Stairs are an important and responsible attribute in every home. They must provide comfort, reliability and safety for every resident. It is desirable that the staircase structure takes up little space in its area. And in order for it to meet all standards, it must be designed correctly.
How to calculate a staircase: the basics
The most common material for making staircases is wood. It is considered the “warmest” and most pliable material, which should be worked with very carefully. The most common types of wood are beech, oak, ash, birch, larch and pine.
To make calculations for any type of stairs, you must first determine three sizes. First, you need to determine the level of the finished floor and then measure the height of the structure along the wall from it. Secondly, its length should be measured, starting from the wall and ending with the expected completion of the span. And thirdly, you need to find the length flight of stairs, resorting to the Pythagorean theorem. In this case, the lengths of the legs are the found dimensions of the height and length of the staircase; in this case, you need to find the hypotenuse of the resulting right triangle, i.e. march length.
To make it comfortable to walk on the stairs, the depth of the steps should be about 30 cm, and the height should be about 16 cm.
Knowing the dimensions of the steps, you need to divide the length of the flight of stairs by these dimensions, and you will get their number.
For convenience, you need a width of at least 80-90 cm. If it is intended for household purposes, i.e. leads to the basement, then it is better to make it about 120 cm. If the structure is directed towards attic room, then it can be made narrower, about 70-80 cm.
Should be 40-45°. The most comfortable is the staircase design, which is inclined at an angle of 45 °. But due to the fact that it takes up a lot of space, it is rarely used in construction. You can also choose an acute angle of inclination of 30-36 °, especially since such a design will take up no more than two meters on the floor. It will be convenient to climb up this installation, but you can only go down backwards due to the steepness of the inclined descent.
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Calculation of stairs
Required:
- selected low-knot wood for bowstring.
Let's take a closer look at how to make the calculation correctly. Any staircase structure consists of flights and landings. It is important that the width of the platforms is not less than the width of the march. Marches consist of steps and load-bearing beams, which are called bowstrings or stringers. They are made from thick and wide boards, the cross-section of which is 80-100x200-250 mm, or they are made from two narrower boards.
The steps consist of treads and risers, the width of which must be correctly calculated. The steepness of the stairs, as well as the ease of walking along them, is determined by the ratio of their sizes. It is necessary that the person’s foot fully stands on the tread, i.e. this is on average about 30 cm, and the average step length was 60-70 cm, which means that the height of the riser is 14-16 cm. In this case, the following formula for calculation applies: the sum of two risers plus the width of the tread is equal to the length of the average step of a person. Considering the tread thickness is 3 cm, it turns out that one step takes up 30 cm horizontally and 15-18 cm vertically.
The obtained figures are necessary to calculate the stairs for the house correctly. Let's give an example: if the height between the first and second floors is 3 meters, and one step measures 30 cm by 15-18 cm, then you get 17-20 risers. In this case, the last step is the floor on the second floor. Next, you need to divide the lifting height of the staircase structure by an integer in this range. It’s better if it’s even, and it will work out exact height steps, consisting of the thickness of the tread and the width of the riser. Let's say you need to make 18 steps, then the height of the step will be 300:18 = 16.7 cm. Such a structure should be divided into two flights of stairs and be sure to make it with a turn.
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How to make a turn correctly
The staircase structure can be turned in three ways. One of them is for a spiral staircase, which is one big turn. It is very compact and takes up little space, but has a fairly large steepness. Since in one 360° revolution the staircase must rise at least two meters, the flight must have from 13 to 15 steps. Due to the design, the width of the tread should be small, so the steps of the spiral staircase are narrow and high. It is best installed either in the attic or in a utility room.
Marching stairs need to be rotated 90° or 180° using platforms, or you can use special steps in the form of a trapezoid. A horizontal landing is arranged if the space allows. Such a staircase consists of straight elements and has classic look. You can make a window on the site itself, which will add elegance and additional lighting during the day. If this is not possible, then the rotation of the staircase structure must be done directly by steps. In this case, in a certain place, maybe not in the middle, you should start installing treads in the form of a trapezoid, which set the rotation of the staircase by 15 ° or 30 ° for each step. As a result, they rotate it to the desired angle.
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 designer stairs you can:
- 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.
- Select railings for all flights and indicate the presence of an invitation step, risers and balustrade.
- The online staircase calculator allows you to choose the material from which the whole staircase will be made or its individual elements. In the production of stairs we use: beech, oak, pine and birch.
- 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.
