How to correctly calculate the stairs with a platform. Stair calculation: basics and rules

impossible to imagine without. This design is both functional and decorative. They are mounted screw or march - it does not matter. The main thing is that the staircase fits into and at the same time improves the appearance, while possessing the necessary strength characteristics. Let's talk about types today. staircase structures and figure out how to calculate all the main dimensions. Calculators specially developed by our team will help you calculate the stairs online.

In addition to being organic appearance in the interior, these structures need a margin of safety. Replacing or repairing is a laborious task, which means that even at the stage, you should think through all the nuances.

Important! The design steps are thought out so that they are convenient. Numerous studies have shown that deviation from standard sizes 2-3 cm sharply reduce the ease of movement on it.

The safety of residents depends on how correctly the installation work is done. This means that you should understand the nuances as carefully as possible, understand how to calculate, determine possible options and only after that stop the choice on one or another form.

Photo examples of various designs: solutions for home craftsmen

Design plays important role in . You should think through everything to the smallest detail. To do this, we suggest that you familiarize yourself with some examples that will help to accept the right decision. For some, samples will become an impetus that will help create an original masterpiece, others will take as an example already turnkey solution.

Amazing, isn't it? At first glance, it seems that one cannot do without a professional designer, but if you dig deeper, it becomes clear that a home master can create such masterpieces without special education. All you need is imagination and courage to implement the most extraordinary ideas. But come up original design- only half the battle. Some of the specifications, which should have . Let's talk about them.

Related article:

In the article we will consider what designs are, what are the advantages metal frame how to properly illuminate straight and spiral staircases, as well as recommendations from specialists that must be taken into account during installation.

Technical parameters: the optimal angle of inclination of the stairs and the dimensions of the steps

The type of construction is selected depending on the area of ​​​​location. So, if the free space for installation has dimensions of 1.5 × 1.5 m or more, then a flight ladder is installed. If you need to place a compact structure, a screw version is suitable.

It's important to know! The screw version fits more neatly into any interior, but has one drawback - the inability to move large-sized furniture and things. This is also taken into account when building a structure.

A slope of 25÷33° is considered convenient for walking, but this is not always possible due to the small space. The limit is a tilt angle of 45°. With a smaller slope, a ramp is mounted, and with a larger one, side or even wall ladders are used. About the size of the steps themselves: according to research, optimal size 28÷30 cm wide and 16÷18 cm high. These are not empty numbers for example. This size is convenient for the movement of an adult.

When calculating the steps of the stairs, it is taken into account that the width of the march must be more than a meter. Otherwise, it will be inconvenient to move around on it. The exception is screw structures in rooms where there is not enough space for a full span. Do not forget about. They are required with a flight of stairs of three or more steps.

There are enough varieties of such structures. We note the main ones:

• straight spans;
• two-march;
• three-march;
• screw;
• designs on bowstrings;
• With winder steps(rotate 90° or 180°).

We will return to the types of structures later. It is worth devoting a separate section of today's article to this. But the materials from which they are made should be considered immediately.

Determination of the main technical parameters of the stairs

Such structures are made not only from or metal. Stone, glass or concrete is often used. However, the most widespread combined options containing multiple materials.

Useful information! Stone or concrete is not suitable for wooden houses due to the large weight. But wooden, metal or glass structures, and especially combined ones, will come in handy. Such designs can decorate any interior.

design constraint flight of stairs only the imagination serves. Bold ideas give amazing results, although fanaticism is useless. As the stairs are made, new ideas can be born that will add uniqueness to the finished product. Experience here is rather harmful, imposing certain limits. House master, without suspecting it, can adhere to the line of the previously created design.

To create a drawing, you can refer to the stairs, which are now quite a few on the Internet. However, the most important is the calculation of the dimensions of the steps of the stairs and its steepness. And for this you should consider various options.

Calculation of a wooden staircase: some nuances of calculations

If you make all the calculations yourself, then the dependence of the length of the horizontal projection of the flight of stairs on the height and angle of inclination can be denoted by the formula:

D = H / tgα , where

• D is the length of the horizontal projection;
• H - height;
• α - tilt angle.

