Hong Life CalculatorsUnderstanding the stair calculator — concept and principle
This calculator lays out a straight flight of stairs: how many risers you need, the exact height of each step, the total horizontal run, the pitch angle and the comfort check 2R + G. Enter the total rise from finished floor to finished floor, the tread going you want and the maximum riser height allowed. It is used for planning a new staircase, checking whether it fits the space, and testing it against building rules.
How it is calculated
- Number of risers n = ⌈total rise ÷ max riser⌉.
- Riser height R = total rise ÷ n.
- Total run = (n − 1) × going G.
- Pitch = arctan(R ÷ G).
- Comfort value = 2R + G (550–700 mm is the usual comfortable range).
The principle
All risers in a flight must be equal, because people adjust their stride to the first few steps and an odd step is a trip hazard. Dividing the rise by the maximum allowed riser and rounding up gives the fewest risers that stay within the limit; dividing the rise by that count spreads it evenly. A flight has one tread fewer than risers, since the top riser steps onto the upper floor, so the run is (n − 1) × G. The 2R + G rule dates back to the 17th-century French architect François Blondel and reflects the average human stride: a taller step pairs with a shorter tread.
Worked example
Default inputs: total rise 2,700 mm, going 250 mm, max riser 190 mm.
- Risers = 2,700 ÷ 190 = 14.21, rounded up to 15.
- Riser height = 2,700 ÷ 15 = 180 mm.
- Total run = 14 × 250 = 3,500 mm.
- Pitch = arctan(180 ÷ 250) = 35.75°.
- 2R + G = 2 × 180 + 250 = 610 mm, within 550–700.
| Max riser height (mm) | Number of risers |
|---|---|
| 47.5 | 57 |
| 95 | 29 |
| 142 | 19 |
| 190 | 15 |
| 238 | 12 |
| 285 | 10 |
| 380 | 8 |
How to read the result
Rules differ by country and building type. In England, Approved Document K allows a private stair a maximum rise of 220 mm, a minimum going of 220 mm and a maximum pitch of 42°. The US International Residential Code limits risers to 7¾ in (about 196 mm) with a minimum tread depth of 10 in (254 mm), so this example's 250 mm going would be too short there. A pitch of roughly 30–37° feels comfortable for most people. If the run is too long for the space, a landing or winder may be needed rather than steeper steps.
Common mistakes
- Measuring rise from subfloor instead of finished floor, which makes the top or bottom step uneven.
- Counting treads as risers, overstating the run by one going.
- Ignoring headroom above the stair.
- Forgetting nosing, which overlaps treads and is not part of the going.
Frequently asked questions
What is a comfortable stair riser height?
Roughly 150–190 mm for homes, with goings of about 250–300 mm.
How many steps for a 2.7 m floor height?
About 15 risers at 180 mm each, with 14 treads.
What is the difference between going and tread?
The going is the horizontal distance between nosings; the tread is the board itself, which can be deeper because of the nosing overlap.
Sources: HM Government, Approved Document K — Protection from falling, collision and impact · International Residential Code (IRC), Section R311.7 — Stairways