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Any stationary staircase in the house must meet certain standards so that its design can ensure safety, as well as comfortable conditions for moving along it. For this purpose a calculation is made wooden stairs to the second floor, which is not much different from the calculation of 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 bowstrings in a staircase, and stringers, depending on the width of the flight and its design features, you can find 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 so that when a person moves up the stairs, his step does not go astray.
At the second stage, they begin to calculate the width (or depth) of the tread. Standards allow their sizes from 23.50 to 35.50 cm, but the optimal width is considered to be 28-32 cm. To more accurately determine this parameter, a formula for calculating stair steps is used, which indicates that the sum of the height (h) and depth (b) the steps in the 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 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 the horizontal plane of the step and the step itself. bottom ceiling structure located in front of the stairwell. The vertical distance here should be more than 1.90-2.00 meters, so that a tall person climbing or descending cannot accidentally injure himself.
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.
The creation of a staircase is preceded by the project development stage. At the design stage, the engineer:
Of course, it is better to trust any work to professionals. But if you want to save 30-40% of the cost of the stairs, then the described work can be done yourself using special software.
Online 3D calculation designer
Anyone can design a 3D model of the staircase of their dreams. There are online services for this on the Internet.
They work quite simply. The user must set the following parameters:
- type of stairs;
- march length;
- width and height of the step;
- construction material.
Additionally, you can select a tint color from the list provided and decorative design designs.
Similar programs can be found on the websites of staircase manufacturers. In this case, you can not only look at the staircase you created yourself, but also find out how much it will cost to manufacture it from a specific manufacturer.
DIY design - calculator program
Well, if you need to design a staircase from scratch, you will need a calculator program. Today there are programs that specialize in designing stairs. These include StairCon, Stair Designer, Compass/ND, Consultec Stairon.
With their help you can:
Typically, in order to get finished project, the following initial data is sufficient for the program:
- type of stairs;
- width and length of the opening;
- opening height;
- overlap thickness.
Construction calculator Zhitov
The described programs, of course, will facilitate the design task and allow you to save a considerable amount, but they themselves are not cheap.
As an alternative, you can use Zhitov’s construction calculator, which will help you calculate a wooden, metal or reinforced concrete staircase online.
The design of a single-flight staircase begins with the program requesting the following data:
- desired step sizes;
- dimensions of the protrusion on the steps;
- opening dimensions;
- minimum stringer width;
- the position of the initial step in relation to the floor level of the 2nd floor;
- direction of rise.
Based on this data, the program draws a drawing indicating the main dimensions of the structure and the angles of the steps in relation to the string, with markings of the main dimensions of the steps.
It should be noted that design in the program is carried out taking into account ergonomic requirements. According to which, the slope of the stairs should be 30-40, the height of the step should be no more than 25 cm, and the depth of the step should be 28-31 cm.
Well, if you want to creatively approach the process of creating a staircase for own home, then you can, armed with a calculator, pencil and paper, perform the calculation and drawing yourself.
How to calculate the stairs correctly
Screw metal
The design of a spiral staircase begins with measurements of the height of the room (H) and the size of the opening (D 1). The height of the room is measured from the finished floor level of the lower floor to the floor level of the upper floor. The size of the opening determines what diameter (D 2) the staircase can be installed.
The diameter of the stairs is taken to be slightly smaller than the opening. To make climbing the stairs comfortable and safe, the diameter is 1500-2000 mm.
Having determined the diameter, find the length of the step (D 3): D 3 = D 1 /2-d, where
d is the internal diameter. It is taken taking into account the diameter of the support post. Typically this value is 100-200 mm.
For further calculations, it is necessary to determine the angle of rotation of the stairs. If the entrance and exit from the stairs are on the same line, then the rotation of the stairs is 360 0.
At the next stage, the length of the march is determined using the formula: L = 2πR, R = D 2 /2. Since you need to determine the length of the march along the ascent line, and it retreats from the edge of the room by 2/3, the formula takes the form: L = 2*2/3πR.
Knowing the length of the march and choosing the tread depth (h 1), you can calculate the number of steps (n): n= L/ h 1. In this case, the optimal tread depth is 25-27 cm. If the calculation results in an odd number, then it is rounded. As a rule, the level of the upper step coincides with the floor of the upper floor, so it is not taken into account in the calculation.
If you divide the height of the room by the number of steps, you will find out its height. The normal height of the steps is 17-18 cm. If the height is greater, then it is necessary to increase the number of steps.
To make sure that the staircase fully complies with ergonomic standards, it is necessary to calculate the depth of the tread along the line of movement and along the outer edge. To do this, you need to divide the length of the march by the number of steps. The resulting tread depth along the movement line should be 20-25 cm, and along the outer edge - 30-35 cm. The tread depth inside the march can be calculated or taken as 100-200 mm.