However, there is no need to calculate the values ​​manually. This can lead to an error that can become critical when building a structure. We suggest using the online calculator, which has already included all the necessary formulas. The ladder calculation program will eliminate the human factor and protect against errors.

Staircase in most cases is a mandatory attribute country house. In addition, structures of this type can be used in duplex apartments or offices. Stairs today perform not only a practical function, they are also additional elements interior and bring zest to the overall design of the room.

Staircase options

According to certain design features, stairs can be represented by a marching, spiral or combined variation. Which of the above types of structures is most appropriate to use in a particular case will depend on the total area and features of the layout of the room.

It is necessary to ensure that installed design answered all necessary requirements ergonomics.

marching stairs

Such execution of a ladder differs in reliability and extreme simplicity of production.

The design in this case will consist of one or more marches (this is the name of a rectilinear fragment with steps).

To maintain ergonomics, the number of steps in one march should not exceed sixteen pieces.

Spiral staircase

This design consists of a support rod, around which steps are arranged in a spiral.

The total area of ​​the classic variation of the spiral staircase does not exceed one square meter, as a result of which it can be installed even in small spaces. A feature of this staircase is the possibility of its location anywhere in the room.

Combined ladder

In this case, we are talking about an arched architectural structure.

The combined staircase combines elements of mid-flight and spiral structures. This allows you to implement design tasks of any level of complexity.

Before starting the corresponding calculations, it is necessary to take into account the features of the layout of the room. You should also take into account total area rooms. It may be necessary to create a project that will coordinate all further actions during the implementation installation work. On the initial stage the following points should be taken into account:

• distance from the floor of the first floor to the ceiling;
• features of the location of the walls;
• features of the placement of doorways;
• the total area of ​​the premises;
• planning features.

The height of the individual steps of the stairs must be absolutely identical. It is recommended to avoid the formation of differences in these indicators. The width of the landing should be equivalent to the width of the march. The length of one rectilinear fragment with steps should be no more than 3 m. Minimum in this case, it will be kept at a level of 1.5 m.

The size of each individual step depends on the total number of these elements. The length of the span or section is also taken into account. The total width of the stairs is determined by the required level of it bandwidth. The minimum figure for one person will be 0.7 m.

The level of comfort during ascent and descent will depend on the height of the steps. Most often, this indicator varies in the range from 12 to 20 cm. The optimal depth of the steps is 28-30 cm. Subject to the implementation of an uneven step, these indicators should be calculated based on the total length and height of the structure.

How to determine the angle of inclination?

The angle of inclination should be such that a person can proportionally move forward while walking up the stairs. The formation of the final indicator will depend on the height and width of the steps.

In most cases, it is recommended to stop at a number that is in the interval from 23 to 37 degrees. At the same time, it should be noted that a very steep angle of inclination can somewhat complicate the procedure for lifting and transporting heavy objects up the stairs.

Important! How more angle slope of the stairs less space may be required for placement. However, a too steep angle significantly complicates the procedure for climbing to the second floor.

If the angle of inclination is less than twenty-three degrees, then you can resort to installing a ramp. Such a flat design will facilitate the descent and ascent. It should also be noted here that the stairs, the angle of which is more than forty degrees, can become an insurmountable obstacle for users.

Handrail and railing options

When carrying out the appropriate calculations before installing the stairs on the second floor, the parameters of the railings and some of the railings of the structure should be taken into account. In particular, the following points need to be determined:

• baluster height;
• handrail length;
• the height of the support posts;
• railing width.

The optimal width of the railing will be equivalent to 100 mm. This indicator will contribute to the comfortable operation of the stairs by an adult. Railings are most often located at a height of 900 mm. Based on this, it is easy to conclude that the height of the baluster will be approximately 800 mm. In this case, you should pay attention to the way the baluster is installed. If this element is mounted in grooves, then its length should be slightly larger. The final indicator is formed taking into account the depth of the groove.

