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How to correctly calculate the stairs formula. Correct calculation of staircase parameters for a private house. Calculation of wooden stairs

When you undertake work such as a metal staircase with your own hands, calculations in this matter are extremely important. On the one hand, it may seem that calculating the design parameters for ascent and descent is not so difficult, but in practice, during the manufacture of stairs, a lot of serious defects may be revealed that cannot be corrected. And then you will have to re-do not only all the calculations, but also the resulting design.

Quite often used for tasks such as calculation metal stairs a program called a calculator. It greatly facilitates the calculation of parameters. But even when using it, do not forget that it is better to master the technology according to which the calculation is carried out thoroughly yourself in order to be able to control and correct the data obtained if they do not fully correspond to the existing conditions of your premises.

Parameters used in calculations

The calculation of a metal staircase to the second floor, as well as the structure and any other material, is carried out on the basis of special formulas where the main parameters are used.

Before you begin the calculations, you should decide on the location of the structure in your home, the location landing and other nuances.

• It is best if your design connects exactly those rooms where there is high level pedestrian load. For example, it would be most advantageous to place the entrance to the second floor next to the corridor or hallway.
• Designs with one or two flights will take up enough large area. Therefore, the installation of such stairs in small spaces undesirable. In order to save space, it is more advisable to install a spiral staircase or a prefabricated one in a small room.

• The calculation of the metal staircase and its placement must be done so that the exit to the second floor is located in the very convenient place. It is impossible for there to be a sloping roof directly above the exit, as happens if your house has attic floor, because in dark time days, you risk getting injured when moving up stairs.

• In its upper and lower parts, the structure must be equipped with free platforms, the minimum width of which must be at least 0.8 m. This factor has a significant influence on the choice of location for the stairs, because not every room allows the installation of large structures.

Note! Usage sliding stairs or folding type designs can be called additional option. In order to obtain a stable and reliable design and at the same time save space, it is better to give preference to a spiral staircase.

Main design parameters

Calculation metal frame stairs are the first thing you have to do. Of course, using modern calculators, you can plan your design much faster, but the effectiveness of this approach is lower, since the programs do not always take into account the relationship between the key parameters of the staircase.

The width of the frame depends on the purpose of the stairs:

• basement and attic spaces usually not used as often as residential ones, so you can afford to save on space and take a staircase that is only 0.8 m wide;
• the structure for the second floor in a residential area must have a minimum width of 1 m; if you are planning a main staircase with an exit from the living room, then you can make a frame 1.5 m wide, provided that the area of ​​your room allows the installation of such a large structure;
• double-flight structures are placed as closely as possible; you can take a frame 0.75 m wide.

Now you can proceed to calculating the height parameter of the structure.

Note! This indicator depends on such an element general design like a skylight. Therefore, in your calculations you should definitely build on it.

When calculating the height it is necessary to take into account:

• lifting height should be measured from flooring on the first floor to the same level on the second floor;
• clearance, which is the distance from the surface of the step to an obstacle located above it, as a rule, such an obstacle can be the ceiling of the upper floor;
• The minimum clearance size should be 1.9 m or more, otherwise you will have to expand the passage to the second floor or make the structure more flat.

Note! The clearance requirements for basement and attic stairs are not as stringent, since such structures are used very rarely.

Planning steps and landings

When you are calculating a metal staircase, the platform plays an important role, because it allows you to make small corrections to the angle of elevation.

This method works under the following conditions:

• having the same number of steps, with equal parameters, and the length of the flight, you can use this element to reduce the angle of rise of the structure;
• using a simple design option to facilitate your calculations, you can consider the platform as a large step, and you have the opportunity to increase the flight of stairs due to it;
• The most optimal placement of the site is strictly in the middle of the march.

Note! The staircase requires more reliable and durable fastening than other steps.

You can use special programs and applications that help you design and calculate the stairs.

Free applications, of which you can find quite a lot on the Internet, are also suitable for such purposes.

Such a design stage as calculating the steps of a metal staircase is carried out last. Such calculations are based on the average width of a human step, as a rule, it is 60-60.5 cm. The formula used for calculations looks like this: Z + 2M = 60-60.5 cm, where M is the riser height indicator, and as Z – an indicator of the width of the tread.

If we summarize the parameters of the steps for standard projects, then the height is approximately 15-20 cm and the width is 25-35 cm.

Note! You should not deliberately increase the width of the tread, since such a staircase will not be comfortable and you will constantly lose your step.

