There is always one more riser than tread, every riser has to be identical, and the whole flight is set by one measurement — floor to floor. Get any of those wrong and the staircase is scrap timber.
Enter the total rise and how deep you want the treads. We'll work out the risers, the treads, the run and the stringer length — and check the result against the limits an inspector will use.
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Floor to floor. There is always one more riser than tread, every riser has to be identical, and both facts follow from that single measurement. Get it wrong and the staircase is wrong in a way that cannot be adjusted afterwards. Measure finished floor to finished floor, not subfloor to subfloor — forgetting the flooring thickness at one end is what makes the last riser different, and one odd riser is a trip hazard as well as a code failure.
By exactly one tread thickness. Drop the stringer by the tread thickness at the base, or every riser except the first will be right — which is the same problem as every riser except the first being wrong. It is the classic stair-setting-out error and it is invisible until the treads go on.
Headroom is the other constraint: around 2 m / 6 ft 8 in clear above the pitch line. A flight that fits the floor but not the ceiling opening is a wasted weekend. Cut one stringer and use it as the template for the others, because marking each independently guarantees they will not match. Handrail and balustrade are separate and usually mandatory, with gap limits set in law — a small child's head must not pass through. And this is a setting-out tool, not a structural design: stringer size, material and support come from a code or an engineer.
Divide the total finished floor-to-floor rise by your target riser height, round to a whole number, then divide the rise by that number to get the actual riser. Every riser must be identical, and there is always one more riser than tread.
Because the tread sits on top of it. Drop the stringer by one tread thickness at the base, otherwise the first riser finishes taller than all the others once the treads are laid.
Around 2 m (6 ft 8 in) clear, measured above the pitch line. A flight that works for the floor height but not the ceiling opening is a common and frustrating mistake.
Usually yes, and they are separate from the stringer calculation. Gap limits are set in law in most places, on the principle that a small child's head must not pass through.