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How to Calculate Stair Steps

From the Blondel rule to using BIM software: here’s how to calculate stair steps for user comfort and safety

Internal stairs serve as vertical connections between different levels in a building, whether it’s a mezzanine, an upper, or lower floor. Designing stairs requires a precise evaluation of measurements, considering the height difference to overcome and consequently, the number of steps and the plan layout. One crucial aspect in creating a staircase is the optimal calculation of the rise and tread, essential elements to ensure comfort and safety during use. Incorrect ratios between the rise and tread are serious trip and fall hazards. Let’s explore all the rules to correctly calculate stair steps and how the use of 3D building design software can be immensely supportive.

Determining the rise/tread ratio: the Blondel Rule

In the field of staircase design, one of the key concepts is the ratio between the rise (height of the step) and the tread (depth of the step). One of the most known formulas is the “Blondel rule,” which states:

2a+p=62/65 cm

where a represents the height of the rise, and p represents the length of the tread.

This ratio is commonly used; however, it has evident limitations, especially on low step heights. For minimal heights, the result is unsatisfactory, and in fact, the toe tends to hit against the rise.

Beyond the Blondel Rule: André Hermant’s Proposal

Architect André Hermant introduced another perspective in determining step proportions, considering the movement during stair ascent. Hermant formulated a ratio based on walking speed and step length at different speeds, emphasizing that the speed remains constant even with different inclinations. The formula proposed by Hermant:

h*p=600

where h represents height and p the step, leads to different proportions compared to the Blondel rule but can be adapted to various conditions.

Other calculation proposals

Many other scholars have ventured into formulas and rules to achieve the right proportion between rise and tread, such as Sacchi, Bosco, Colombo, and other English authors like Warth.

Here’s a table below that, given the rise value, expresses the tread value according to different theories.

 RISE TREAD – SACCHI TREAD – BOSCO TREAD – WARTH 12 38 34 36 13 36 33 34,7 14 34 32 34,7 15 32 31 32 16 30 30 30,7 17 28 29 29,4 18 26 28 28 19 24 27 26,7 20 22 26 25,4

Based on experience, for an internal staircase, it’s recommended to adhere to the following values:

• Minimum tread depth 28 cm;
• Maximum rise height 19.7 cm;
• Minimum rise height 15.2 cm.

Additionally, it’s essential to observe several other rules, including:

• All steps should be equal, at least for each floor level;
• A resting landing every maximum of 15 steps;
• Landing platforms with a width not less than that of the ramps;
• Straight-axis ramps;
• etc.

To know more, I recommend reading also:

How to design a spiral staircase using a BIM model: professional and technical guidelines

Cantilever Staircase: Where Engineering Meets Modern Design

Calculating and checking stair steps with a BIM software

To verify that the designed staircase has comfortable step heights and that no design errors have been made, which could be embarrassing and inconvenient during the construction phase, you can use BIM software for 3D building design.

With the support of BIM software, you quickly create the 3D model of the staircase, using the specific parametric object that allows you to set the staircase’s shape, tread length, height difference to overcome, structural type, etc. Once these parameters are entered, the software automatically calculates the height that each rise must have to overcome the indicated height difference. Hence, there’s no need for manual calculations by dividing the inter-floor height by the number of steps; the software automatically processes the calculation, and the technician only needs to carry out verifications based on project choices, staircase usage (public, private, fire escape, interior/exterior, etc.), and prevailing regulations.

The 3D model also allows you to quickly hypothesize different design solutions and choose the most convincing one. You have a multifunctional tool to create photorealistic renders, project video presentations, and virtual tours within the complete model, inclusive of materials, details, and finishes.

Internal Staircase Design | Executive Table

Directly from the 3D model, you can automatically create numerous project sections and check the ramp and step heights to ensure the right distance between the tread and the upper floor’s intrados. You have full control over the project, avoiding errors that could slow down works on-site and result in additional expenses for your clients.

Lastly, you can use the same BIM model to perform staircase calculations in compliance with technical construction standards, using a structural calculation software.