Do-it-yourself wooden staircase materials and calculations 3 important steps

Determining the required geometric dimensions

To correctly perform the calculations, it is necessary to take into account certain geometric measurements. According to experts, three parameters are mainly important:

height is the distance from the floor surface on the first floor to the floor surface on the second. To correctly determine the distance from the step to the ceiling, you need to take the height of the tallest person in the family and add 100 mm;
the length is equal to the length of the march or the sum of all marches. At the same time, a landing is added between them;
width - the distance of the structure from the wall or the gap between two handrails.

In the diagram you can see the relationship between the angle of inclination and steps

It is necessary to take into account the width of the marching structure:

1 ÷ 1.2 meters - will provide comfortable movement;
1.5 meters - a high level of comfort;
0.8÷1 meter can be used for a ladder installed against the wall;
less than 0.8 meters - for auxiliary models.

Calculated data example

The minimum allowable width for winder stairs is 1.1 meters. The width cannot be less than 1.1 meters for a screw design. The comfort zone starts from 1.4 meters.

The video below shows a simple way to calculate the stairs:

Ladder angle (steepness)

The angle of inclination determines the ease of use of the stairs. A too steep staircase saves usable space, while a flat one makes moving along it more comfortable. The view of the stairs, depending on the steepness, is shown in the photo below. Here you can clearly see at what angle the stairs should be in the living room. The most comfortable option for movement is in green.

The diagram shows different angles of inclination

For your information! Stairs can only be placed in a residential area if the premises on the first and second floors are heated. If not, then the installation is carried out in non-residential premises.

An example of calculating the length, calculating the height and width of stairs in a private house

One of the most important points is the competent calculation of the stairs. Dimensions should be such that it is convenient to move up the stairs. It is necessary to determine exactly what the height and width of the stairs should be.

The height of the step should not be too small so as not to knock down the step. The optimal indicator varies between 150 ÷ 180 mm. The width of the tread should be such that the sole fits completely on it. The best option is from 250 to 320 mm. Often the tread is made with an overhang over the bottom step.

To find out the optimal ratio of width and height, you can use the following relationship:

2h + b = 600÷640, where

h is the step height;
b - tread width;
600 ÷ 640 - the approximate length of a human step, or rather its average value.

Recommendations for step sizes

The disadvantage of the formula is that it does not take into account that the step width can be smaller or larger, and also does not take into account the slope of the march.

Step standards

To calculate the stairs to the second floor more accurately, use the special online calculator below, which uses other formulas.

Method for trigonometric calculation of step dimensions

To determine the distance between the edges of the steps, the following formula is used:

G / sin 63° = (0.5 × L) / sin (27° + α),

Segment G is the hypotenuse in a triangle in which the legs are the width and height of the step.

From here:

h \u003d G × sin α \u003d G × cos (90 - α);
b \u003d G × cos α \u003d G × sin (90 - α).

But to find out the dimensions, it is easier to use the online calculation of the stairs.

Calculator for calculating the optimal dimensions of the steps of a mid-flight staircase

A simple way to calculate the steps is presented in the video below:

Determination of the optimal angle of inclination of the stairs

Almost all stairs have a slope of 45 degrees.The width of the step usually corresponds to 45 foot size, but it should not be less than 30 cm.

Consider the main angles of inclination:

for domestic stairs, the angle varies from 30 to 45 degrees;
for gently sloping structures and ramps - 30;
for attached and steep options - 45 ÷ 75;
utility stairs - more than 75.

There is a certain relationship between the steepness of the stairs and the place of its installation. The following relationship is used for the calculation:

D = H / tan α, where

D - the length of the horizontal projection of the stairs;
H - the height of the flight of stairs;
α is the angle of steepness.

Staircase in a private house as an important element of the convenience of planning

When choosing a material and design, it is necessary to be guided not only by aesthetic preferences, but also by keeping in mind safety and ergonomics. The following criteria will help you choose the right design and materials for the stairs:

location matters - in the center of the hall or as a secondary option in other rooms;
dimensions and area for the construction of stairs;
the level of safety of the structure;
the thickness of the walls to which the ladder will be mounted;
the surrounding interior in the room where the structure will be placed.

