Calculate a staircase using the step formula: riser, tread, number of steps, run length and pitch angle – checked against DIN 18065 limits.
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Calculating a Staircase: Step Formula, Riser and Tread
A good staircase follows the human stride. The step formula, proven since the 17th century, states: 2 × riser + tread = 59 to 65 cm, ideally 63 cm – the average stride length on level ground. The calculator determines the suitable number of risers from your floor-to-floor height (target: around 18 cm riser), derives the tread from it and checks the result against the DIN 18065 limits for residential buildings: riser 14–20 cm, tread at least 23 cm.
The standard example: 280 cm floor height
280 cm ÷ 16 risers = 17.5 cm riser. The step formula yields 63 − 2 × 17.5 = 28 cm tread. Since the top riser ends at floor level, the staircase needs 15 treads and thus 15 × 28 = 420 cm run length at about 32° pitch – the classic, comfortable residential staircase. If less space is available, enter the existing run length: the calculator distributes it across the treads and reports whether the step formula still holds.
Comfort and safety rules
Besides the step formula, the trade literature knows two further rules of thumb: the comfort rule t − r = 12 cm describes how effortlessly the stairs climb; the safety rule t + r = 46 cm ensures enough foothold when walking down. Only the 17/29 combination satisfies all three rules exactly – real staircases are always a compromise, which the calculator states transparently.
What building law additionally requires
DIN 18065 and the German state building codes regulate more than riser and tread: usable flight width of at least 80 cm (required stairs in residential buildings), 200 cm headroom, an intermediate landing from 18 risers upwards, and for winder stairs the step formula applies along the walking line. A basement staircase with 250 cm height over 250 cm length fails arithmetically on the tread, by the way – exactly such cases are flagged by the check with concrete alternative riser counts.
