Stair Calculator
Enter the floor-to-floor rise, your maximum riser height, and the tread depth (going). The calculator returns how many risers you need, the exact riser height, the total horizontal run, the stringer length, and the pitch angle — with a Blondel-formula comfort check.
Number of risers (steps)
15
- Actual riser height (mm)
- 180
- Number of treads
- 14
- Total run (mm)
- 3,500
- Stringer length (mm)
- 4,420.41
- Pitch angle (°)
- 37.65
N risers = ⌈total rise ÷ max riser height⌉; actual riser = total rise ÷ N; stringer = √(rise² + run²). Blondel comfort: 610 mm — comfortable (target 550–700 mm).
How to use this calculator
Measure the total rise from finished floor to finished floor — not floor to the top of the upper joist, and not floor to underside of upper subfloor. Enter it in millimetres (108 inches = 2,743 mm; 9 ft = 2,743 mm; 2.7 m = 2,700 mm). Set the maximum riser height for your jurisdiction: UK Approved Document K1 caps domestic risers at 220 mm but 175–200 mm is comfortable; the US IRC R311.7 caps residential risers at 7¾ in (196.85 mm); the US IBC caps commercial risers at 7 in (177.8 mm). Enter the tread depth (the "going") in millimetres: UK K1 requires at least 220 mm, IRC requires at least 10 in (254 mm), IBC requires at least 11 in (279.4 mm). The result panel returns the number of risers, the actual riser height (always ≤ the maximum), the number of treads, total run, stringer length, and pitch angle, with a Blondel comfort check on 2R + G.
How the calculation works
The number of risers is the ceiling of total rise ÷ max riser height — you cannot have a partial step, and the maximum is a hard ceiling for safety, so any remainder bumps the count up. The actual riser height is total rise ÷ number of risers, which is always at or below the maximum. Number of treads is risers − 1 (the top "step" is the upper landing, not a tread). Total run is treads × tread depth. The stringer — the diagonal board that supports the steps — is the hypotenuse of a right triangle with legs equal to the total rise and total run, so its length is √(rise² + run²) by the Pythagorean theorem. Pitch angle is arctan(rise ÷ run). The Blondel "stepping formula" (François Blondel, Cours d'Architecture, 1675) says comfortable stairs satisfy 2R + G between 550 and 700 mm — a low-and-deep step or a tall-and-shallow step both feel wrong because the body's natural step rhythm fights them.
Worked example
UK domestic flight, 2,700 mm floor-to-floor, target 180 mm riser, 250 mm going. Risers = ⌈2,700 ÷ 180⌉ = 15. Actual riser = 2,700 ÷ 15 = 180.0 mm. Treads = 14. Total run = 14 × 250 = 3,500 mm. Stringer = √(2,700² + 3,500²) = √19,540,000 ≈ 4,420 mm. Pitch = arctan(2,700 ÷ 3,500) ≈ 37.6°. Blondel 2R + G = 360 + 250 = 610 mm — squarely inside the 550–700 mm comfort range, so the rhythm of the stairs should feel right underfoot. For a US IRC residential equivalent (108 in / 2,743 mm rise, 7¾ in / 196.85 mm max riser, 10 in / 254 mm tread), the calculator returns 14 risers at 195.9 mm each, 13 treads totalling 3,302 mm of run, a 4,293 mm stringer, and a 39.7° pitch — both 2R + G (646 mm) and pitch are within UK and IRC code.
Frequently asked questions
What is the difference between rise, run, riser and tread?
Rise is the vertical distance from one floor to the next (the "total rise") or the vertical face of a single step ("riser height"). Run is the horizontal distance covered by a flight ("total run") or the depth of a single step ("tread depth" or, in UK code, "going"). A staircase has one more riser than it has treads — the top step is the upper landing, not a tread you cut. So a 14-tread stair has 15 risers.
How is the number of risers calculated?
Risers = ⌈total rise ÷ maximum riser height⌉, rounded up to the next whole number. You can never exceed the code maximum, so any fractional remainder bumps the count up by one. The actual riser height then drops to total rise ÷ risers, so all steps are equal and at or below the maximum. UK Approved Document K1 caps domestic risers at 220 mm; IRC R311.7 caps US residential risers at 7¾ in (196.85 mm); IBC caps commercial at 7 in (177.8 mm). Most builders target 175–200 mm because the comfort window peaks well below the code maximum.
How is stringer length calculated?
The stringer is the long diagonal board that the treads and risers attach to. Its length, measured between the bottom newel and the top floor connection along the diagonal, is the hypotenuse of a right triangle: stringer = √(total_rise² + total_run²). For 2,700 mm rise and 3,500 mm run, √(2,700² + 3,500²) = √19,540,000 ≈ 4,420 mm. Order timber 10–15 % longer to allow for cuts at the top and bottom housings and at the joist hanger or angle bracket.
What is the Blondel formula and the 2R + G comfort check?
François Blondel (1675) noticed that humans climb stairs with a roughly constant stride energy — taller risers force a shorter step, shallower risers allow a longer step. He proposed 2R + G ≈ 600 mm for the most comfortable rhythm, where R is the riser height and G is the going (tread depth). Modern UK Approved Document K1 and most European codes formalise this as 550 mm ≤ 2R + G ≤ 700 mm. The calculator flags any combination outside that range so you can adjust the tread depth or the maximum riser before committing to a layout.
Does this work for US, UK and international stairs?
The math is universal — risers, treads, stringer length and pitch angle are pure geometry regardless of jurisdiction. The differences are the code limits you should set on input: UK K1 domestic max riser 220 mm and min going 220 mm; US IRC R311.7 residential max riser 7¾ in (196.85 mm) and min tread 10 in (254 mm); US IBC commercial max riser 7 in (177.8 mm) and min tread 11 in (279.4 mm). Australia AS 1657 and BCA D2.13 are close to UK figures with subtle variations. Always check your local code before ordering timber — and for any load-bearing structural element, have a competent person sign off the design.
What about headroom, handrails, landings and stringer thickness?
This calculator returns the stair geometry only — it does not size handrails, intermediate landings, headroom clearance, baluster spacing, or the structural thickness of the stringer board. Minimum headroom is typically 2,000 mm (UK) or 80 in / 2,032 mm (US IRC). Handrails are required on at least one side for flights of 3 or more risers (US IRC) or any "common" stair (UK K1). Stringer thickness for a typical 800–1,000 mm-wide domestic stair is usually 38–44 mm-thick softwood; wider or commercial stairs use 50 mm+ or a steel sub-frame. For any structural stair always have the design checked by a competent person.