − pad height. The smallest count that keeps the riser at or below the maximum is chosen.

Units and rounding

All geometry is stored in millimetres as double-precision numbers, with 1 in = 25.4 mm exactly. Inputs are converted once, when you type them. Results are rounded only for display: to the nearest 1/16 in by default (1/8 or 1/32 on request), or 0.1 mm. A "≈" mark means a displayed fraction is rounded. Switching between inches and metric re-formats the stored millimetre values and never re-reads a rounded display, so toggling cannot drift the geometry.

Riser counts use a tiny tolerance (10⁻⁹ of the ratio) so that exact divisions such as 105 ÷ 7.5 = 14 are not pushed to 15 by floating-point noise.

Input validation

Zero, negative, non-numeric and absurd inputs are rejected or flagged with an explanation instead of being silently coerced. Examples: a maximum riser typed in the wrong unit (which would need more than 60 risers), a nosing as large as the going, a board too narrow to notch, a tread thicker than the riser, ground steeper than 1 in 1. A rise of one riser or less is shown as a single step with no treads, and the angle is reported as not applicable rather than as NaN.

Informational checks

Calculators compare geometry with reference values from named editions and sections (see sources). Each item is labelled "within reference", "outside reference" or "check". The site never labels a stair as passing, compliant, approved or safe, because that depends on local adoption, amendments, exceptions, the building's use and inspection.

How the engine is tested

The calculation code is separate from the page code and covered by automated tests (Vitest) that run before every build:

• Reference fixtures with expected values derived independently of the code, by hand and with a separate Python script, not by running this engine. The table below is recomputed during every site build; the build fails if any value disagrees.
• Property tests (fast-check) over thousands of random inputs: risers × riser height = total rise; riser ≤ maximum and one fewer riser would exceed it; run = treads × going; tan(angle) = riser ÷ going; no negative or non-finite outputs; stringer marks exactly one step apart; deck risers within the maximum at the actual landing point.
• Parser tests for fractions, feet and inches, Unicode fractions, metric suffixes and rejected inputs, plus round-trip tests for unit conversion.
• Copy tests that re-derive the numbers quoted in the guides and calculator pages.
• Browser tests (Playwright) for the main flows, error states and layout at phone to desktop widths, with automated accessibility scans.

Reference fixtures (computed at build time)

What the tools do not calculate

• Structural capacity: stringer spans, lumber grades, fasteners, connections, footings, guard strength.
• Headroom under the floor opening (flagged as a check, not computed).
• Winders, spiral stairs, curved stairs, and multi-flight stairs with landings.
• Housed (routed) stringers, carriage-and-skirt assemblies and other joinery details.
• Local code adoption, amendments and exceptions; permits; inspection.

The tests show the arithmetic matches independent derivations under the stated conventions. They do not show that a stair built from the results is safe or approved; that depends on the build and on local review. No licensed engineer, architect or code official has reviewed this site.

Change history

• 2026-10-24: first release of the stair, stringer, deck and angle engines, with the fixtures above.

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