Brazil Staircase Calculator: Steps, Riser and Run

The Blondel formula

Proposed by French architect François Blondel in the 17th century, this rule is still the comfort standard worldwide. It starts from a simple observation: a human stride on flat ground is roughly 63–65 cm, and climbing stairs consumes that same stride — except part of it goes vertically.

The relationship is 2 × riser + tread = 63 to 65 cm. The riser is doubled because lifting the body costs about twice the effort of moving the same distance horizontally.

Worked example with this calculator’s defaults: a 280 cm floor-to-floor height divided by a target riser of 18 cm gives 15.56 steps. Since half a step does not exist, round to 16. The actual riser becomes 280 ÷ 16 = 17.5 cm. With a 28 cm tread, Blondel gives (2 × 17.5) + 28 = 63 cm — right at the comfortable lower bound.

Note the design logic: the riser you type is only a target. The whole number of steps is what governs, and the real riser comes from the division. Every step must be exactly the same height, which is why nobody builds a staircase with a neat 18.00 cm riser — the round number has to be the step count, not the height.

Steps required by floor height

Generated with this calculator using an 18 cm target riser and a 28 cm tread — the three most common residential floor heights in Brazil:

Note the 260 cm case: rounding down to 14 steps produces an 18.57 cm riser, above the 18 cm maximum, and a Blondel value of 65.14 cm, outside the comfort range. Lowering the target to 17.3 cm forces 15 steps, giving a 17.33 cm riser and a Blondel value of 62.67 cm — much better, at the cost of 28 cm of extra run.

Brazilian standard NBR 9077

ABNT NBR 9077 covers emergency exits in buildings and is the technical reference most Brazilian designers use for step dimensions. It requires risers of 16–18 cm, treads of 28–32 cm, a Blondel value between 63 and 65 cm, a minimum clear width of 1.20 m on escape routes, and a landing every 3.20 m of vertical rise as well as at every change of direction.

One nuance is often missed: NBR 9077 governs escape routes. A private staircase inside a single dwelling is not an escape route and is formally regulated by the municipal building code instead, which commonly accepts treads from 25 cm and widths of 80 cm. The Blondel relationship, however, still applies as the comfort and safety criterion.

Also allow at least 2.00 m of clear headroom (2.10 m is better) measured vertically from the step nosings wherever the staircase passes beneath a slab or an upper flight.

Common mistakes

The most dangerous and most common error is a first or last step that ends up a different height from the rest. It happens when the height is measured on the raw screed and a 2 cm floor finish is added later: every riser keeps its height except the final one. The body memorizes a staircase’s rhythm within two steps and then climbs on autopilot, so a 1.5 cm difference at the top is enough to cause a fall. Always measure from finished floor to finished floor.

Two other frequent slips: forgetting that the number of treads is always one fewer than the number of risers, which throws off the total run; and omitting the handrail, required in Brazil on any flight of more than three steps, mounted between 80 cm and 92 cm above the nosing line.

Frequently asked questions

Sources

• ABNT NBR 9077 — Saídas de emergência (texto)
• Clube do Concreto — Escadas pela NBR 9077
• Guia Reforma — Escada: dimensionamento e normas

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