Calculate the length of the stairs. Staircase size calculator
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Online calculator for calculating stairs
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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 entire staircase or its individual elements will be made. 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.
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.
When calculating according to bearing capacity The staircase elements are divided into statically definable beams - cantilever or single-span, and are calculated using the appropriate formulas. Since stairs are subject to dynamic loads, the rigidity load-bearing elements increased requirements are imposed: their deflection should not exceed 1/400 of the span. Loads acting on flights of stairs and landings must be collected by adding the dead weight of the structures and temporary loads: in residential buildings- 300 kg/m².
When lifting, a person expends approximately twice as much energy as when moving horizontally (Fig. 2). Practice has established: a staircase is comfortable and safe if twice the height of the riser, added to the width of the step (tread), is equal to the average human step. The length of a person's stride on a plane is approximately 600–640 mm. Based on this, the tread and rise are determined by the formula: 2a+b = 600…640 mm.
Fig.2. Calculation of the height and width of ordinary steps
As an alternative, you can use another, easier to remember, formula: a+b = 450 ± 20 mm, where a is the height of the step (riser), b is the width of the step (tread).
The width of the tread should ensure that the foot rests with the full foot, that is, it should be no less than 200 and no more than 320 mm. The optimal height of the riser is 150, and the width of the tread is 300 mm. If the tread width increases too much, you will certainly lose your step, and if the tread width decreases too much, descending will be difficult. When designing winder steps, it must be taken into account that the minimum width of the steps at the narrow end should be at least 100 mm, and the overhang of the tread over the bottom step should be no more than 50 mm. Also, the overhang of the upper step over the lower one is done when other methods fail to increase the width of the tread; in this case, the amount of overhang should not exceed 30 mm for wooden and 50 mm for reinforced concrete steps.
The most convenient staircase angles are in the range from 23 to 37°. The steeper the staircase, the less space it needs to be installed in the house, and accordingly, the more positioned the staircase is, the more space needs to be provided for it. If the angle is less than 23°, the staircase can be replaced with a ramp (a flat inclined platform); if it is more than 45°, then the staircase becomes an attached or folding one (Fig. 3). Optimal angle rise of spiral staircases - 25–35°. Most complex process when the flight of stairs is steeper than 40°, descent from the stairs is possible, and at angles greater than 45°, descent can only be done backwards.
rice. 3. Standard dependence of the size of steps on the steepness of the stairs The number of steps depends on the height of the floor and the angle of inclination of the stairs. Knowing the location of the staircase in the plan and the height of the room, the number of steps can (and is easier) be determined graphically, and then, using safety formulas, determine the width of the tread.
To graphically construct a staircase on graph paper or checkered paper, you need to draw a flight of stairs to scale (Fig. 4), measuring it with the height of the floor.
rice. 4. An example of a graphical calculation of the number of steps and riser height. Height table for steps in buildings with standard floor heights The height of the floor is the difference in the elevations of the finished floor levels of the lower and upper floors, that is, the thickness of the floor coverings must be included in the size of the floor height. For example, the floor of the lower floor is tiled ceramic tiles, and the floor of the upper floor is laid with parquet along the joists and a plywood “subfloor”. When calculating the floor height, all layers of these floor structures must be included: below - the thickness of the leveling screed, tile adhesive and tiles; at the top - the thickness of the logs, plywood and parquet. In Russia, since the existence of the USSR, floor height has been a regulated value. Typically, the standard floor height is 2.8 or 3 m, less often - 2.7 or 3.3 m, which allows you to design a room height (distance from floor to ceiling) of at least 2.4 m. This floor height allows you to easily fit a staircase with step sizes that meet the requirements of the safety calculation formula (Fig. 4, Table 2). If your floor height differs from the standard and is not a multiple of 3, then the height of the steps must be calculated (rounded) with an accuracy of one millimeter, but so that the heights of all risers are the same. It is better to distribute the calculation error resulting from the rounding of heights onto the lower frieze step, and make the remaining steps of the flight of the same height.
Steps of different heights lead to the construction of a dangerous staircase. This staircase becomes especially dangerous when descending at night. When going down the stairs, muscle memory tells us that there should be a step. The weight of the body is transferred to the leg, but there is no step under it... It is lower! And only two or three tens of millimeters, but they twisted their leg... and it’s still good if they didn’t roll head over heels.
In houses with non-standard height floor to level the height of the steps, it is allowed to lower the level of the finished floor of the upper floor landing slightly lower relative to the level of the finished floor of the rest of the floor. It is better not to make a threshold, but to make the floor of the floor area in the form of a ramp, that is, inclined. To adjust the height of the steps, you will only need a few millimeters so that the slope is unlikely to be very noticeable. Alternatively, if the landing is enclosed by walls with doors, the floors between these rooms can be made with a small threshold. This solution is well known to everyone: the level of floor areas in apartment buildings, as a rule, below the level of clean floors in apartments. We don’t break our legs here - we’re used to it.
Table 1, Figure 3 shows the dimensions of the steps for “compacted” stairs, suitable for country houses. Often, in the layouts of these houses, so little space is left for stairs that in order to make the stairs shorter, one has to sacrifice the width of the tread. So, for example, in a staircase with a riser height of 200 mm, the tread width is 250 mm. An adult cannot rest his full foot on such a tread and he has to go down the stairs sideways or backwards. Table 2, Figure 4 shows the height dimensions of the risers for standard heights floors. Calculating the width of the tread using safety formulas is not difficult. But there is another way to determine the size of the steps - graphically.
