The rules of thumb, and where they came from
Four formulas, three centuries, and no agreement between them.
Blondel's rule (1675)
2R + G = 600 to 660mm (23.6–26″)
François Blondel, directing the Royal Academy of Architecture in Paris, reasoned that a person on the level covers about 600–650mm per pace, and that climbing costs roughly twice the effort of walking. So two rises plus one going should come to one pace. Three hundred and fifty years later it is still the formula that produces the most comfortable stairs, and it is the one StepCalc uses to derive a going when you do not specify one.
UK Approved Document K
2R + G = 550 to 700mm
Blondel's rule with the band widened, written into the regulations rather than left as advice.
Rise plus run
R + G = 17 to 18″ — an American carpenter's rule, quick to check on a tape with
no arithmetic. It tolerates a steeper stair than Blondel does.
Rise times run
R × G = 71 to 74 square inches — the least intuitive and the most forgiving at
the extremes, which is both its use and its weakness.
Why StepCalc shows all four
They disagree. A 7″ rise with an 11″ going satisfies Blondel (635mm) and rise-plus-run (18″) but misses rise-times-run (77 sq in). Averaging them into a single score would hide that, and the disagreement is information: a stair that satisfies all four is comfortable by any tradition, and one that satisfies only the loosest is worth a second look.
What actually matters more than any of them
Uniformity. The research on stair falls is consistent: people descend by rhythm, having learned the step from the first two, and look at the stair far less than they believe. A flight of identical 7¾″ risers is safer than a flight of mostly-7″ risers with one odd one — which is why the codes cap the variation at ⅜″ and why that is the limit worth defending on site.