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Stair calculator

Number of steps, riser height, tread depth, stringer length and stair angle from total rise and run, checked against IRC riser and tread limits.

Atualizado Exemplos verificados: 5

Mais opções
The stair uses the fewest risers that keep each one at or under this height.
Experimentar
Risers
Risers: 15
Número inteiro; Ao mais próximo; empates afastando-se de zero
Riser height
7.2in / 182.9mm
Treads
14
Tread depth
10in / 254.0mm
Stringer length
176.82in / 14.73ft
Stair angle (pitch)
35.8°
IRC riser and tread check
Meets IRC riser and tread limits

15 risers of 7.2 in (183 mm) and 14 treads of 10 in (254 mm) climb 108 in (2,743 mm) at a pitch of 35.8°. Both dimensions are within the IRC limits.

Stair profile

run 140 in (3,556 mm)rise 108 in (2,743 mm)35.8°each step 7.2 × 10 in (183 × 254 mm)pitch line (dashed) · stringer 14.73 ft
Como é calculado S

  1. Number of risers

    n=⌈1087.5⌉=15n = \left\lceil \frac{108}{7.5} \right\rceil = 15

    Rounded up so no riser is taller than the target.

  2. Riser height

    r=10815=7.2 in(≤7.75 in: passes)r = \frac{108}{15} = 7.2\ \text{in} \quad (\le 7.75 \text{ in: } passes)

  3. Tread depth

    t=14015−1=10 in(≥10 in: passes)t = \frac{140}{15 - 1} = 10\ \text{in} \quad (\ge 10 \text{ in: } passes)

    The top floor serves as the last step, so there is one tread fewer than risers.

  4. Pitch

    θ=arctan⁡rt=arctan⁡7.210=35.75∘\theta = \arctan\frac{r}{t} = \arctan\frac{7.2}{10} = 35.75^\circ

    The slope of the line through the tread nosings.

  5. Stringer

    s=1082+1402=176.82 ins = \sqrt{108^2 + 140^2} = 176.82\ \text{in}

    From the foot of the first riser to the top nosing; buy a board long enough to add the bottom and top cuts.

  6. Comfort check

    2r+t=24.4 in2r + t = 24.4\ \text{in}

    Blondel's rule of thumb: 24–25 in (about 63 cm) feels natural.

  7. England: Approved Document K, private stair

    2R+G=2×182.9+254.0=620 mm2R + G = 2 \times 182.9 + 254.0 = 620\ \text{mm}

    Table 1.1 limits: rise 150–220 mm, going 220–300 mm, pitch at most 42°, 2R + G between 550 and 700 mm. This stair meets all four.

Sobre Stair calculator

The number of risers is the floor-to-floor rise divided by the tallest riser you will accept, rounded up, so every riser is the same height and none exceeds your limit. The run is divided by one fewer than the risers to give the tread depth, because the upper floor forms the top step. The pitch is arctan(riser ÷ tread), the slope of the line through the nosings, and the stringer length is √(rise² + run²).

The default stair, 108 in (9 ft) floor to floor over 140 in of run, gives 15 risers of 7.2 in and 14 treads of 10 in at a pitch of 35.8°. That meets the US residential limits of a 7¾ in maximum riser and 10 in minimum tread (2021 IRC R311.7.5; 2024 IRC R318.7.5).

Measure the rise between finished floor surfaces. Tread depth here is the going, nosing to nosing. The check covers risers and treads only; stair width, headroom, handrails and local amendments need checking separately.

Exemplos resolvidos

9 ft floor to floor, 140 in of run

Total rise (floor to floor)
108 in
Total run available
140 in
Risers
15
Riser height
7.2 in
Treads
14
Tread depth
10 in
Stringer length
176.82 in
Stair angle (pitch)
35.8 °
IRC riser and tread check
Meets IRC riser and tread limits

Fonte de verificação: Python decimal: ⌈108/7.5⌉ = 15; 108/15 = 7.2 in; 140/14 = 10 in; √(108² + 140²) = 176.816 in; pitch atan(7.2/10) = 35.754°, pitch being the slope of the line through the nosings (Approved Document K, 2013, Appendix A)

Edge: 3-4-5 stair lands on an exact riser count

Total rise (floor to floor)
105 in
Total run available
140 in
Risers
14
Riser height
7.5 in
Tread depth
10.769 in
Stringer length
175 in
Stringer length
14.58 ft

Fonte de verificação: Hand calculation: 105/7.5 = 14 exactly; 140/13 = 10.769 in; 105:140:175 is a 3-4-5 triangle

Short run fails the tread minimum

Total rise (floor to floor)
100 in
Total run available
100 in
Tallest riser you'll accept
7.75 in
Risers
13
Riser height
7.692 in
Tread depth
8.333 in
Stair angle (pitch)
42.7 °
IRC riser and tread check
Tread under 10 in