Based on these calculations, a drawing of a spiral staircase is constructed and calculated required amount materials.
How to correctly calculate a wooden staircase to the second floor
With a rotation of 90 0
Before starting the calculation, measure the height from the floor of the first floor to the floor of the second floor and the dimensions of the opening in which the staircase will be installed.
And the width of the step (b) should be within 27-30 cm. You can check how comfortable the staircase is after calculations by multiplying the height of the steps by two and adding the width. The resulting value should be in the range of 600-650 mm. Using the same formula, you can calculate the width of the step using the formula: b=650-a*2
In order to avoid resting your head on the ceiling while climbing the stairs, it is necessary to maintain the clearance height within the range of 1900-2000 mm. You can understand whether the designed structure meets this requirement by performing the following calculations:
- Subtract 70 cm from the length of the opening and divide by the width of the steps. The resulting number is the number of steps located above the opening.
- Multiply the value from the first point by the height of the step.
- Subtract the value obtained in the second paragraph from the floor height. This number will be equal to the height of the clearance.
If the number is less than normal, you can do the following:
- increase the opening;
- reduce the number of steps, thereby increasing their height.
If it is impossible to increase the opening, and reducing the steps will lead to the fact that the slope of the stairs and the height of the steps will not correspond to the norm, it is better to design the stairs with a turn of 90 0.
This design consists of two flights located in relation to each other at an angle of 90 0. This allows you to fit the staircase even into a room with small area and with a small opening.
The marches can be connected to each other by a platform or winder steps. The first option is much more convenient, and the calculation in this case is not much different from what has already been described. The main task is to determine at what height from the floor level it is necessary to arrange an intermediate platform.
First, they calculate how many steps are needed for the upper flight, located between the platform and the second floor. To do this, the required clearance height (2000 mm) is divided by the accepted step height (15-18 cm). The resulting number is rounded to whole numbers and reduced by one (since the upper frieze step coincides with the floor level).
To find out at what height the platform will be, the height of the steps is multiplied by their number and this number is subtracted from the height of the floor.
The number of steps for the lower flight is calculated in the same way. Wherein landing when calculating, it is considered a step. The width and length of the platform are taken equal to the width of the stairs.
With a 180 0 turn and a platform - drawings
It is customary to install a two-flight staircase with a turn of 180° when the floor height is more than 3 m.
For convenience, the calculation is performed simultaneously with the construction of the drawing on graph paper. First, the staircase is drawn.
Knowing the width of the staircase, calculate the width of the flight. To do this, subtract the gap value (100 mm) from the width of the staircase and divide the value by two.
Well, to find out what height is allocated to each flight, the height of the floor is divided by two.
Further calculation involves calculating the number of steps. To do this, again, it is enough to divide the height of the march by the height of the step.
Well, in order to determine what the length of the march will be and to construct its horizontal projection on the plan, you need to multiply the number of steps by the width.
The resulting dimensions are transferred to the plan. And then they draw a section of the staircase.
Having the drawings in hand, it will not be difficult to break down the structure in the house.
Online designer of 3D calculations, designing stairs with your own hands - calculator program, Zhitov, how to correctly calculate a screw, metal, wooden staircase to the second floor with a turn of 90, 180 and a landing - formulas, drawings
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In order to perform calculations of the future staircase data with your own hands, you will need to find whole line parameters. If you do not know the basic design rules, you can make serious mistakes, which will further affect the safety and convenience of the design. To make the task easier, we introduced standard specifications and special formulas have been developed.
Types of structures
- straight one-march;
- single-flight with winder steps;
- two-flight with an intermediate platform;
- rotatable 90 degrees (L-shaped);
- swivel 180 degrees (U-shaped);
- with an arbitrary degree of rotation.
Calculating the parameters of a staircase with your own hands may seem like a difficult task for a beginner. In order to avoid significant mistakes, you need to familiarize yourself with the basic indicators, established standards and formulas for calculations.
Options for staircase designs to the second floor
SNiP standards
Before calculating stairs for climbing to the second floor, you need to familiarize yourself with the SNiP and GOST standards. If you decide to completely make the entire structure with your own hands, this step is mandatory.
First of all, you should pay attention to the following parameters:
- Slope. Reflects the angle of inclination of a flight of stairs; for residential premises this indicator should be within 30-40 degrees.
- Number of steps. The exact value depends on the length of the span and the number of marches, the minimum number is three, the maximum is 16 for double-flight models and 18 for single-flight models.
- Site size. If a two-flight structure with a platform is installed to ascend to the second floor, the width of the latter must be no less than the width of the flights leading to it.
