Blondel Theorem – Formula to Calculate Stairs

Next, you yourself will be able to Calculate Stairs using the Blondel’s Law Formula. Let’s see…

The stairs as architectural elements, have the function of allowing to go up and down from one level to another, in a house. This activity can be carried out during the day, several or many times, by the same person.

For these reasons, a Formula to Calculate Stairs is necessary , whose design must be comfortable, guaranteeing the necessary safety for people of different ages and genders.

tread riser ratio

Formula to Calculate Stairs – Blondel’s Law

The French architect Jacques François Blondel , in the 18th century, devised a very useful formula for calculating stairs.

In the so-called Blondel’s Law , the ideal relationship that should exist between the tread (horizontal part of the step) and the riser (vertical part of the step) of a staircase was established. This law establishes that:

2C + 1H = 64cm, where C is the riser and H is the stair tread.

According to François Blondel , the ideal ratio is:

  • C=18cm
  • H=28cm

How to Get the Measurements of a Stair?

The result of this formula for calculating stairs and its regulations varies slightly from one author to another, and also from one country to another.

In Germany , for example, the architect Ernest Neufert, in his book “Art of Projecting in Architecture”, established that 2C + 1H = 62.5cm , which would result in a slope or inclination of the stairs, much softer and more comfortable, but it would also result in a longer staircase, which would occupy more area and space within the home or building.

In regulations of some countries, it is established as the ideal inclination or slope of the ladder at 35 degrees , which, implicitly, is establishing another relationship for the 2C + 1H formula.

In general, a slope of the stairs between 20 and 40 degrees of inclination is accepted.

In Spain, since 2006, the regulations for the construction of buildings establish that Safety to prevent the risk of falling establishes the requirements that must be met when designing and building stairs.

Then it is specified that: the tread (H) and the riser (C) along the same stair, must satisfy the following relationship:

  • 540mm≤2C
  • H≤700mm .
Formula to Calculate Stairs
Measurements of treads and risers of a staircase

Actually, any of the relationships between treads and risers explained above are adequate, and all of them have certain advantages and disadvantages, depending on the space measurements in which the stair is to be built.

Also, a distinction must be made between stairs for interiors or exteriors , and stairs for public or private spaces, since the measures that are proposed are not exactly the same.

Stairs for public and outdoor spaces often require higher levels of safety and comfort.

How to Calculate a Stair?

Straight Stairs Calculator

Enter ValuesHeight Between Finished Floor Levels

Difference between floors in centimetersRiser Proposal15.

Proposal for height of steps in centimetersStep Length (Tread)25.025.526.026.527.027.528.028.529.029.530.030.531.0

Step length in centimetersResultsNumber of Risersriser heightNumber of FootprintsStair Length

By now you should have been able to calculate your own STAIR DESIGN. Let’s see a practical example and then I’ll tell you how to calculate the volume of a staircase.

Practical Example of Calculation of a Stair

If we want to make a staircase between two floors, with a height difference of 280 cm, we must divide the height of 280 cm by the height of a step, which is 18 cm.

280cm / 18cm = 15.55

So we will have 16 steps, since it must be rounded up.

Formula to Calculate Stairs
Staircase with 16 risers

Subsequently, we divide the free height (280cm) by the number of risers (16 risers) to find the measurement of each riser.

280 cm / 16 steps = 17.50 cm

That is, each step will have a riser height of 17.5cm.

So, now we apply Blondel’s Law like this, 2C + 1H = 64cm, where C = 17.5cm

How to calculate a ladder?
Stair calculated with 17.5cm riser to save 2.80m in height

Remaining 2x (17.5cm) + H = 65cm

We clear H and we have that H = 65cm – 2 x (17.5cm)

H = 30cm, that is, the footprint is 30cm.

3d staircase

The stair, to save a 280cm difference in level, would have 15 treads of 30cm, 16 risers of 17.5cm, and a length (looking at the plan) of 480cm .

I also explain with a practical example, how to calculate a STRAIGHT STAIR WITH 3 METERS HEIGHT .

If you want a TABLE TO QUANTIFY THE CONSTRUCTION MATERIALS of a concrete staircase, visit this link.

If you want to know what THE PARTS OF A LADDER are, continue with this other link.

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