L-Shaped Stair with Landing (Quarter-Turn)

About L-Shaped Stair with Landing Calculation

This calculator determines the geometry of an L-shaped stair with landing and a 90° turn based on the opening dimensions, floor-to-floor height, number of steps in the lower and upper flights, flight width, tread thickness, stringer parameters, and optional risers and handrails.

The results include the rise and going of the step, the staircase angle, the landing level, the lower and upper stringer lengths along different edges, as well as riser dimensions and the estimated handrail length. The calculation is suitable for layout selection, walking comfort checks, and preparation for fabrication or detailing.

Reference points and recommendations

Principle of the geometric calculation

Total staircase height. The starting vertical dimension is the floor-to-floor height H in mm. This value is divided by the total number of rises, after which the uniform rise of one step is determined.

h = H / N

Here h is the rise of one step, mm. N is the total number of rises. In this calculator, it is formed from the lower flight, the upper flight, and the position of the top step relative to the second-floor level. If the top step is below the floor level, one additional rise is added to the count. Therefore, the final value depends not only on the number of steps in the flights, but also on the selected stair termination option.

Landing level and height distribution

Landing. The landing level is calculated as the sum of the rises of all steps in the lower flight. In this calculation, the lower flight includes the lower steps and the rise onto the landing.

Hpl = Nlow × h

Here Hpl is the landing level, mm. Nlow is the number of rises up to the landing. This value is important because the lengths of the lower and upper stringers are then calculated from it.

Step going and the effect of the landing

Horizontal division. For each flight, the calculator first determines the available plan length. The landing width is subtracted from the opening length or width, and the remainder is then divided by the number of steps in the corresponding flight.

btop = (L - Bpl) / ntop

blow = (W - Bpl) / nlow

Here L is the opening length, mm. W is the opening width, mm. Bpl is the landing width, which in this model is equal to the flight width, mm. ntop and nlow are the numbers of steps in the upper and lower flights. The final calculated going is taken as the smaller of the two directions so that the staircase fits inside the opening in both flights at the same time.

b = min(btop, blow)

This choice means that the calculator uses one uniform going for the whole staircase and bases it on the more restrictive plan limitation.

Nosing and actual tread depth

Effective tread depth. After determining the basic going from the opening, the calculator adds the tread nosing. If the riser option is enabled, the riser thickness is also included in the total geometric depth of the tread element.

bstep = b + a + tr

Here bstep is the final tread depth as an element, mm. a is the nosing, mm. tr is the riser thickness, mm. This should be understood as follows: the calculator separately determines the geometric stair step and separately forms the size of the tread as a physical part.

Staircase angle

Flight angle. The stair angle is determined from the ratio between the step rise and the basic going without using the element depth created by the nosing.

α = arctan(h / b)

The result is shown in degrees. Therefore, when the going becomes smaller or the rise becomes larger, the angle increases. This is the parameter that the calculator compares with the common practical comfort range of 30-40°.

Walking comfort check

Practical reference. Although the script itself does not use a separate comfort formula to block the result, usability is conveniently checked by the classic relationship:

2h + b ≈ 600-640 mm

If the value is noticeably smaller, the staircase is usually too shallow. If it is noticeably larger, the climb becomes steeper and less comfortable. For residential stairs, rises of about 150-200 mm and goings of about 270-320 mm are often used, which matches the ranges additionally indicated in the calculator results.

Stringer lengths

Calculation along the slope. The basic length of one step along the flight line is calculated as the hypotenuse of a right triangle formed by the step rise and its basic going.

lstep = √(h2 + b2)

For the upper flight, the stringer length along the lower edge is calculated as the product of the number of upper steps and the length of one step. If the stringer width is specified, the calculator adds a correction for the sloped end cut, so the length along the upper edge becomes greater.

Ltop,bottom = ntop × lstep

Ltop,top = Ltop,bottom + k × tan(α)

Here k is the stringer width, mm. For the lower flight, the calculation starts from the vertical difference between the stair base and the landing, after which the upper-edge length is obtained along the slope, and the lower-edge length is reduced by a correction related to the stringer width and the angle. For this reason, the calculator provides two values for each stringer, one along the lower edge and one along the upper edge.

Risers

Riser height. If this option is enabled, the riser height is determined as the difference between the step rise and the tread thickness.

hr = h - ts

Here hr is the riser height, mm. ts is the tread thickness, mm. The number of risers is taken as equal to the total number of rises, and their length is taken as equal to the flight or landing width. This gives a quick fabrication size without detailed modeling of fixing joints.

Handrails

Estimated handrail length. For the lower flight, the handrail length is taken as equal to the sloping length along the line of ascent. For the upper flight, a horizontal part corresponding to the tread depth as an element is added to the sloping length if the top step finishes at the second-floor level.

This is an approximate calculation for estimating the blank length. For ordering completed railing systems, turning components, extensions beyond the first and last posts, and the connection details of the joints are usually considered additionally.

Typical ranges in practice

Residential stair dimensions. In private houses, a flight width of about 800-1000 mm, a wooden tread thickness of 35-50 mm, and a nosing of 20-50 mm are often used. A smaller width saves space, but the stair becomes less comfortable to use. A larger width improves comfort and increases the mass of the structure.

Top step position. If the top step is below the second-floor level, the staircase receives one additional rise and a different height distribution. If the top step finishes at floor level, the total number of rises is reduced by one compared with that arrangement. This directly affects the step rise, the angle, and the stringer lengths.

Standards reference. In Europe, stair geometry for residential use is usually coordinated with national building rules, while the design of load-bearing members and loads follows the Eurocode system. For the overall design basis and combinations of actions, EN 1990 Eurocode. Basis of structural design is used. For imposed loads on stairs and landings, EN 1991-1-1 Eurocode 1. Actions on structures. Densities, self-weight, imposed loads for buildings is used. For timber stringers and treads, EN 1995-1-1 Eurocode 5. Design of timber structures is applied, and for steel load-bearing members, EN 1993-1-1 Eurocode 3. Design of steel structures is used. If the stair belongs to industrial access, additional reference is commonly made to EN ISO 14122 Safety of machinery. Permanent means of access to machinery.

FAQs

Why does the step rise change when I change the position of the top step?

Because the calculator recalculates the total number of rises across the full floor-to-floor height. When the top step is below the second-floor level, one additional rise appears, and the total height is divided into a larger number of equal steps.

Why is the step going not selected separately for each flight?

In this model, one uniform going is used for the whole staircase with a landing. The available going is first calculated for the lower and upper flights, and then the smaller value is taken so that both flights definitely fit inside the specified opening.

What do two stringer lengths for the same flight mean?

A stringer has a section width, so its upper and lower edges have different lengths along the slope. This is useful for preparing blanks and for understanding the real material consumption, especially when the stringer or carriage is wide.

Can this calculation be used as a final stair design?

It is suitable for selecting dimensions, checking comfort, and preliminary detailing. For final fabrication, clearances, supports, fixings, loads, material thicknesses, and the applicable building requirements in the country of use are usually checked additionally.

Is this calculator suitable for both timber and steel staircases?

From the geometry point of view, yes, because the calculation is based on the opening dimensions, height, number of steps, and flight parameters. But the load-bearing capacity of the members, section sizing, and construction details for timber and steel must be checked separately under the relevant European standards.