Fonte de verificação: Python decimal: ⌈100/7.75⌉ = 13; 100/12 = 8.33 in < 10 in (2021 IRC R311.7.5.2); pitch atan(7.6923/8.3333) = 42.709°

Metric: 2800 mm rise, 3600 mm run, 180 mm target

Total rise (floor to floor)
2800 mm
Total run available
3600 mm
Tallest riser you'll accept
180 mm
Risers
16
Riser height
175.0 mm
Tread depth
240.0 mm
IRC riser and tread check
Tread under 10 in

Fonte de verificação: Hand calculation: ⌈2800/180⌉ = 16; 2800/16 = 175 mm; 3600/15 = 240 mm < 254 mm

Perguntas

What is the maximum stair riser height allowed by code?

In US homes it is 7¾ in, with treads at least 10 in deep and no more than 3/8 in difference between the tallest and shortest riser in a flight (2021 IRC R311.7.5.1–R311.7.5.2; 2024 IRC R318.7.5). Buildings under the 2021 IBC (§1011.5.2) need risers of 4 to 7 in and treads of at least 11 in, except R-3 buildings and stairs inside R-2 dwelling units, which may use 7¾ in and 10 in.

How many steps do I need for a 9 ft rise?

At least 14 risers. Divide the rise by the maximum riser and round up: 108 in ÷ 7.75 in = 13.9, so 14 risers of 7.71 in; a 7.5 in target gives 15 risers of 7.2 in. There is one tread fewer than risers (13 or 14), because the upper floor acts as the last step. Measure from finished floor to finished floor, including flooring.

How do you calculate stair stringer length?

Apply Pythagoras to the total rise and run: √(rise² + run²). For 108 in of rise over 140 in of run that is √(108² + 140²) = 176.8 in, or 14.73 ft, along the pitch line. The plumb cut at the top and the level cut at the bottom need extra board, so buy the next stock length up, 16 ft here.

What is the steepest stair angle allowed?

For US homes, the IRC's 7¾ in riser over a 10 in tread gives a maximum of arctan(7.75/10) ≈ 37.8°. IBC stairs, at 7 in over 11 in (2021 IBC §1011.5.2), top out near 32.5°. England's Approved Document K, Table 1.1, allows 42° for a private stair, with rises of 150–220 mm, goings of 220–300 mm and twice the rise plus the going between 550 and 700 mm.

What other rules apply to residential stairs?

The IRC stairway section (2021 R311.7; 2024 R318.7) requires a clear width of at least 36 in and headroom of 6 ft 8 in. Handrails go 34 to 38 in above the tread nosings (2021 IRC R311.7.8; 2024 IRC R320). Riser heights and tread depths may differ by at most 3/8 in within one flight, so cut every step from the same layout.

Qual é a precisão de “Stair calculator”?

A precisão depende dos dados inseridos e das hipóteses do método. O cálculo decimal usa 50 algarismos significativos, mas estimativas, métodos numéricos e dados de origem podem ter menor precisão; o arredondamento exibido não elimina essas limitações. Exemplos resolvidos verificados com fontes independentes: 5. Por exemplo, “9 ft floor to floor, 140 in of run” é verificado com Python decimal: ⌈108/7.5⌉ = 15; 108/15 = 7.2 in; 140/14 = 10 in; √(108² + 140²) = 176.816 in; pitch atan(7.2/10) = 35.754°, pitch being the slope of the line through the nosings (Approved Document K, 2013, Appendix A).

De onde vem o método?

City of Boise code handout #437 — IRC R311.7.5 stair treads and risers (riser 7¾ in max, tread 10 in min); International Code Council — 2021 IRC R311.7 stairways (renumbered R318.7 in the 2024 IRC); HM Government — Approved Document K (England), Table 1.1: rise, going and pitch of private stairs.

Sobre esta calculadora

n=⌈risermax⁡⌉,r=risen,t=runn−1,θ=arctan⁡rt,s=rise2+run2n = \left\lceil \frac{\text{rise}}{r_{\max}} \right\rceil,\quad r = \frac{\text{rise}}{n},\quad t = \frac{\text{run}}{n - 1},\quad \theta = \arctan\frac{r}{t},\quad s = \sqrt{\text{rise}^2 + \text{run}^2}

Fontes

  1. City of Boise code handout #437 — IRC R311.7.5 stair treads and risers (riser 7¾ in max, tread 10 in min)
  2. International Code Council — 2021 IRC R311.7 stairways (renumbered R318.7 in the 2024 IRC)
  3. HM Government — Approved Document K (England), Table 1.1: rise, going and pitch of private stairs

Verificado com as referências

Esta calculadora inclui 5 exemplos resolvidos com respostas de fontes independentes. Eles fazem parte do conjunto de testes e você também pode executá-los aqui.

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