As for determining the height of the support posts, here you should also pay attention to the installation features. If the support used is installed on the steps, then its length will be identical to the height of the baluster. Provided that the rack vertical post installed on the floor, standard height add the height of the placed support.

The length of the railing must be equivalent to the length of the flight of stairs. Total length given element may fully correspond to the dimensions of the stairs or be slightly larger. The increase in indicators tends to increase if the handrail goes beyond the steps.

The ladder structure can be prefabricated or monolithic. The first variation of the structure is not very popular, since the installation work in this case will be associated with certain difficulties. In addition, all relevant work must be carried out at the construction site.

Prefabricated stairs made of large-sized elements are in great demand. The installation procedure of the entire structure is not associated with special difficulties. This variation of stairs can be used not only in private country house but also in buildings public interest. Additionally, marches of structures of this type can be reinforced with frames.

Marches with solid steps are presented in the form of a panel, which is significantly reinforced on the sides due to the use of special stiffening ribs. The upper plane of such a panel is distinguished by a stepped structure.

To make the staircase comfortable for use, it is necessary to fulfill many requirements for its design and shape. It is also important to calculate the stairs for safety reasons, because it must withstand all the loads placed on it. Dimensions may vary depending on their location and room parameters. In this article, we will provide you with information on calculating the dimensions of stairs with all acceptable standards.

Why is it necessary to calculate the stairs

During the design phase of a house, a lot of calculations are performed, but we are only interested in those that relate to stairs. The calculation of the stairs to the second floor in an apartment or house must be performed primarily for safety reasons and to save effort and money.

Performing calculations helps determine:

• how much material is needed for construction;
• what loads must correspond to the materials to give required strength designs.

Regardless of whether it will be a staircase to the 2nd floor, to the attic, to the basement or viewing hole in the garage, carrying out calculations will help not only do the job correctly, but also protect against injury, eliminating the possibility of structural damage.

How to calculate the stairs to the second floor

Using, which you can find on our website, is one of the easiest ways to calculate.

Also, for the calculation, you can use the formulas from this article.

Ceiling opening size

The calculation of the ceiling opening must be performed in order to avoid inconvenience during the operation of the stairs. The distance from the stairs to the edge of the ceiling opening should be such that a person does not need to bend down when descending and ascending.

Ceiling openings are classified according to the form of execution and are divided into:

The width of the march to the 2nd floor will depend on the functionality of the stairs:

• For safe use the width of the span should be at least 90-100 cm.
• To transfer furniture between floors and for a calm divergence of two people in the opposite direction, a width of 125-150 cm is required.

The length of the kosour or bowstring

In order to determine how long the bowstring (kosour) should be, you must use the formula

where a is the length of the march; b - the height of the stairs; c - the length of the bowstring (kosour).

The calculation of the stairs in a private house can be started by determining the number of steps, it will be convenient to use the table below. It shows the dependence of the number of steps on the height of the stairs and risers. Dividing the height of the stairs by the height of the riser, we get a number, rounding which, we get the desired number of steps.

The size of the riser depends on the angle of inclination of the structure. The figure below shows the optimal tilt angles for different types stairs and ramps. Optimal Angle slope in residential premises is 24-37°, which corresponds to approximately 140-180 mm, in the figure the area is highlighted in green.

To determine the step width, it is more convenient to use the formula shown in the figure, the dependence of the step width (600-640 mm) and the height of the riser. There are a number of restrictions that must be adhered to when calculating:

• the edge of the tread should not hang down more than 50 mm;
• the width of the tread should not be less than 100 mm.

The width of the steps based on the formula is: 600 - 2 * 160 \u003d 280 mm.

In the event that the width of the steps is less than the calculated one, this will lead to big problems when descending due to the fact that the foot will not fully stand on the step.

On what the parameters of the steps can depend

The main parameter on which any straight staircase, turn or spiral depends, is the size of the room in which it is located.