Do-it-yourself wooden staircase materials and calculations 3 important steps

Scheme of the ladder structure

There are special requirements and norms of SNiP that must be observed. Before work, drawings and calculations are carried out. For the convenience of calculations, various online ladder calculators are used.

The following technical requirements should be taken into account:

load-bearing walls must withstand the ladder structure;
the supporting parts must be installed at a certain angle and on a special surface;
it is important to maintain the recommended distance between the steps;
railings must withstand a certain load of 400 N;
it is necessary to maintain the correct distance between the bowstrings;
between spans there must also be the required distance;
marches should have a gap and the same slope.

Main constituent elements

The main structural elements can be seen in the table below:

Important components of the ladder structure	What can it consist of (options)
Basic structure	Bowstrings are side elements that support steps from the ends and from below. They look like curved beams. Installed at an angle. Stringers - support the steps in the lower part. Bolts - special bolts that help fix the steps and walls of the building. Support for the screw structure - a vertical stand on which all elements are fixed. Bearing parts can be made of different materials.
steps	The steps can be arched, running, beveled or straight. The stairs can be two-flight or multi-flight. In this case, a step is mounted between the marches.
fences	Guardrails guarantee safe movement. These include the following elements: The baluster is a vertical post that supports the railing; The railing is used to protect marches and platforms; The handrail is an inclined railing element that is fixed on the balusters. Sometimes handrails can be mounted to the wall

11 useful tips

Avoid height differences in stairs. All of them must be exactly the same.
The landing in width should be equivalent to the width of the march.
A rectilinear fragment with degrees in length should not be less than 1.5 m and not exceed 3 m.
The size of the steps depends on their number.
The minimum width of the stairs is 0.7 m, which ensures the passage of 1 person.
The formation of the angle of inclination depends on the parameters of the steps, but it must necessarily ensure a proportional advancement of the person forward.
Less space is occupied by a staircase with a large angle of inclination, but it is more difficult to climb it.
Ideally, the width of the railing should be equivalent to 10 cm.
The optimal height of the railing is 90 cm, and the height of the baluster is 80 cm. At the same time, if it is supposed to be installed in a groove, then this figure is slightly increased by adding the depth of the groove.
The support posts in height should be equal to the corresponding size of the balusters, but if they are installed not on the steps, but on the floor, then the distance from the steps to the floor is added to this height.
The length of the railing and the flight of stairs are equivalent to each other.

Table showing the relationship between step parameters and inclination angle

Do-it-yourself wooden staircase materials and calculations 3 important steps

The dependence of the height of the riser on the number of steps and the height of the ceiling

Competent calculation will save you from mistakes and unnecessary rework, save time and money.

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Calculate a wooden staircase to the second floor

A simple online calculator will calculate the exact amount of required building materials for a wooden staircase. Start calculating right now!

Stair calculation program, free calculation of steps, stair bowstrings

The program for calculating the steps of the stairs will give you data not only on the number of steps required, but also the length of the string of the stairs, the angle of inclination of the stairs, the height and depth of the steps, the height of the riser of the stairs. The tread calculator may recommend that you reduce or increase the number of treads. And also the online staircase calculator will provide you with a summary of “convenient” or “not convenient” stairs according to the parameters you specified.

Convenient stairs. What is she?

The convenience of the stairs is immediately affected by several parameters, such as the angle of inclination of the stairs, the height of the steps, the depth of the steps of the stairs, in some cases even the width of the flight of stairs. The ideal dimensions of the steps are a guarantee of safety. The depth of the steps (the tread of the steps) should be about 28-30 cm (according to the size of an adult's foot), and the height should be 15-18 cm. Having stepped onto the stairs with your right foot, you could have climbed onto the landing of the stairs with your right foot and vice versa, it is really more convenient this way. The height of the stair railings should lie above the center of gravity of an adult, with an average height, the optimal railing height is 90 - 120 cm.The optimal angle of inclination for a straight wooden staircase is between 30 and 36 degrees. If the angle of inclination of the stairs is less than 20 degrees, then the stairs go into the category of ramps, if more than 45 degrees, then into the category of side, folding, where the descent is carried out only backwards, such stairs cannot be called convenient, and even more so are not intended for daily use.

