Stair calculator
A flight of 112 inches divided by a 7 inch target gives exactly 16 risers at 7 inches. If the rise were 114 inches you would still use 16 risers, at 7.125 each — not fifteen at seven and one odd one at nine. People climb stairs by feel, not by looking, and a single riser that differs by more than about 5 mm is the classic trip hazard that building regulations exist to prevent.
Divide the total floor-to-floor rise by a comfortable riser height, round to a whole number, then divide the rise by that count to get the actual riser. Every riser in a flight must be the same to within a few millimetres, that is a regulation, not a preference.
How to set out a staircase
Stairs are governed by two relationships that carpenters have used for centuries. The first is 2R + T: twice the riser plus the tread should sit around 25 inches, or 630 mm, because that is the length of a natural stride. The second is that riser and tread trade against each other: a taller riser needs a shallower tread and produces a steeper, more tiring flight. Building regulations set outer limits on both, and they differ by country: England allows a maximum 220 mm rise and minimum 220 mm going for a private stair, while the US model codes cap the riser at 7¾ inches with a 10 inch minimum tread.
Questions
Around 7 inches or 175–180 mm. Under 6 inches feels shuffling; over 8 inches is tiring and starts to feel like a ladder.
Twice the riser plus one tread should be about 25 inches (630 mm). It matches the length of a natural stride and produces stairs that feel right.
It is the hypotenuse of the total rise and total run: shown above. Add extra at both ends for the cuts and the fixing.
The top riser lands on the upper floor, which acts as the last tread. A flight of 16 risers has 15 treads.
Barely. Most codes allow no more than 5 mm or 3/8 inch difference across a flight, because an uneven riser is what people trip on.