When not very large area the room in which it is necessary to fit a straight single-flight staircase will have to change the angle of inclination of the structure to a steeper one in order to reduce the length of the bowstring. Changing the angle of inclination directly affects all the parameters of the steps, except for their length, the dependence is shown in the figure.

To maintain the optimal riser height, the step width must be reduced.

Calculation of the angle of inclination of the stairs

Depending on the angle of inclination, the stairs are divided into:

• ramps - angle of inclination up to 30 °;
• For residential premises - a slope of 30-45 °;
• 45-75 ° - attached, steep;
• more than 75 ° - evacuation, fire.

Knowing the principles of calculating the angle of inclination of the stairs, you can design and build a comfortable staircase.

Features of the calculation of turning stairs

There are a number of ways. The calculation of a U-shaped staircase is practically no different from the calculation of a staircase with a 90 ° turn.

by the most in a simple way calculation is the method of proportions, you can find options for calculations by other methods on our website. You can also use the construction calculator of our site to calculate U-shaped and L-shaped stairs.

Graphic method

The method is based on the proportional placement of steps at the turning point, the calculation of stairs with a turn of 90 and 180° is identical. Consider, for example, the calculation of a U-shaped staircase:

1. Draw a staircase (top view) on a scale with the designation of the extreme steps to the turn and the central turning post.
2. Draw an axis in the middle of the stairs (in the center of the support post).
3. On both sides of the axis, you need to draw an equilateral right triangle.
4. Divide the hypotenuse of the triangle into 3 equal parts.
5. We connect the central turning column with the marks on the hypotenuse with lines, as a result of which each of the sides, separated by the axis from paragraph 2, is divided into 3 parts.

Features of the calculation of spiral staircases

Principle d is in many ways similar to the calculations of simple mid-flight and turning stairs, but, of course, there are points that should be paid attention to due to design features.

When making a spiral staircase to the second floor with your own hands, you should be aware that there are certain limits in the size of spiral staircases, beyond which it is not advisable to go for reasons of safety and ease of use:

• step depth in middle line not less than 200 mm;
• at a distance of 150 mm from the support post at least 100 mm;
• in the wide part at the edge no more than 400 mm;
• ladder diameter from 1300 to 3300 mm;
• march width from 530 to 1430 mm;
• opening diameter from 1300 to 3300 mm.

Consider, for example, the calculation of a spiral staircase for a room with a height of 2700 mm and a march width of 1000 mm.

1. It is necessary to calculate the diameter of the future staircase and, accordingly, the diameter of the ceiling opening. The main thing when calculating to double the width of the march is not to forget to add the diameter of the central support column, with such a width of the march it should be at least 200 mm. As a result, we get: D \u003d 1000 + 1000 + 200 \u003d 2200 mm. This size falls within the parameters described earlier.
2. Let us determine the radius of ascent, which is equal to the sum half the width of the march and the radius of the support. Rn=500+100=600 mm. We take half the width of the march due to the fact that in the middle of the span the most optimal width tread, which is 200 mm.
3. Knowing the radius of rise Rn=600 mm and the width of the tread 200 mm, we determine the number of steps per one turn of the stairs using the formula: L=2πr/200=2*3.14*600/200=18.84. Rounding the resulting number, we learn that one turn consists of 19 steps.
4. To calculate the height of a step, it is necessary to determine the distance between the turns of the stairs. Consider an example of the use of stairs by people whose height is not more than 180 cm. In this case, the distance between the turns should be at least 200 cm. Thus, we determine that the height of the steps is 2000/19=105 mm.
5. The number of steps for our room with a height of 2700 mm is 2700/105=26 pcs.

steps, and, accordingly, on the entire staircase:

This option will be more economical, due to the fact that the entire staircase will require 9 steps less.

Which of the options to use is up to you. The difference is that the climb spiral staircase steeper than on a simple march, and the use of less high steps makes it easier to climb.

How to calculate the attic stairs in the house

An attic folding ladder is calculated in the same way as a simple attached ladder, based on the fact that the angle of inclination is 65 °. To determine the length of the stairs, you must use the formula.