The overhang of the step should also not be made too large; 5 cm will be enough.

Screw design parameters

To calculate a spiral metal staircase, you need to take basic measurements, which are taken in the same way as in the case of conventional structures.

Let's look at the example of calculating a staircase with the following parameters:

• opening width – 2 m;
• floor height – 2.5 m;
• twist angle – 2,700.

Basic calculations:

1. The diameter should always be less than the width of the opening, so it is calculated in our case as follows: 2 m – 0.2 m = 1.8 m.
2. To calculate the length of the step you need to take half the diameter, that is, the radius: 1.8 m: 2 = 0.9 m.
3. Using the formula L = 2Р, you can calculate the circumference. With our parameters it should be: 2x3.14x0.9 = 5.65 m.

Note! A spiral staircase cannot be called a complete circle, so the result obtained is multiplied by 3/4 (this figure corresponds to 2700). The resulting length of the staircase is 4.24 m (outer radius). If the rotation angle is 1800, then this indicator is divided in two.

1. You can calculate the estimated length of the stairs based on the indicator of a convenient line of movement, which is located at a distance from the center - 2/3R. The calculations look like this: 4.24 m x 2/3 = 2.83 m.
2. With a floor height of 2.5 m, you can calculate the number of steps (steps of 15-20 cm). Formula: 250:17 = 14.7.
3. To find out the exact step height, we round the previously obtained figure (14.7) to 15, and according to the formula we get: 250:15 = 16.75 cm.

Note! If, after calculating the exact step height, you do not get a whole number, you can round this figure to tenths (in our case it will be 16.7 cm), and taking this into account, you can simply make the first step of the staircase lower.

To do this, a calculation is performed: 250–14x16.7 = 16.2 cm.

Working with the calculator

The calculator for calculating a metal staircase will allow you to calculate the most important structural parameters. Even the most standard application can cope with this task. At the first stage, you just need to enter all the initial data into the program.

Source data includes:

• the height of your opening;
• length of the lifting part of the stairs;
• the planned number of flights in the structure and steps on each of them;
• step parameters (tread, overhang, etc.).

As a result, the program will provide you with the necessary drawing, which shows all the dimensions necessary for the manufacture of the stairs.

To make a staircase comfortable for use, it is necessary to fulfill many requirements for its design and shape. It is also important to calculate the ladder 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 size of stairs with all acceptable standards.

Why is it necessary to calculate the stairs?

At the house design stage, many calculations are performed, but we are only interested in those that relate to stairs. Calculation of the stairs to the second floor in an apartment or house must be done primarily for safety reasons and to save effort and money.

Performing calculations helps determine:

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

Regardless of whether it is a staircase to the 2nd floor, to the attic, to the basement or inspection hole in the garage, carrying out calculations will help not only do the work correctly, but also protect from injury, eliminating the possibility of structural destruction.

How to calculate the stairs to the second floor

Using, which you can find on our website, is one of the simplest methods of calculation.

You can also use the formulas from this article for calculations.

Ceiling opening size

Calculation of the ceiling opening must be performed to avoid inconvenience when using 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 over when descending and ascending.

Ceiling openings are classified according to their design and are divided into:

The width of the flight to the 2nd floor will depend on the functionality of the staircase:

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

Length of string 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 – height of the stairs; c – string length (stringer).

When calculating a staircase in a private house, you can start 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 required 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 the inclination in residential premises is 24-37°, which corresponds to approximately 140-180 mm, the area is highlighted in green in the figure.

To determine the width of the step, 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 making calculations:

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

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

If 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 leg will not fully stand on the step.

What can the parameters of the steps depend on?

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

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

To save optimal height riser, it is necessary to reduce the width of the step.

Calculation of the angle of inclination of the stairs

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

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

Knowing the principles of calculating the angle of a staircase, you will be able to design and build a comfortable staircase.

Features of the calculation of turning stairs

There are a number of methods. Calculation U-shaped staircase practically no different from calculating a staircase with a 90° turn.

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

Graphical 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. Let's look at the example of calculating a U-shaped staircase:

1. Draw the staircase (top view) to scale, indicating the outer steps towards the turn and the central turning pillar.
2. Place the axis in the middle of the stairs (in the center support pillar).
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 pillar with the marks on the hypotenuse with lines, as a result of which each of the sides, separated by the axis from step 2, turns out to be divided into 3 parts.

