A worked example: 3000mm floor height, 175mm desired riser
A 3000mm floor-to-floor height with a 175mm desired riser needs 17 steps, each with an actual riser of 176.5mm and a recommended tread depth of 277mm.
The formula: round to a whole number of steps, then adjust
Number of steps = round(total rise ÷ desired riser). Since a staircase can't have a fractional step, the total rise is then divided evenly across that whole number, giving an actual riser slightly different from the desired one — 176.5mm here, close to but not exactly the requested 175mm.
Where the tread depth comes from: the 630mm comfort rule
Tread depth = 630mm − 2 × actual riser, a widely cited rule of thumb (not a building-code figure) for proportionate, comfortable stairs. A taller floor height with a bigger riser — 2700mm at 180mm riser, giving exactly 15 steps and a 180mm actual riser — produces a 270mm tread instead, shrinking as the riser grows, per that same 2-to-1 relationship.
Why the desired and actual riser rarely match exactly
Only a floor height that divides evenly by the desired riser will produce an exact match — for any other combination, rounding to a whole step count is unavoidable, and the small adjustment to the actual riser is the price of having a consistent, whole number of equal steps rather than one oddly-sized step.
What this calculator doesn't determine
This gives the riser and tread dimensions only — the actual diagonal stringer board length needed to build the staircase depends on both this tread depth and the number of steps, a separate calculation from the total rise and run.