L-Shaped Winder Stair (Quarter-Turn)
About L-Shaped Winder Stair Calculation
This calculator performs a geometric calculation of an L-shaped winder stair with a 90° turn and winder steps. It helps determine the main step dimensions, the stair angle, the effective run length of the flights, the approximate lengths of stringers or stair carriages, and also the sizes of risers and handrails for the selected stair layout.
The calculation is suitable for preliminary stair layout planning inside an opening, comparing several options, and preparing drawings. It is based on dividing the total rise by the selected number of rises and then determining the depth of straight steps from the available opening length and width.
Reference points and recommendations
Calculation principle for the rise
Total stair height. The starting value is the height from the finished floor of the lower storey to the level of the upper storey in mm. The calculator then determines the total number of rises and divides the total height by that number. The height of one step is calculated by the formula h = H / n, where H is the total stair height in mm and n is the total number of rises.
Number of rises. The calculation includes the lower straight steps, the upper straight steps, the winder steps and, depending on the selected position of the top step, it either additionally includes or does not include the final rise to the upper floor level. For this reason, the final step height depends not only on the floor-to-floor height but also on the selected completion scheme of the staircase.
Riser height. If riser calculation is enabled, their effective height is determined as the difference between the step height and the tread thickness. The formula is hr = h - t, where hr is the riser height in mm, h is the step height in mm, and t is the tread thickness in mm.
Calculation principle in plan view
Flight width. The selected flight width in mm is used as the base plan dimension. It defines the effective length of the straight part of the tread and at the same time takes part in the construction of the winder zone.
Straight step depth. For the upper and lower flight, the calculator first determines the available horizontal section in the opening after subtracting the width of the turning zone. For the upper flight, the expression is b1 = (L - M) / n1, and for the lower flight it is b2 = (B - M) / n2, where L is the opening length in mm, B is the opening width in mm, M is the flight width in mm, and n1 and n2 are the numbers of straight steps in the respective flight.
Final tread depth. Of the two obtained values, the smaller one is selected. In other words, the calculator takes the limiting dimension from the two opening directions so that the staircase fits both the length and the width. The selection logic is expressed as b = min(b1, b2).
Nosing and riser board. The specified front nosing in mm is added to the final step depth for output. If riser calculation is enabled, the thickness of the riser board is also added to the overall depth. Therefore the reported value is a = b + s + tr, where a is the full step depth in mm, s is the nosing in mm, and tr is the riser board thickness in mm.
Stair angle and step length along the flight
Stair angle. After determining the step height h and the effective depth of the straight part b, the calculator finds the stair angle as the slope angle of the straight flight. The relationship used is α = arctan(h / b). This angle is shown in degrees and serves as the main reference for stair steepness.
Distance between steps along the stringer. For straight flights, the sloping length of one step is determined by the formula l = √(h2 + b2). This is the geometric distance between adjacent steps along the line of the stringer or stair carriage.
Practical reference point. For domestic stairs, people often aim for a step height of about 150-190 mm, a tread depth of about 250-320 mm, and a stair angle of about 30-40°. These are not rigid normative values for every case, but common reference ranges for comfortable movement.
Calculation of stringer or stair carriage lengths
Lower flight. For the lower flight, the calculator first determines the sloping length of the section from the number of lower steps. It then subtracts a correction related to the width of the stringer or stair carriage and the angle of inclination. For this reason, the calculator shows two dimensions, the length along the lower edge and the length along the upper edge. This is useful for cutting the member and checking the geometry.
Upper flight. For the upper flight, the same geometry is used, but with the number of upper steps. The length of the upper part is determined as the length of one sloping step multiplied by the number of upper steps, with an angular correction added according to the width of the stringer or stair carriage.
Meaning of the two values. The difference between the upper and lower length appears because the member has its own width in mm. In an inclined element, the outer and inner edges travel different distances, so the calculator shows them separately instead of one averaged figure.