Features of calculating spiral staircases

The principle is in many ways similar to the calculations of simple marching and turning stairs, but of course there are points that you should pay attention to due to design features.

When making a spiral staircase to the second floor with your own hands, you should know 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 midline not less than 200 mm;
• at a distance of 150 mm from support post not less than 100 mm;
• in the wide part at the edge no more than 400 mm;
• staircase diameter from 1300 to 3300 mm;
• march width from 530 to 1430 mm;
• opening diameter from 1300 to 3300 mm.

Let's look at the example of calculation spiral staircase for a room with a height of 2700 mm and a flight 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 the double 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=1000+1000+200=2200 mm. This size falls within the parameters described earlier.
2. Let us determine the radius of the rise, which 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 because in the middle of the span the most optimal tread width is 200 mm.
3. Knowing the lifting radius Rn=600 mm and the tread width 200 mm, we determine the number of steps per turn of the staircase using the formula: L=2πr/200=2*3.14*600/200=18.84. Having rounded the resulting number, we find out that one turn consists of 19 steps.
4. To calculate the height of the step, it is necessary to determine the distance between the turns of the staircase. Let's consider an example of the use of a ladder by people whose height is no more than 180 cm. In this case, the distance between 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, the entire staircase:

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

Which of the proposed options to use is up to you. The difference is that a spiral staircase is steeper than a straight staircase, and using lower steps makes the climb easier.

How to calculate an attic staircase in a house

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

A properly designed staircase fits perfectly into the interior and is as convenient as possible to use.

The staircase allows you to organize access to upper floors building, it is also part of the interior. With its help you can give the room your own special style. You can do the calculation of the stairs to the second floor yourself if you know how.

Is it possible to do the calculations without the help of qualified specialists? Can. In order to calculate the stairs to the second floor you need desire and basic knowledge school geometry. Although advice from professionals will not hurt. You can also use special computer programs for calculations.

What is important for calculating a staircase structure? The correct calculation of the stairs is carried out taking into account the layout and size of the rooms. This will affect the choice of location and type of staircase structure. Do not forget that for interfloor stairs It is not only the area on the ground floor that is important, but also the ability to provide a convenient staircase opening on the upper level.

At the first stage, the following points must be taken into account:

• height from the first floor to the second (room height);
• total area of ​​premises (first and second levels);
• location of load-bearing and interior walls;
• location of door and window openings.

This will allow you to determine the size of the area that can be allocated for the construction of the staircase, the size of the opening for access to the second floor and select the optimal model.

If the area for installing the stairs measures 160x160 cm or more, then it is better to choose a marching one staircase structure. If you have a more modest area, you will have to limit yourself to a screw design.

Straight stairs

A straight flight of stairs (flight) is the simplest option for installation and calculation. This form is very convenient for wooden structure. Straight flights have one drawback - their installation requires a significant area of ​​the room.

Generally accepted norms and construction standards will help you draw up a project correctly and accurately carry out calculations. For example, if the staircase has an inter-level platform, then its width should correspond to the width of the span. In this case, the minimum width of the flight is 0.7 m. One person can go up or down such a staircase.

For comfortable movement of two people, as well as for convenient transportation of large items, such as furniture, to the second floor, household appliances, width flight of stairs should be larger - from 1.2 to 1.4 m.

The length of one straight section with steps should not be more than 3 m ( minimum size- approximately 1.5 m). The steps must be the same height and depth.

Turning stairs

In order to save space in the house, most stairs to the second floor have to be made with turning sections. The easiest way to rotate is to install a platform. There are U-shaped and L-shaped structures, where rotation is realized using winder steps.

Important parameters of the stairs that need to be calculated:

• inclination angle value;
• dimensions of the area between marches;
• step height;
• depth of straight and winder (if provided) steps;
• fencing parameters.

Angle of inclination of flight of stairs

The angle of inclination of the stairs is the angle between the flight of stairs and the horizontal (floor). It is he who is primarily responsible for the convenience of the staircase design. The angle of inclination should allow a person to easily go up/down the stairs.

Building codes and regulations (SNiP) determine the optimal parameters of stairs: the most convenient and safest are staircase structures with an inclination angle in the range of 30-45 degrees. It is these slopes that are chosen for indoor and outdoor stationary stairs. If this angle is less than 20 degrees, install a ramp.

How to calculate stage parameters

When calculating the staircase structure to the second floor, two values ​​are important: the height of the tread and the depth of the tread (the horizontal landing of the step). These parameters determine the degree of convenience and safety when moving (ascending/descending) stairs. It is important to determine them correctly, since these values ​​are involved in the design calculations.

