About Stair Calculator (Rise, Run & Code Check)
The stair calculator turns a floor-to-floor rise into a complete straight-flight stair design: number of risers, actual riser height, number of treads, total run, stair pitch angle, and the stringer length needed to cut the carriage. Starting from your target riser height it selects n = round(totalRise / targetRiser) risers, computes the resulting uniform riser R = totalRise / n, and lays out treads = n − 1 at the tread depth you enter or one derived automatically from the Blondel comfort rule.
Every result is checked against the selected building code — IBC commercial (riser ≤ 178 mm / 7 in, tread ≥ 279 mm / 11 in), IRC residential (riser ≤ 196 mm / 7.75 in, tread ≥ 254 mm / 10 in), OSHA standard stairs (riser and tread ≤/≥ 9.5 in), or your own custom limits — plus the classical comfort rules: Blondel 2R + T of 610–635 mm (24–25 in), R + T of 432–457 mm (17–18 in), R × T of 70–75 in², and a stair angle between 30° and 37°. Optional inputs check the flight against an available run and compute the headroom under a floor opening.
How It Works
- Choose the unit system (millimetres or inches) and enter the total floor-to-floor rise and your target riser height; the calculator picks the nearest whole number of risers and shows the one-more / one-fewer alternatives.
- Enter the tread depth (going), or leave it at zero to derive it from the Blondel rule T = 630 mm (25 in) − 2R, floored at the code minimum tread.
- Select the code preset — IBC, IRC, OSHA, or custom limits — and the tool checks the actual riser and tread against the maximum riser and minimum tread with the pass/fail margin.
- Optionally enter the available run, a nosing projection, and the floor-opening length with deck thickness; the tool then checks the flight fits the plan and that headroom at the opening edge meets the 2032 mm (6 ft 8 in) minimum.
- Read the results: risers, riser height, treads, total run, angle, stringer length, 2R + T, and the full compliance table.
Worked Example
A commercial stair has a floor-to-floor rise of 2800 mm and a target riser of 175 mm. The calculator selects n = round(2800 / 175) = 16 risers, so the actual riser is R = 2800 / 16 = 175 mm with 15 treads. With no tread entered, the Blondel rule gives T = 630 − 2 × 175 = 280 mm, so the total run is 15 × 280 = 4200 mm and the stringer length is √(2800² + 4200²) = 5048 mm. The stair angle is atan(175 / 280) = 32.0°, inside the 30–37° comfort band, and 2R + T = 630 mm sits inside the 610–635 mm Blondel band. Against IBC the riser passes (175 ≤ 178 mm) and the tread passes (280 ≥ 279 mm), so the design is code-compliant and comfortable.
Formulas
- Riser count and actual riser
n = round(H / R_target); R = H / n- Treads and total run
treads = n − 1; run = (n − 1) × T- Blondel comfort rule
2R + T = 610–635 mm (24–25 in)- Stair angle
θ = atan(R / T), comfort 30–37°- Stringer length
L = √(H² + run²)- Headroom at the floor opening
h = R × (L_open / T) − t_deck ≥ 2032 mm (80 in)
Standards & References
- IBC 1011.5.2 — riser ≤ 178 mm (7 in), tread ≥ 279 mm (11 in)
- IRC R311.7.5 — riser ≤ 196 mm (7.75 in), tread ≥ 254 mm (10 in)
- OSHA 1910.25(c) — standard stairs: riser ≤ 9.5 in, tread ≥ 9.5 in
- Blondel (1675) step formula 2R + T
Frequently Asked Questions
How do I calculate the number of stairs I need?
Divide the total floor-to-floor rise by your target riser height and round to the nearest whole number: n = round(H / R_target). The actual riser is then H / n so that every step is exactly equal, which codes require — riser uniformity is typically limited to a 9.5 mm (3/8 in) variation within a flight. The calculator also shows the designs with one riser more and one fewer so you can trade riser height against total run.
What is a comfortable riser and tread size?
The classical Blondel rule says two risers plus one tread should equal an average stride: 2R + T between 610 and 635 mm (24–25 in). Companion rules put R + T at 17–18 in and R × T at 70–75 in², with the stair angle between about 30° and 37°. A 175 mm riser with a 280 mm going (about 7 in on 11 in) satisfies all of them and is the sweet spot for most stairs.
What are the code limits for risers and treads?
IBC commercial stairs allow a maximum 178 mm (7 in) riser and require a minimum 279 mm (11 in) tread. IRC residential stairs are more lenient: riser up to 196 mm (7.75 in) and tread down to 254 mm (10 in). OSHA standard industrial stairs permit risers and treads of 9.5 in. Always confirm the governing code and any local amendments for your project before construction.
How do I calculate stringer length?
The stringer (carriage) runs along the hypotenuse of the stair triangle, so its length is √(totalRise² + totalRun²). For a 2800 mm rise with a 4200 mm run that gives √(2800² + 4200²) ≈ 5048 mm. Order stringer stock a little longer than this to allow for the top and bottom cuts and any seat or ledger details.
What headroom does a stair need and how is it checked?
IBC and IRC both require at least 2032 mm (6 ft 8 in) of vertical clearance measured from the line of the nosings to the ceiling or floor structure above. Walking down under a floor opening, the flight drops R × (openingLength / T) below the top landing by the time you reach the opening edge; subtracting the floor construction depth gives the available clearance. If it is short, lengthen the floor opening or steepen the stair within code limits.
Does the nosing count toward the tread depth?
Codes measure tread depth from nosing to nosing horizontally, which equals the going used for the run, so the nosing does not add to the code tread depth or the total run. It does enlarge the physical surface your foot lands on — the calculator reports this as the effective tread. IRC limits nosing projection to 32 mm (1.25 in) so it does not become a trip hazard.