How we calculate
Each calculator is specified, unit-tested and cross-checked before it goes live. This page lists the formulas, sources and limits.
Stair geometry
All math runs in inches. Input in feet, inches, fractions or millimeters is converted first; results are rounded only for display, to the nearest 1/16" (and to the whole millimeter).
riser = total rise ÷ risers
treads = risers − 1
run = treads × tread run
angle = arctan(riser ÷ tread run)
layout = treads × √(riser² + tread run²)
throat = board width − riser × run ÷ √(riser² + run²)
board = risers × √(riser² + run²), rounded up to 8, 10, 12 … 20 ft
stringers = ceil((width − 1 1/2") ÷ max spacing) + 1, never fewer than 3 for cut stringers
The tiny subtraction in the first line stops floating-point noise from adding a riser: 108 1/2" ÷ 7 3/4" is exactly 14, but a computer returns 14.000000000000002.
The calculators assume a standard mount, where the upper floor serves as the top step. Winders, spiral stairs and flush-mounted top treads are not covered yet.
Sources
- International Code Council, 2021 International Residential Code, section R311.7 (stairways): riser, tread, nosing, width, headroom, flight height, landings, handrails.
- American Softwood Lumber Standard (PS 20): actual sizes of dressed lumber, 2x10 = 1 1/2" × 9 1/4" and 2x12 = 1 1/2" × 11 1/4".
- American Wood Council, DCA 6: Prescriptive Residential Wood Deck Construction Guide (2015): 2x12 minimum for stringers, cut stringers analyzed with 5.1" of depth at a 7 3/4:10 rise to run, at least three cut stringers and 18" maximum spacing, stair footings and a landing above 12' of total height.
- The 2R + T comfort range (24"–26") is a long-standing design rule of thumb, shown as guidance and not as a code requirement.
Testing
The browser runs the same JavaScript file that our automated tests run, so the page and the tests cannot drift apart. Before each release the stair math passes 44 checks: hand-worked examples, a published comparison case, unit conversions, fraction formatting and property tests (no riser above the limit for any height from 20" to 150", total run never shrinking as the rise grows).
Results were also compared on five sample stairs with an independent online stair calculator. Rise, total run, stringer length, stringer height and angle matched on all five to within 0.01". Throat, board length and stringer count were checked by hand.
Limits
These tools give geometry, not structural engineering. They do not size beams, check fastener loads or replace a permit review. Code figures are from the model code; your jurisdiction may have adopted a different edition or local amendments.
Report a problem
If a number looks wrong, email [email protected] with the page, the values you entered and what you expected. Confirmed errors are fixed, turned into a new test case so they cannot return, and recorded below.
Change log
- 2026-11-05 — stair and stringer calculators published.