Drawing of a wooden staircase

In addition to all calculations for building materials, the program will draw a drawing of your wooden staircase. Please note that the smaller the angle of inclination of the stairs, the more building materials will be required. It is necessary at the design stage of a country house to decide on the parameters of the stairs and allocate enough space for the construction of a straight staircase.

Step size.

recommended values.

Master Novitsky Oleg Vadimovich in the book "Modern stairs. Design, manufacture, installation. »

(highest commendation to the author and this marvelous work)

mentions the recommended and repeatedly tested values for the rise (h) and tread (a) steps:

h x a = 150×300, 160×300, 170×290 mm .

These dimensions are good, but unfortunately cannot be used if the house is already built and the total height of the stairs (H) is not a multiple of a single step (h).

In this case, we can refer to the calculation formulas:

Formula of convenience and formula of safety.

Widely known convenience formula:

According to this ratio, the stairs will be the most convenient.

The ladder is considered safe if the sum of the dimensions (c) of the width of the tread and the height of the riser is 45 cm. (30 + 15, 27 + 18, 25 + 20).

Accordingly, this equation is called safety formulas.

The difficulty is that these formulas are applicable in a small range of sizes and it is not always possible to realize the necessary proportion in practice. In this case, one should “get” into the indicated formulas with a minimum deviation or use the universal Blondel formula, which takes into account the average step of a person. (more details below ).

In the special literature under the authorship Samoilova V.S. "Modern country house" the following table is recommended:

The height and width of the steps with their different number of steps and slope

Please note: in single-flight stairs, as well as in one flight of two- and three-flight stairs, no more than 18 rises (steps) are allowed within the ground floor. Maximum step height 220 mm

(SNiP 21-01-97)

The maximum step height is 220 mm. (SNiP 21-01-97)

To design a simple wooden staircase on stringers, measure the height between floors (the vertical distance from the bottom floor to the top floor).

By the way, the height between floors is the most “sick” size. In houses made of stone, very often there are deviations from the project by 4-5 cm, and wooden houses are subject to shrinkage and shrinkage (up to 15 cm per floor). Ideally, you should wait for the complete shrinkage of the log house in a few years.

Also, it is better to take the dimensions for calculating the stairs when the finishing floors are laid or to clearly set the horizontal height levels.

So, let the height in our case be: H=278cm.

Choose the height of the riser: let h = 18 cm. dividing the height between floors by the height of the risers, the required number of steps is obtained: 270. 18 = 15

To determine the optimal step width, use the convenience formula. a - h \u003d 12. h \u003d 18 cm. Comfortable tread width: a = 12 + h = 30 cm.

Thus, 15 steps with a width of 30 cm and a length depending on the width of the opening in the interfloor ceiling are required.

Let's check the ladder according to the safety formula: a + h = 46 + 3 cm

In this case: 18+ 30 = 48 cm.

The ladder is safe and easy to use.

( This example of calculations is given by Stolyarov A.N. "We build stairs." )

Back in 1672, a French architect and engineer proposed the following ratio:

in which S is the average step of a person, which lies within 600 - 640 mm .

That. Blondel's formula can be transformed into an inequality:

600

The lower practical result will be min. step rise:

h = 120 mm, a = 400 mm, slope 17 degrees. With a smaller angle, it is no longer a staircase, but a ramp (ramp) - a gentle inclined platform.

h = 220 mm, a = 200 mm, slope 48 degrees. At the upper limit of the Blondel formula, a staircase is not the most convenient, suitable for use only when moving towards the steps.

Going down the stairs is more dangerous than going up, so the ease of use is evaluated on the way down.

An example of the master's thoughts according to the Blondel formula:

We measure the height between floors H = 3050 mm.

