How the stair calculator works
Every step in a flight must have the same height, because the body learns the rhythm after two or three steps and trips on any riser that differs. So the total rise is divided by the tallest step you allow and rounded up to a whole number of risers; the real riser height is then the total rise shared equally between them. The tread depth, called the going, comes from the stride rule first published by the French architect François Blondel: two risers plus one going should match an average adult pace of about 63 cm.
Risers = ⌈ total rise ÷ max riser ⌉ · R = rise ÷ risers · G = 63 cm − 2R · Run = (risers − 1) × GThere is one tread fewer than risers because the upper floor itself is the last step. The angle is the arctangent of R ÷ G, and the stringer length is the diagonal of the total rise and total run, before adding the extra needed for the top and bottom cuts.
Worked example
A floor-to-floor height of 265 cm with an 18 cm maximum gives 265 ÷ 18 = 14.7, so 15 risers of 17.67 cm. The going is 63 − 2 × 17.67 = 27.67 cm. Fourteen treads of 27.67 cm make a horizontal run of 387 cm, the flight rises at 32.6° and the stringer is about 469 cm long. In imperial, a 108 in rise with a 7.5 in limit needs 15 risers of 7.2 in; the 24.8 in stride gives 10.4 in treads and a run of 145.6 in, just over 12 ft, at 34.7°. That 108 in is typical of an 8 ft ceiling plus about 12 in of joists and flooring: ceiling height alone always understates the rise.
Typical code limits for homes
| Rule set | Max riser | Min going / tread | Other |
|---|---|---|---|
| US IRC (one- and two-family houses) | 7¾ in (196 mm) | 10 in (254 mm) | Headroom 6 ft 8 in; variation between steps max 3/8 in |
| US IBC (commercial buildings) | 7 in (178 mm), min 4 in | 11 in (279 mm) | Stricter than residential |
| England, Approved Document K, private stair | 220 mm | 220 mm | Max pitch 42°; 2R + G between 550 and 700 mm; headroom 2.0 m |
| Germany, DIN 18065, small dwellings | 200 mm (min 140) | 230 mm | Stricter values for larger residential buildings |
| French practice (Blondel) | about 16–18 cm | about 25–30 cm | 2R + G between 60 and 64 cm |
These figures are a planning aid only. Stairs are structural and safety-critical: check your local building code or have a qualified builder or engineer confirm the design before cutting stringers.
Design pitfalls
- Measuring to the subfloor. Coverings added later only change the end steps. 20 mm of tiles on the lower floor makes the first riser 20 mm shorter; 20 mm of boards on the upper floor makes the top riser 20 mm taller. Either way the flight is no longer even, so measure finished floor to finished floor.
- Forgetting the nosing. The going is measured nosing to nosing; the tread board itself is usually 20–30 mm (about 1 in) deeper so it overhangs the riser below.
- Headroom under the opening. A long run needs a long stairwell opening above; check the vertical clearance above the pitch line along the whole flight.
- Too steep for the space. If the run does not fit, a landing or a quarter turn is usually safer than pushing the angle past 40–42°.
Frequently asked questions
How many steps do I need for a 9 ft ceiling?
Measure finished floor to finished floor: a 9 ft ceiling plus about 12 in of floor structure is roughly 120 in. At a 7.5 in maximum that is 16 risers of 7.5 in and 15 treads; at the 10 in minimum US tread the run is 150 in.
What is the ideal riser height and tread depth?
Most people find 17–18 cm risers with 27–29 cm treads comfortable, or roughly 7 in by 11 in. Both satisfy the 2R + G stride rule of about 63 cm (25 in).
What is the 2R + G formula for stairs?
Twice the riser height plus the going should equal an average stride of 60–65 cm. For a 17 cm riser the going is 63 − 34 = 29 cm.
How much horizontal space does a staircase need?
Multiply the number of treads by the tread depth. A typical house flight of 14 treads at 27 cm needs about 3.8 m of run, plus a clear landing at the bottom.
What is the maximum stair angle?
Most comfortable house stairs are between 30° and 37°. England limits private stairs to 42°, and anything steeper is treated as a ladder or alternating tread stair with its own rules.
Last reviewed: 2026-09-27 · How we calculate