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Stairs Calculator

Number of Steps

13 Steps

The Numbers

  • Number of risers: 14
  • Actual riser height: 19.59 cm
  • Tread depth: 24.86 cm
  • Total run (horizontal length): 323.12 cm
  • Stringer length: 423.86 cm

Analysis

  • This staircase's angle (40.3°) is steeper than the commonly-cited comfortable range of 30-35° — consider a smaller max riser height or more total run if space allows.

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How This Calculator Works

A staircase’s step count and dimensions are worked out from the total height it needs to climb and how tall each step is allowed to be. Enter the total floor-to-floor rise, the maximum height a single riser is allowed to be, and a rise + run comfort target, and this calculator works out the number of steps, the exact riser height, the tread depth, the total horizontal run, and the stringer (diagonal) length.

The Formula

Number of risers, rounded UP — rounding down would let a single riser exceed the maximum height you entered:

Risers=⌈Total RiseMax Riser Height⌉\vD{\text{Risers}} = \left\lceil \dfrac{\vA{\text{Total Rise}}}{\vB{\text{Max Riser Height}}} \right\rceil

Actual riser height (always at or below the max, since it just divided the total evenly across however many risers were needed):

Riser Height=Total RiseRisers\vE{\text{Riser Height}} = \dfrac{\vA{\text{Total Rise}}}{\vD{\text{Risers}}}

Number of treads = Treads=Risers−1\vF{\text{Treads}} = \vD{\text{Risers}} - 1, since the top riser lands you on the upper floor itself, which doesn’t need its own tread.

Tread depth = Tread Depth=Rise + Run Target−Riser Height\vG{\text{Tread Depth}} = \vC{\text{Rise + Run Target}} - \vE{\text{Riser Height}} — the classic “rise + run” stair-comfort guideline (commonly cited as 17–18 in / 43–46 cm) used to derive a comfortable step depth from whatever the actual riser height works out to.

Total run = Total Run=Treads×Tread Depth\vH{\text{Total Run}} = \vF{\text{Treads}} \times \vG{\text{Tread Depth}}.

Stringer length (the diagonal cut length), from the Pythagorean theorem:

Stringer Length=Total Rise2+Total Run2\text{Stringer Length} = \sqrt{{\vA{\text{Total Rise}}}^2 + {\vH{\text{Total Run}}}^2}

Worked Example

A 274.32 cm (9 ft) floor-to-floor rise, a 19.685 cm (7.75 in) max riser height, and a 44.45 cm (17.5 in) rise + run target:

  1. Risers: 274.32÷19.685=13.94\vA{274.32} \div \vB{19.685} = 13.94, rounded up to 14\vD{14}.
  2. Actual riser height: 274.32÷14≈19.59\vA{274.32} \div \vD{14} \approx \vE{19.59} cm.
  3. Treads (steps): 14−1=13\vD{14} - 1 = \vF{13}.
  4. Tread depth: 44.45−19.59≈24.86\vC{44.45} - \vE{19.59} \approx \vG{24.86} cm.
  5. Total run: 13×24.86≈323.12\vF{13} \times \vG{24.86} \approx \vH{323.12} cm.
  6. Stringer length: 274.322+323.122≈423.86\sqrt{{\vA{274.32}}^2 + {\vH{323.12}}^2} \approx 423.86 cm.

Source: Standard stair-building rise/run and "rise + run" comfort formula.

Frequently Asked Questions

What is the difference between a riser and a tread?

The riser is the vertical part of a step (its height); the tread is the horizontal part you actually step on (its depth). A staircase with N risers only needs N-1 treads, since the top riser lands you on the upper floor itself.

What is the "rise + run" comfort rule?

A commonly-cited guideline for comfortable stairs is that a riser height plus a tread depth should add up to around 17-18 inches (43-46 cm) — taller risers should pair with shallower treads and vice versa, which is exactly how this calculator derives tread depth from your actual riser height.

What is the stringer length?

The stringer is the diagonal structural board the risers and treads attach to — its length is the diagonal distance from the bottom of the stairs to the top, found with the Pythagorean theorem from the total rise and total run.