We determine the rise of steps h by dividing H by the possible number of rises (n).

With 17 lifts: h = H / n = 3050 / 17 = 179.4 mm. At 18: h = H / n = 3050/18=169.4 mm. At 19: h = H / n = 3050/19 = 160.5 mm.

Next, we calculate the line of motion: A = 5000 mm

The length of the travel line must not be less than the height between floors (H) (otherwise the stairs will be impractically steep ).

In our example: A (5000) > H (3050)

At n=18 tread a \u003d 5000 / ( n - 1) \u003d 294 mm.

(n-1) The actual number of steps is 1 less than the calculated value. This fact is easy to accept if the first step is considered at the floor level.

Blondel step parameter: 169 x 2 + 294 = 632. Therefore, the size is acceptable, organic and lies within the average step of a person.

That. we have determined the width of the tread and the height of the riser for easy movement, but this is not enough to build a comfortable and safe staircase.

The line of play (A) was just mentioned in the reflections. Let's take a closer look at this and other parameters that must be considered when designing stairs.

Stair parameters with 180 degree turn

Do-it-yourself wooden staircase materials and calculations 3 important steps

Rice. 1 General drawing of stairs

Y - opening height - usually determined by the height of the floors of your house
X - the length of the opening - depends on how much space you can allocate in your house for the stairs
E - the width of the stairs - depends on how much space you can allocate in your house for the stairs
Z - the thickness of the steps - the geometric parameter of the material (for example, boards) from which you plan to build a staircase
F - protrusion of steps - the distance by which the upper step will hang over the lower
C - total steps - how many steps will it take you most comfortably to move from floor to floor
P - steps on the lower bowstring - the number of steps to the platform depends on your preferences and the geometric characteristics of the house

Do-it-yourself wooden staircase materials and calculations 3 important steps

Rice. 2 Designation of steps

"Show risers: H" function

Do-it-yourself wooden staircase materials and calculations 3 important steps

Fig.3 Execution of stairs with risers

You can build your stairs with or without risers. This function allows you to see how the design will look like with both options.

"Upper step below floor 2nd floor: SP" function

Do-it-yourself wooden staircase materials and calculations 3 important steps

Rice. 4 Stair version, with the top step below the floor 2 floors

Depending on the mutual placement of the structure and the floor of the upper floor:

The top plane of the top step is flush with the plane of the floor of the top floor;
The upper plane of the upper step is lower than the floor plane of the upper floor by the height of the step.

The choice of this or that mutual placement may depend on: the thickness of the interfloor ceilings, the desired relationship between the number of steps and their height, the length of the blanks for the stringers and the length of the opening, the desired angle of inclination of the stairs, or simply the tastes and preferences of the owner of the house

Please note that in the figure, in which the upper step is below the floor of the 2nd floor, the thickness of the interfloor overlap is greater than in the figure, in which the upper step is at the floor level of the 2nd floor. If the thickness of the floor is less than the height of the step, the stringer simply does not rest against the floor (therefore, when demonstrating the second option, this thickness had to be increased)

"Black and white drawing:" function

Do-it-yourself wooden staircase materials and calculations 3 important steps

Rice. 5 Black and white drawing of stairs

It is useful to use this function in two cases:

If you are used to working with standard GOST drawings, and, accordingly, better perceive graphics without color content.
If you are going to print the results of the calculator.Then you will spend less paint / toner and the visual perception of the drawings on paper will be better. And, of course, this function is used when printing on a black and white printer.

"Change lift direction: LR" function

Do-it-yourself wooden staircase materials and calculations 3 important steps

Rice. 6 View of stairs with different directions of ascent

A specific staircase, which is placed in a certain way in the house, can be approached from the side from two sides or only from one side - when the staircase is in contact with the wall. In the latter case, there are two options for placing the structure relative to the observer:

Rise from left to right;
Climb right to left.

This function allows you to visualize both of these options.