Winder steps and the turning zone
90° turn. At the centre of the calculation is a square or near-square turning zone related to the flight width. The winder steps are distributed inside this zone by sequentially dividing the quarter turn by the selected number of steps. In other words, the angle of one winder step is taken as 90° / nw, where nw is the number of winder steps.
Construction logic. The geometry of the winder steps is formed not by arbitrary proportions but by the overall flight width and by angular division of the turn. Therefore, when the number of winder steps changes, the shape of each of them and the step distribution in plan also changes.
Number of winder steps. In practice, 3 winder steps are often used for a 90° turn because this gives clear geometry and usually fits well with domestic dimensions. With a smaller number, the turn becomes sharper. With a larger number, the angular change per step becomes smaller.
Step width and riser lengths
Step length. To output the tread length, the calculator uses the flight width but does not allow this size to exceed half of the opening width. Otherwise, the step in plan would become wider than the allowable overall size. Therefore the final size is selected as the smaller of two values, the flight width or half of the opening width.
Risers. When the option is enabled, the number of risers is taken as equal to the total number of rises. Their length is reported according to the same logic as the tread length, that is, according to the effective plan width adopted for the flight.
Handrails
Lower flight handrail length. This is taken from the sloping length of the lower section of the staircase. It is an approximate geometric size without allowing for returns, extensions, posts or decorative end details.
Upper flight handrail length. This is determined from the length of the upper section and, if the top step is at the upper floor level, it also takes into account the additional dimension of the final step. For this reason, this size may differ from the pure stringer length.
Normative reference points
General design principles. When selecting stair proportions, it is common to consider requirements for comfort and safety of movement, as well as clearance and guard checks. For the general design framework of structures, reference is usually made to EN 1990 Eurocode. Basis of structural design.
Loads on stairs. For assigning imposed loads to stair flights and landings, reference is generally made to EN 1991-1-1 Eurocode 1. Actions on structures. Part 1-1. General actions. Densities, self-weight, imposed loads for buildings.
Verification of load-bearing members. If the staircase is made of timber, verification of structural capacity is usually linked to EN 1995-1-1 Eurocode 5. Design of timber structures. Part 1-1. General rules and rules for buildings. For steel stringers and stair carriages, reference is generally made to EN 1993-1-1 Eurocode 3. Design of steel structures. Part 1-1. General rules and rules for buildings. This calculator performs geometric layout only and does not replace a separate structural verification.
FAQs
Why is tread depth determined not separately for each flight, but from the smaller value?
Because an L-shaped staircase must fit inside the opening in two directions at the same time. If the larger value were used, one of the flights would exceed the allowable overall size. For this reason, the staircase calculator selects the limiting size that works in both directions.
Why does the stair angle change when the number of steps changes?
The height of one step is calculated by dividing the total height by the number of rises. When the number of steps changes, the rise height changes, and with it the ratio h / b from which the angle is determined. For this reason, the geometry of the whole staircase is recalculated as one system.
What do the two stringer or stair carriage lengths mean?
These are lengths along different edges of a member that has its own width. In an inclined member, the inner and outer lines are not equal, so for a staircase with stringers or stair carriages it is useful to see both dimensions. This makes it easier to assess cutting and material allowance.
Does the calculation take into account the usability of winder steps?
The calculator builds the winder steps according to the geometric scheme of a 90° turn and the selected number of such steps. This gives a clear and repeatable step shape, but ease of use should still be assessed from the drawing, the tread width along the walking line, and the overall stair angle. For a final stair design, this is usually not sufficient without additional verification.
Can these results be used directly for manufacturing a staircase?
For preliminary layout, size estimation and preparation of a sketch, this calculation is usually sufficient. But if the staircase is a permanent building structure, structural capacity, fixings, guards and compliance with local requirements should be checked separately. This is especially important for timber and steel staircases with long flights and narrow winder steps.