The dream of any person to have their own apartment, and also better house. A building with several floors indicates that the owner has a decent income or is a jack of all trades. But it's not about whether any two- or three-story house needs a staircase. It is good if, during installation, its specialists took into account all the nuances: the slope, height and width of the steps. Then the ladder will be equally convenient for climbing for both old people and children, and most importantly, it will also be safe. Let's find out how to calculate the steps for such a staircase.

Height and width of stairs

Steps of different height and width are a direct threat to humans. After all, going down them in the dark, you can stumble, twist your leg or miss the steps and fall. Therefore, before designing a staircase indoors, make a drawing and calculate how many steps you need, what height and width they will have (the plane for the foot).

Stair slope

Ideally, when the stairs have a slope of 24-38º. If the angle of inclination is more than 45º, then it is required to go down such a steep staircase with your back forward. However, it saves space in the room, for a flat one you will need more space.

Calculation of the number of steps

To calculate the number of steps, we need two values: h and l, where h is the height of the stairs, l is the length. It is very easy to measure these values: h is the distance from the floor of the first floor to the floor of the second, l is the projection of the stairs onto the floor of the first floor, in other words, the distance that the product will take on the first floor. Let's say that h = 2.4 m, and l = 3.6 m, and we need to calculate steps for a ladder of such parameters.

Knowing these measurements, you can choose the number and size of steps. It is comfortable if one step has a riser height of 16.5-23.5 centimeters, and a tread width (a) of 22.5-26 centimeters. Based on this, we calculate the number of steps (n). To do this, you need to divide the total height (h) by the height of the riser (h1), we have a comfortable h1 = 20 centimeters, we get:

n = h / h1 = 240 / 20 = 12 steps.

Therefore, the width (a) of the tread of the step will be equal to the projection of the flight of stairs on the floor (l), divided by the number of steps (n):

a \u003d l / n \u003d 360 / 12 \u003d 30 centimeters, a little more than the above norm, which is not so important.

Materials for the manufacture of stairs

For the purchase of materials, we also need a size, namely the length of the stairs itself (c). Geometry will help us find this value: based on the theorems on right triangles, the square of the hypotenuse (c) is equal to the sum of the squares of the legs (a, b):

c² = a² + b² = h² + l² = 2.4² + 3.6² = 5.76 + 12.96 = 18.72 m²;

Stair angle

Also according to the rules right triangle we can easily calculate the slope angle of the stairs:

sin α \u003d h / c \u003d 2.4 / 4.33 ≈ 0.55;

α ≈ 34°, this is a good, comfortable slope.

Before proceeding with the manufacture of stairs, carefully recalculate, preferably several times, the results obtained. Carefully take measurements so that there are no mistakes and the flight of stairs is exactly the same as you drew. Thanks to a clear reduced diagram of the product on graph paper, you can find errors in the calculations. With the help of this figure, it will be much easier for you to calculate the number of steps and other parameters.

Designing a staircase in a private house is a complex process that includes determining the length and width of the flight of stairs, the angle of rotation and inclination of the structure, dimensional characteristics and the number of steps. Sometimes, without knowledge from the field of mathematics, geometry and architecture, it can be difficult to make calculations on your own. In this case, online and offline design programs can come to the rescue. What services should be used to obtain accurate, visual results - read the article.

In order to create a staircase project on a sheet of paper or in a graphical editor, it is necessary, first, to calculate the basic dimensions of the structure: the width and length of the march, the height and angle of the stairs, the dimensional characteristics of the steps. This can be done both with the help of formulas and independent calculations, and by means of automatic programs for calculating stairs.

The main components of the structure leading to the second floor, which the staircase drawing should contain:

• The location of the structure in the plan;
• Type of construction (angular, mid-flight, screw, etc.);
• Height and angle of inclination of the stairs;
• The number of steps (main and winder, if the design implies such);
• Tread width and riser height of each individual step;
• The dimensions of the lap above the step.

In some drawings, supports and poles, stringers and bowstrings, type of risers (straight, radius, etc.) are indicated.

