U-Shaped Stair with Landing
About U-Shaped Stair with Landing Calculation
This calculator determines the geometry of a U-shaped stair with landing and a 180-degree turn based on an intermediate landing. It helps define the dimensions of the flights, rise and tread values, landing level, pitch angle, and the calculated lengths of stringers or carriage beams for a timber or steel structure.
The calculation is suitable for preliminary staircase design when the opening length, opening width, and total height are known. The result is useful for checking layout, preparing drawings, and coordinating the main dimensions before detailing the connections.
Guidelines and recommendations
Calculation model
Geometric model. The staircase is treated as two straight flights connected by a horizontal landing. The calculation uses the opening dimensions in mm, the total height between finished floor levels in mm, the landing width in mm, the number of lower and upper treads, tread thickness, nosing overhang, gap between flights, and the dimensions of the stringer or carriage beam.
Height distribution principle. First, the total number of rises is determined. For the lower flight, the calculator always adds one rise to the number of lower treads. For the upper part, the position of the top tread is also taken into account. If the top tread is below the second-floor level, one additional rise is added to the upper flight. If the top tread is at the second-floor level, no additional rise is added.
R = H / Nrises
Riser height. Here, R is the calculated height of one rise in mm, H is the total height between levels in mm, and Nrises is the total number of rises for the whole staircase. This is the value shown as the final riser height.
Landing level and height allocation
Landing. The landing level is calculated from the total height of the lower flight. For this purpose, the number of rises in the lower flight is multiplied by the calculated height of one rise.
Hland = (nlower + 1) × R
Meaning of the result. The value Hland shows the elevation of the top of the landing relative to the lower floor level. This value is needed to check that the 180-degree turn fits within the opening height and does not conflict with the slab or floor structure above.
Upper remaining height. After the landing level is determined, the calculator calculates the remaining height up to the upper level. If the top tread is set at the second-floor level, no additional rise is subtracted from the total height. If the top tread is below the second-floor level, one rise is reserved separately. This affects the number of risers, the length of the upper stringer, and the handrail length.
Tread depth and pitch angle
Horizontal run. The landing width is subtracted from the opening length. The remaining distance is distributed between the flights. To calculate the tread depth, the calculator uses the larger of the two tread counts in the flights. This means the tread depth is selected from the longer section so that both flights remain geometrically consistent.
T = (Lopening - Blanding) / max(nupper, nlower)
Final tread depth. The resulting step depth includes not only the calculated tread but also the nosing overhang. If risers are included in the calculation, their thickness is also added to the geometric depth.
G = T + Soverhang + triser
Meaning of the selection principle. The calculator shows the final tread depth G as the working horizontal step dimension. When risers are included, this value increases because the actual construction thickness of the vertical element is taken into account.
Pitch angle. After the rise height R and the horizontal tread T are determined, the flight angle is calculated as the angle of a right triangle.
α = arctan(R / T)
Practical guideline. On this page, the convenient range is highlighted as 30-40° for the pitch angle, 150-200 mm for riser height, and 270-320 mm for tread width. This is not a structural capacity check. It is a geometric guideline related to walking comfort.
Step width and gap between flights
Step length. The length of one step across the flight is taken from the opening width with the gap between flights deducted. The calculator divides the remaining width into two symmetrical flights.
Bstep = (Bopening - Zbetween flights) / 2
What this means. The larger the gap between flights, the smaller the usable tread length in each flight. This affects both comfort and the required dimensions of the fabricated parts.
Stringers and carriage beams
Base inclined step length. For one stringer or carriage beam step, the calculator first determines the distance between adjacent treads along the inclined line of the flight.
Lstep = √(R2 + T2)
Lower stringer, upper edge. The upper edge of the lower stringer is calculated from the inclined length between the lower level and the landing, with the tread thickness taken into account. This length depends on the number of lower treads, the rise height, and the pitch angle.
Lower stringer, lower edge. For the lower edge, the width of the stringer or carriage beam is additionally considered. As a result, the lower edge is shorter than the upper edge by a value that depends on the member width and the pitch angle.
Upper stringer. The length of the upper stringer is calculated as the sum of the inclined steps in the upper flight. In this geometric model, the upper and lower edges of the upper stringer are shown as equal, which means the calculator uses the same final dimension for this part.
Purpose of the result. These lengths are convenient for preparing parts, but they do not replace verification of cross-sections, deflection, or support details. For final sizing of timber members, Eurocode 5 EN 1995-1-1 is commonly used. For steel members, Eurocode 3 EN 1993-1-1 is commonly used.
Risers and handrails
Riser height. If risers are included in the calculation, their visible height is defined as the difference between the rise height and the tread thickness.
hriser = R - ttread
Number of risers. The number of risers is taken as equal to the total number of rises. The length of each riser is taken as equal to the step length across the flight.
Handrails. For the lower flight, the handrail length is taken from the upper edge length of the lower stringer. For the upper flight, one calculated tread depth is added to the inclined length if the top tread is below the second-floor level. This allows for the additional exit at the upper level.
Normative references
Geometry and usability. This calculator solves a geometric layout task rather than a full code-based staircase design. For the general design basis of buildings in Europe, EN 1990 is commonly considered together with EN 1991-1-1 for permanent and imposed actions.
Structural verification. If the staircase is made of timber, the final verification of load-bearing members, joints, and deflection is usually performed according to EN 1995-1-1. For a steel frame, the usual reference is EN 1993-1-1. For residential buildings, local requirements for guards, clearances, and safe use should also be checked.
FAQs
Why is the number of rises not equal to the number of treads?
This is because the staircase is calculated by vertical level changes rather than only by the number of horizontal treads. In the lower flight, there is always one additional rise, and in the upper flight this depends on whether the top tread is below the second-floor level or flush with it.
Why does the tread depth depend on the longer flight?
The calculator uses the larger tread count of the two flights to distribute the available opening length according to the governing section. This approach helps maintain consistent geometry for the U-shaped staircase with a landing.
What does the landing level mean in the results?
This is the elevation of the top of the landing above the lower floor level. It is useful for checking headroom under the slab, turning comfort, and the geometric connection between the lower and upper flights.
Can these results be used directly to fabricate stringers?
For preliminary marking and blank preparation, yes, because the calculator provides the calculated lengths and the base staircase geometry. Before manufacturing a real staircase, it is still advisable to verify the actual support details, finishing build-ups, material tolerances, and structural capacity according to the relevant European standards.
Does the calculator verify staircase strength?
No. It primarily calculates the geometry of the U-shaped staircase rather than the structural resistance of the construction. A full engineering verification requires loads, support conditions, material, cross-sections, and checks according to the relevant Eurocodes for timber or steel.