A few more recommendations

If we conduct another small educational program, we should talk a little about the interdependence of the geometry of the stairs and the height of the floors. Height is the difference between the level (mark) of the clean floor of the lower floor and the upper one. Thus, when calculating the floor height yourself, do not forget to include the thickness of the finish (screed, ceramic tile, parquet or linoleum, etc.) in it. In the design of private housing, the most common floor height is 2.8 or 3.0 m, as well as 2.7 or 3.3 m (the main thing: more than 2.4 m and a multiple of 300 mm). With the indicated heights, you can easily place the stairs in the living space, and the accepted dimensions of the steps will meet safety standards.

It is important to take into account in the drawing the thickness of the floor and finish, if any. When the height of the floor in your home is different from the norm, you will have to calculate the dimensions of the steps with millimeter accuracy with your own hands

Do not forget about parameters such as a safe angle of inclination. Also, make sure all risers are the same height. Stepping up stairs with different step heights can be traumatic, so it is better to add all roundings during the calculation to the size of the lower frieze panel

When the height of the floor in your home is different from the norm, you will have to calculate the dimensions of the steps with millimeter accuracy with your own hands. Do not forget about parameters such as a safe angle of inclination. Also, make sure all risers are the same height. Stepping up stairs with different step heights can be traumatic, so it is better to add all roundings during the calculation to the size of the lower frieze panel.

Do-it-yourself wooden staircase materials and calculations 3 important steps

To round the dimensions, you can use a special podium step.

Calculation of stairs to the 2nd floor using an online calculator

There are many online calculators on the network that make it as easy as possible to calculate the stairs and quickly resolve all issues.

The basis of programs for online calculators are the requirements for stair structures and the norms regulated by GOST. An example of one of the good calculators is zamer-doma.ru.

It works simply, just enter data such as height, opening length, number, thickness of steps, the height of their edge, the maximum width of the stringer, as well as the direction of ascent and the orientation of the first step relative to the floor of the 2nd floor to get: • staircase drawing; • length upper bowstring; • the angle of inclination of the structure; • the size of the step between the cuts under the steps on the bowstring; • the height and depth of the steps; • the height of the blunt; • recommendations for changing parameters to increase the comfort of the stairs.

Stair parameters required for calculation on the calculator

Another free online calculator lestnicmir.ru. With its help, you can calculate the most acceptable design, get recommendations for improving its ergonomics.

To do this, you only need to select the type of stairs, enter the required overall dimensions and data on the steps, the calculator will do the rest.

Sketch for the calculation of stairs with a turn

Estimated dimensions of the stair string

Good ladder calculator domaizbrusa-pestovo.ru

It is easy to use - you just need to pay attention to the prompts and enter the parameters required by the system

This online service allows you to perform design calculations. There is also a material calculator here.

The program will also issue a drawing of the stairs, where the main dimensions will be indicated, the marking of the upper points of the steps on the bowstring, the angles at which the steps are located relative to the bowstring, and other defining dimensions.

Stair Calculator domaizbrusa-pestovo.ru

The o-builder.ru calculator will quickly calculate a straight staircase

Standard elements.

Every good owner knows how to count money. Building stairs is no exception. You can save a lot if the details of the stairs at the design stage can be adjusted to the standard of blanks accepted in our country.

Economic considerations can be the key argument that will allow the owner to choose the only option for the location of the stairs from several possible ones.

Step standards:

Available with fillet R 12.5. Invitation steps: H 220 x 400 x 1200, R200 and H220x400x1400, R200

A triangular winding step of a non-standard size to order is calculated as a rectangular (from it simply cut out the necessary ). Therefore, it is advisable to order rectangular. The cost is identical, and trimmings will come in handy in the work.

Large steps can be made from furniture board sizes: 38 x 400 x 2000, 38 x 500 x 1500, 38 x 500 x 2000, 38 x 700 x 1500, 38 x 1000 x 1000, 38 x 1100 x 1100, 38 x 1200 The same shields can be used for landings.

Available in 18 mm thickness. Width: 180 and 120 mm. Length: 900, 1000, 1100, 1200, 1300, 1400 mm.