All values ​​must be in the same scale (1:100, 1:50).

Calculation of the design of the stairs using programs: advantages

In order for the design to turn out to be convenient, reliable and safe, and to assemble it was not difficult, all calculations must be accurate. Even small deviations from the norm or not taking into account any parameters (for example, not entering the bowstring width into the scheme) can complicate the installation of the structure, cause costs and material for alterations. As for professional construction programs, the probability of an error in the calculations is reduced to zero here: the program takes into account everything, even the most small parts, and impeccably adheres to the accepted building codes and standards.

At the same time, the calculation with the help of programs makes it possible to obtain a three-dimensional model of the structure, which can be viewed from different angles; provides ample opportunity to instantly change the parameters of the stairs and allows you to move away from standard schemes and drawings.

Popular stair design software

Today, there are a huge variety of both online and offline programs for designing stairs of various types. All of them differ in the principle of operation, the way the results are presented, and the interface language. The most popular and convenient are programs that have been developed for specific purposes. So, for example, in AutoCAD you can draw an excellent three-dimensional model of a staircase, but for this you will have to produce preliminary ones yourself. While specialized programs perform all calculations automatically and require only the input of the initial data of the room.

To date, the following programs are considered the most convenient:

1. Stair designer. This is a universal program for creating designs. various types(angular, screw, marching, etc.) from various materials(marble, wood, stone, reinforced concrete, etc.). Calculations in the program are based on the Blondale formulas, architectural norms and principles. The resulting 2 and 3D models contain all the necessary constituent elements (railings, pillars, steps, etc.) and their dimensional parameters. The scheme can be easily printed or converted into AutoCAD and finalized there.
2. Consultec Staircon is a program designed for 3D visualization, automatic recalculation of estimates, control of installation and manufacture of stairs. Consultec, although it belongs to the category of professional, but requires minimal system resources, and its interface is not only intuitive, but also made in Russian, which is a tangible plus. The results obtained during the design process can be adjusted depending on your own wishes.
3. Staircase Compass is effective tool, which has a wide library of mechanisms for building and assembling stairs (SNIP system, welding, etc.). And the presence of several options for models makes it possible to choose exactly the design that fits into the interior in the best way.

All calculations in the programs are made taking into account international and state standards safety, building codes and engineering recommendations.

You can download programs quickly and free of charge using the Internet protocol Torrent.

Sema stair constructor

Sema is a convenient, multifunctional construction program that has been specially modified for designing stairs and creating three-dimensional models of future structures.

The main differences between Sema and other similar programs are:

• Wide library (Sema can offer not only wooden connections for mounting stairs, but also plastic fasteners, tongues, brackets);
• The possibility of introducing external images and floor plans into projects;
• Possibility of combining different types of structures;
• Preview function;
• Integration of the program with equipment for processing and assembling stair elements (templates for creating stairs can be automatically transferred from the program to CNC machines).

Calculation of stairs online 3d

You can design a staircase and create its three-dimensional model without installing programs, having only an Internet connection. For this use online programs for modeling.

Often, to build, you need to specify:

• Stair type (straight or curved);
• Dimensional characteristics of the opening (length, width);
• Width and length of the structure;
• The desired number of steps (if the design suggests, then the number of winder and lower steps).

In addition to the visual result, some online constructors display textual recommendations (for example, “LS-225m ladder is suitable for climbing to a height of 2.7 to 2.8 meters”) and construction drawings of the structure indicating all dimensional values ​​in metric system, the total number of steps, the name of the material of manufacture.

AutoCAD - stairs (video)

Today, everyone has the opportunity to simply, quickly and efficiently build an accurate, three-dimensional staircase model with their own hands. This is realized thanks to online and offline construction programs, which not only provide a visual design of the future stairs, but also perform complex calculations, taking into account the optimal values ​​for comfortable and safe operation designs. Programs do not limit the imagination and do not set limits, they allow you to combine different kinds designs for maximum comfort and spectacular view stairs. All that remains is to decide on your own preferences!