Risers, treads and the stringer line for a single flight
A flight is 4 figures you hold and this page holds none of them: the total rise off your tape, the tread depth off the stock you are cutting, the maximum riser height you read off the rule you are held to, and whether the top tread is the landing. Type them and the risers, the exact riser height, the total run and the stringer line are worked out, with the working printed in section B: the divisions and the stacks as rows you can re-do from the characters on the screen, and the stringer line as the diagonal it is, in a sentence, because no square root is printed as a row. Five flights are told apart here: one still being typed, a rise of zero or less, a rise that splits into whole sixteenths, a rise that does not, and a riser the next sixteenth up puts past your own ceiling.
No figure here is computed yet, because this page waits until you type a total rise, a tread depth, a maximum riser height of your own and the choice about the top tread.
AThe four figures you type
BThe working
The chain re-foots on every keystroke: the rise over your own ceiling gives a whole riser count, the count gives the exact riser height, the count gives the run at your tread depth, and the run with the rise gives the stringer line. The count is a whole number, and that is where the chain is blunt. It is taken up to the next whole riser, so your own ceiling reaches the count, the height, the run and the stringer line only by changing that count: move the ceiling between two crossings and all four stay exactly where they were. The exact riser height is the rise over that count. The tread count is that count, or that count less one where the top tread is the landing, and the run is the tread count times your tread depth, so the rise reaches the run only through the count - and where the tread count is nought, which is a flight of one riser whose top tread is the landing, the run is nothing and the stringer line is the rise itself whatever tread depth you type. Neither the tread depth nor the landing choice moves the count or the height.
Where the rise does not split into whole sixteenths, both directions are shown, because the direction is yours: the height rounded down with the remainder it leaves, and the height rounded up with the deficit it costs. Where it splits into whole sixteenths there is one height, so one row prints and there is no direction to choose.
CThe flight, riser by riser
Each mark is the nearest sixteenth of that riser's cumulative height, so nothing piles up on the way and the last mark is the rise you typed. The top riser takes whatever is left to the floor line.
DWhat this page will not tell you
This page computes geometry against the limits you type and never supplies a limit of its own. It cites no rule, no document and no authority, it says nothing about stringer stock, grade, species, span, fasteners, bearing, handrails, guards or landings, and no figure it prints is a judgement about the stair you are cutting.
Nothing you type is stored or sent anywhere. Between visits this page holds nothing at all. It does send one beacon of its own, on load, when the offer comes into view and if you click the buy link: this page's address, which of those three it is, the host you came from, and a random id that goes no further. The arithmetic is also published as JSON, with the formulas and a worked flight, at api.json.
Printed from otherworldlabs.com/stair-rise-run-and-stringer/ — every figure above is computed from the four dimensions typed on the page.
EThe one-stair cut list
The workbook is the sheet that goes to the saw and stays with the job: a line for each flight on its Cuts sheet, carrying the date, the dimensions as you typed them, the whole riser count, the exact riser height, the height rounded down to the sixteenth and the height rounded up to it, the tread count, the total run and the stringer line. Every figure the sheet works out is a live formula, and nothing in the file is a pasted value, so a rise re-measured when the slab is not where the drawing said re-foots that whole line in place instead of being retyped. Its Summary sheet foots the flights on the list, and its Check sheet works each of the Summary's figures a second way out of the cells you typed and prints the difference beside it. The PDF that comes with the workbook is the rules in plain language, each with a worked example, and the decisions the arithmetic does not make.
Take the one-stair cut list — $19
The kit is two files, for one price, yours to keep. No account, no subscription.