Available in 18 mm thickness. Dimensions: 200 x 2000, 300 x 2000, 350 x 1000, 350 x 1500, 350 x 2000, 350 x 2500, 350 x 3000, 350 x 3500

Section: 80x80, 100x100.

Length: 1200, 2000, 2500, 3000.

Of course, other sizes are available on request.

Standards: 40 x 350 x 2500, 40 x 350 x 3000, 40 x 350 x 3500, 40 x 400 x 4000, 50 x 300 x 3500, 50 x 350 x 3500, 50 x 400 x 4500

Sections: 40x70, 45x70, 45x80, 45x90, 60x60, 70x70, 70x90, 80x100

Length: from 3500 to 6000 mm.

Round diameter: 30 and 47 mm.

The square part of others: 40x40, 45x45, 50x50, 60x60, 70x70, 80x80,

Diameters: 75, 95, 115, 140, 145 mm.

In addition, it makes sense to get acquainted with the price list of the nearest supplier within walking distance even at the stage of calculations.

So, it's not the gods who burn the pots! We hope we managed to dispel the myth that the design and construction of stairs is available only to the elite. Read the articles, literature to which we referred in this text, take measurements, sketches and drawings.

In fact, the task in the bottom line looks simple: Based on the layout of the house, the location of the stairs, the aesthetic preferences of the owners, it is necessary to calculate the parameters given in this article, which must be organically entered into the norms of comfortable and safe movement in a country house or multi-level apartment.

Comfort and goodness to your home!

Features of constructive calculation

Thanks to our resource, you have already been able to get acquainted with the types of staircase designs, and with the main building materials used for their manufacture. In a residential building, the most common are mid-flight stairs made of wood, less often - metal or reinforced concrete structures. Before proceeding with the element-by-element design of stairs with your own hands, you need to estimate the length of the flight of stairs, select the material and calculate the bearing capacity of the staircase frame.

Do-it-yourself wooden staircase materials and calculations 3 important steps

Even a complex, at first glance, design can be assembled without problems on your own, if you approach this issue correctly.

To determine the bearing capacity, it is customary to divide the entire structure into separate beams - necessarily statically determinate. Depending on the type of pinching of the flight of stairs - rigid on both sides, articulated, or maybe even cantilevered - a formula is selected to determine the main force factors

What is especially important to consider when calculating the structure with your own hands? Walking and running up the stairs is a kind of dynamic influence, even if it is insignificant. Therefore, the load-bearing structures of the stairs must have sufficient rigidity, which will ensure a deflection of no more than 1/400 of the span.

The total load (permanent + temporary) on flights of stairs and landings of a residential building should be no more than 300 kg / m2.

Ways of fastening the supporting stringers of a wooden ladder to the platform beam.

Getting acquainted with the rules for calculating steps

It has been scientifically confirmed that the energy costs for overcoming a horizontal distance for a widow are less than the energy costs for climbing an inclined surface. Thanks to this, the staircase formula has been practically established, which will be as comfortable and safe as possible for operation: the size of the tread and twice the height of the riser should give an average step for an adult. The projection of the human step is considered to be equal to an average of 600 - 640 mm. Then, denoting the height of the riser with the letter a, the width of the tread with the letter b, the formula will look like: 2a + b \u003d 600-640 (mm).

Alternative Method for Calculating Step Sizing

You can also calculate these parameters in a simpler way: a + b = 450 (mm). This value can be adjusted by 20 mm from the larger or smaller side.

Following these recommendations, we can conclude that the step must provide a comfortable step when the foot rests on the tread with the entire plane. Therefore, for the tread, a width is assigned in the range of 200-320 mm. Most often, the tread is taken equal to 300 mm, and the height of the riser is 150 mm. These geometric dimensions guarantee that it will be comfortable for you to move up the stairs without danger to health.

By making the tread hinged, you can increase its width. Note that the length of the overhang over the lower step is taken within 50 mm for reinforced concrete stairs or 30 mm for wooden stairs.

Do-it-yourself wooden staircase materials and calculations 3 important steps

An example of overhanging steps in a staircase on the bolts.