- Tread width. Distance from the edge of the step to the riser, optimal distance-29 cm, fluctuations +/-3 cm are allowed.
- Riser height. The distance between steps is considered to be 17 cm as a standard, however, the interval of 14-20 cm does not go beyond the norm.
- Step. The total distance covering 2 treads and 1 riser, the ideal value is 62 cm.
- Width of the stairs. The distance from one edge of the step to the other, for ordinary stairs to the second floor - this is at least 80 cm.
- Dimensions of the staircase. The area of the cage must be sufficient to allow the door to be opened or the person to pass without hindrance.
If the staircase meets all the standards described above, it will be safe and very convenient for movement.
Diagram for calculating the optimal angle of inclination of stairs that meets the standards
In some cases, in particular when the house has already been built and it is not possible to make changes regarding the height of the floors and the layout of the room, deviations from the standard indicators are allowed, the main condition is that the changes made should not seriously affect the safety indicator of the staircase structure.
Opening and dimensions of steps
You can calculate stairs, or rather, steps, only if you have all the formulas available and the basic indicators have been determined. To begin with, they are selected intuitively, based on SNiP standards. You also need to measure the opening; in the future, you can adjust the parameters if some deviations and discrepancies are identified. Since you can calculate the dimensions of the opening for the stairs using a simple tape measure, first measure the distance from the floor to the ceiling, and from the entrance to the second floor to the position of the first step.
In order to calculate the staircase in the house, as well as determine what size the opening should be, you first need to know the number of steps in the flight. Based on this indicator, you will calculate the size of the riser and can use the formula to determine the step. So, let's look at how to calculate the standard stair step. To do this, you need to take the width of the tread and the height of the step. The formula for calculating the step of the stairs is as follows:
2a + b = 60…65
In one step, a person can cover an average of 60-65 cm. This is a comfortable step size, on the basis of which you can calculate the width of the tread (a) and the height of the riser (c).
Measurements required for correct calculation stairs to the second floor
These indicators can also be determined in a slightly different way. To do this, you need to take as a basis such parameters as the height of the rise, the length of the projection and the slope of the stairs. First you need to calculate the lift height:
h = H + D
In other words, you need to sum up the height of the room and the thickness of the ceiling. From here you can find out the number of steps:
Based on the number of steps and the height of the tread, you can calculate the projection length of the staircase, focusing on the opening. We calculate the projection length of the stairs:
If you know the height of the rise and the length of the stairs, you can find out the slope or steepness of a straight staircase:
Based on these data, you can calculate more accurate indicators for a straight staircase:
a = h/n
Convenience and safety
In addition to the dimensions of the structure itself for lifting to the second floor, there are several more criteria for assessing convenience and safety that must be taken into account. Therefore, it is not enough to simply correctly calculate the stairs using the specified formulas; it is necessary to determine the degree of compliance of the design parameters with the required standards. This can be done with your own hands using simple techniques.
Calculation of a safe and convenient step of stairs for private use
First of all, the formula is used to calculate the safety of the stairs:
a + b = 46
This sum of the dimensions of the tread and riser indicates that the preliminary calculations were made correctly and comply with the standards.
There is also a special formula for determining the degree of convenience of the stairs:
a – b = 12
If the difference between these two indicators is 12 units, it means that climbing such a staircase to the second floor will be very convenient for the average person. The opening must also meet the requirements of convenience and safety, provide free access and not impede access to the second floor.
You should not recalculate the entire project if there are minor deviations of a couple of centimeters, this is quite acceptable.
Winder steps, platforms and cages
Separately, it is worth considering the situation with the design of a non-standard staircase structure. So, let's figure out how you can calculate the stairs yourself if you plan to use a winder structure to climb to the 2nd floor. Standard formulas are only suitable for straight marching models. Here's the size calculation winder staircase produced graphically. In this case, the calculation of the staircase and intermediate landings is carried out separately, if any.
Schematic representation of the design of a staircase with winder steps
Let's look at how to calculate a two-flight staircase in a house with your own hands. If an intermediate platform is used, the calculation is as follows interfloor stairs is carried out in two stages. First, the position of the site or intermediate cell is calculated. Then, up to this mark, the parameters are calculated for the standard march, and then for the second similar section. The dimensions of the staircase are calculated based on the width of the last step leading to the second floor and the dimensions of the passage.
Now you know how to correctly calculate the stairs in the house and the opening for it. If you are experiencing some difficulties with design, you can use online programs, but you should not trust them one hundred percent, calculation of stairs – This is a very important stage and in this case it is better to order finished work from a professional.