It is convenient to climb stairs when there is no need to artificially increase or decrease the length of the step. The average step length when moving on a horizontal plane is 63-64 cm, and when climbing - 31.5-32 cm.

Based on these data, the height of the riser is most often in the range from 12 to 20 cm (the optimal size is 14-17 cm). The optimal tread depth is determined from 25 to 30 cm. The maximum permissible step depth during the construction of stairs is 32 cm.

Often, in order to save space when installing staircase structures, models are used with one step overhanging the other. This type of steps gives the staircase a lighter and more beautiful look.

Calculation of the sizes of steps of a flight of stairs

Let's consider the option of calculating the main parameters for simple example. Optimal ratios heights and depths of steps used when designing stairs (cm): 19/27, 18/28, 17/29 and 16/30. Perfect option– 17/29 cm.

We use exactly this ratio to calculate such important design parameters as the angle of inclination, flight length, and total number of steps.

The number of steps is easy to calculate: the height of the floor (for example, 270 cm) must be divided by the height of the step (17 cm): 270/17 = 15.9. We discard the fractional part and get the number of steps on the flight of stairs (15 pieces). If the number is fractional, then you can make the first or last step a little higher or a little lower than the rest.

We specify the height of the steps. To do this, divide the height of the room by the number of steps: 270/15 = 18 cm. Thus, the height of each step is 18 cm.

The depth is calculated taking into account the horizontal step width. For calculation, we select a step equal to 63 cm. From this value we subtract the double height of the step: 63-2x18 = 27 cm.

Calculate the area and angle of inclination

Now you can calculate how much space the stairs to the second floor will take up. It is necessary to determine the area of ​​projection of the flight of stairs onto the horizontal plane. It has the shape of a rectangle, one of the sides is equal to the width of the steps (d), and the second (b) is the projection of the length of the flight onto the horizontal.

Formula for sparing a rectangle: S = b x d.

Length larger side rectangle (b) is obtained by multiplying the depth of the steps by their number: 27x15 = 405 cm. The smaller side of the rectangle (d) is equal to the width of the stairs and is selected independently. It is worth considering that the minimum size for one person to move is 70 cm, for two people the minimum is 100 cm.

Now you can start calculating the length flight of stairs. In this simple calculation, the well-known school formula (Pythagorean theorem) will come to the rescue. The length of the march is the hypotenuse right triangle(c), the legs of which are the height of the room (a) and the horizontal projection of the span (b):

c2 = a2 + b2 = 2702+4052

And the required length (hypotenuse) is equal to square root from the sum of the squares of the legs, i.e. c = 486.7 cm or 486 cm (we do not take into account the fractional part).

To determine the angle of inclination of the stairs, you will have to remember the school trigonometry course: the sine of the desired angle is equal to the ratio of the height of the floor (a) to the length of the flight of stairs (c):

cos(α)=a/c, α = arcos(a/c)

Having performed calculations using these formulas, we determine the angle of inclination - 370.

Convenient service for calculating staircase structures

Walling

When developing a design for a staircase to the second floor, it is worth paying attention to the fence in order to install it correctly. The following dimensions are important for installation:

• baluster height;
• length and width of the railing.

The fences are important element. Their standard height(including handrails) should be from 90 to 100 cm. If there are children in the house, additional handrails should be provided (70-75 cm). The design and material of the fence can be anything.

If you build a staircase according to all standards and rules, then it will be comfortable, durable, safe and will last a long time.

When creating the home of your dreams, you need to pragmatically and accurately calculate your strengths and resources. Using the staircase designer on our website, in ten minutes you can not only create a project, but also calculate the cost of the staircase online.

Using simple and uncomplicated tools of our online staircase designer you can:

1. Construct a 3D drawing of a staircase with millimeter accuracy according to parameters such as height, width of the staircase and steps, the number of steps and turns necessary to create a durable and beautiful staircase.
2. Select railings for all flights and indicate the presence of an invitation step, risers and balustrade.
3. The online staircase calculator allows you to choose the material from which the whole staircase or its individual elements will be made. In the production of stairs we use: beech, oak, pine and birch.
4. Set the parameter according to which each element of the staircase will be painted or tinted. You can choose the option without finishing, if necessary.

When calculating, the program for designing stairs will offer you to choose the region of delivery and assembly, which also affects the final cost of the project.

Do not be surprised if the final cost obtained as a result of calculations using our staircase designer is lower than other offers on the market. Modern equipment park with software Our production allows us to rationally minimize the costs of materials and energy resources, compared to handicraft carpentry and carpentry workshops. Usage modern technologies in production, allows us to reduce production and delivery times to the minimum possible in each specific case.

If you encounter any difficulties at any stage of the design, call us 8 800 775 26 76 and our specialists will be happy to help you.

Any stationary ladder in the house must meet certain standards so that its design can ensure safety, as well as comfortable conditions for moving around it. To do this, a calculation is made of a wooden staircase to the second floor, which is not much different from the calculation of a metal or concrete structure. Its correctness depends on many factors, but first of all it is knowledge and experience, the ability to navigate the standards prescribed in SNiP and GOST.

Basic designs of wooden stairs

Any wooden staircase is assembled from several components:

• support beams, which are bowstrings or stringers;
• support column mounted for screw structures;
• steps, the elements of which are treads and risers;
• railings consisting of balusters and handrails.

The strings are located on the sides of the stairs and cover the ends of the steps, which are inserted between the support beams and then fixed. The treads with risers are, as it were, recessed into the staircase structure. If we talk about the stringer, then the steps are laid on top of it. There cannot be more than two strings in a staircase, and stringers, depending on the width of the flight and its design features, can be found from one to three or four (main and intermediate).

The tread is the horizontal part of the step, and the riser is the vertical part. The second component of the stage may be missing in the design. The railing serves for support and safety of a person ascending or descending.

The calculation of a wooden staircase to the second floor depends on its appearance and design features, and stairs are divided into two main groups:

• curved, including screw and with winder steps;
• marching - straight, with intermediate or turning platforms, as well as without them.

Which staircase will be installed is determined based on the size of the room, the dimensions of the staircase opening and the style solution.

How is the calculation made?

First you need to clarify exactly where the staircase will be located and make necessary measurements. To do this, define:

• floor height between finished floor levels;
• the length of the area allocated for the installation of the stairs;
• dimensions of the staircase opening.

The type of staircase design depends on these parameters. Small sizes the opening and the area intended for its installation dictate the need for a spiral staircase, but in this case the calculations will be more complicated. Therefore, we will consider the simplest option - calculating a staircase on stringers with one flight.

steps

At the first stage, the steps of the staircase are calculated - their number and size. The distance between the finished floor levels of two floors is taken as the height of the stairs. To determine the number of steps, its indicator is divided by the expected size of the riser. Its recommended height is 15-18 cm, although standards allow it to be reduced given size up to 12 cm or increase to 20 cm. The figure obtained as a result of division is rounded. This is the estimated number of steps.

It should be noted that one flight cannot have less than three or more than 18 steps. When obtaining a larger number, it would be better to divide the staircase structure into two or three flights, and provide intermediate or turning platforms between them.

Having finally decided on the number of steps, you can calculate the actual size of the riser. To do this, the height of the stairs is divided by the number of rises. The result is the calculated height of the step.

It is important to know that the dimensions of the height and depth of the steps must be the same within the same flight. This is done to ensure that a person’s step does not go astray when moving up the stairs.

At the second stage, they begin to calculate the width (or depth) of the tread. The standards allow their sizes from 23.50 to 35.50 cm, but optimal width considered 28-32 cm. For more precise definition This parameter uses a formula for calculating staircase steps, which indicates that the sum of the height (h) and depth (b) of the step in plan should be 47 cm. In other words, the depth of the tread:

The result obtained is also rounded and taken as a basis if it satisfies optimal sizes. There is another ratio of height/depth of degree, which can also be used in calculations:

Stair length

You can calculate the length of a flight of stairs in a fairly simple way. To do this, you will need the previously calculated number of steps in the flight, minus one, and their calculated width (or depth). These indicators are simply multiplied together.

If the length of the staircase turns out to be too long, then it is made to rotate 90 or 180 degrees and is supplemented with intermediate platforms or winder steps.

An important role in the calculation and design of a wooden staircase is played by the height of the clearance between horizontal plane steps and the lowest part ceiling structure located in front of the staircase. The vertical distance here should be more than 1.90-2.00 meters, so that the person ascending or descending tall I couldn't accidentally get injured.

The calculation of a wooden staircase should be taken with full responsibility. Competent design and compliance with installation technology will ensure optimal conditions its operation.