This ergonomic method is based on the fact that a person, freely taking a step of 620 mm on a horizontal plane, can with the same ease raise his leg to a height equal to only half of this value, that is, 310 mm. Therefore, if on horizontal axis graphics (Fig. 5) put aside a known number of parts, each equal to one step (620 mm), and on the vertical axis - equal to height leg lift is 310 mm, then this construction makes it possible to obtain the dimensions of the rise and width of the steps for stairs with any inclination. To do this, you need to plot the slope of your staircase on the graph (its height and length are known) and draw perpendiculars at the points of intersection with the graph grid. That's what it is optimal height and the width of the step for a given flight of stairs. Moreover, you can use this method and build a staircase specifically “for yourself”. For example, by setting the step to 600, and the lift, respectively, 300 mm, or by setting the step length to whatever you consider necessary.
rice. 5. Graphic selection method optimal sizes steps (dimensions in mm) 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 manufacturing staircase design- this is a tree. 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 of the flight of stairs using 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 is better if it is even, and you get the exact height of the step, 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 equal to 300:18 = 16.7 cm. This design should be divided into two flights of stairs and be sure to do it with a twist.
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How to make a turn correctly
The staircase structure can be turned in three ways. One of them is for 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. Horizontal landing 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.
The construction of a house with a second floor involves the creation of a staircase that connects the floors to each other. The simplest and most accessible for self-construction An option is a single-flight staircase. However, even in this case, you need to know how to calculate the steps of the staircase at the design stage so that it turns out not only safe, but also comfortable.
Calculation stair steps are produced based on such a parameter as the human step. Its average value ranges from 600 to 640 mm. How, based on this value, can you make a calculation (the height of the riser and the depth of the tread)?
There are formulas that relate the height and depth of a step to specific numerical parameters characteristic of a human step. Here are the most significant ratios:
- Y + 2H = S;
- Y + H = 460 mm;
- Y – H = 120 mm.
Designations: Y – step depth, H – step height, S – average human step (600–640 mm). The first formula is the main one. The second is a simplified version of the first, it is also called the safety formula. Using the third formula will help make the stairs more comfortable. All these ratios were obtained back in the 18th century, but they are still considered standard to this day. If your dimensions match the standard ones, then the staircase will be comfortable and safe.
In addition to formulas that allow you to correctly calculate the size of steps, there are recommended parameters. For example, the area of the step should be such that a person, when walking up the stairs, rests on his entire foot or at least most of it. The depth of the tread determines this area. Minimum value depth – 25 cm. This is especially important for descent. On the other hand, if the depth of the steps is too deep, a person, going up to the second floor or going down, will certainly lose his step. The area of the step, of course, will be sufficient for placing your feet, but walking from floor to floor when the steps are wider than 40 cm is no longer comfortable. Thus, the depth is selected from the range of 25–40 cm. The optimal value is 30 cm.
You can do it differently - take the shoes of those people who will use the stairs and increase their size by a couple of centimeters. The resulting values will become a guideline for choosing the tread depth. If the depth is too small, which happens, for example, due to the large angle of inclination of the stairs, then protrusions (overlaps) are used. The width of the tread section overhanging the underlying step should not exceed 5 cm.
When the tread depth is selected, the calculation can be made according to the formulas described above. But there are also recommended values. The height is selected from the range of 12–22 cm. It is not advisable to make the steps high if children and elderly people will use the stairs. Steps that are too low are also not recommended, since you will have to step often and shallowly, which is inconvenient. The optimal height is 15 cm.
Important! The steps must be the same height. When going down to the bottom floor in the dark, it is very easy to trip when the actual height of the step differs from the expected one, as we rely on muscle memory.
Choosing the width of the march
One of the parameters of the steps is their width. It is more correct to call it the width of the march. The ability to comfortably move up the stairs depends on this value. The width of the march should not be less than 70 cm.
If the stairs will be used by several people at the same time, the structure should not only be stronger, but also wider. When one person goes up to the second floor and another goes down to the first, they need to separate without experiencing any inconvenience. To ensure the ability to walk on the stairs towards each other, the width of the flight must be at least 120 cm.
The length of the steps can be greater when it is necessary to ensure an increase in the so-called bandwidth stairs. In apartment buildings and public buildings, where it participates in movements from floor to floor a large number of people, the flights of stairs reach a width of one and a half meters, or even more. In private buildings, the width of the flight of stairs leading to the upper floor often coincides with the width of the doorway to which it adjoins.
What can the parameters of the steps depend on?
- number of steps;
- height of the stairs;
- tilt angle.
To determine the number of steps, the interfloor distance is divided by the height of one step. Everything is simple, but the problem is that the resulting value may not be an integer. The solution is to make the lower frieze step non-standard. Its area will not change, but its height will be less than that of the others - it is equal to the product of the remainder and the original height of the steps.
Another option is to spread the “extra” over all the steps, increasing their height. The calculation is simple - the remainder is multiplied by the height of the step, the resulting product is divided by the number of steps and this quotient is added to the original height of each step. Obviously, the change will be insignificant if there are many steps.
Graphical method
A method using graphical constructions makes it possible to obtain the parameters of the steps (height and depth), taking as a basis their number (of steps). To do this, a coordinate system is constructed, on the horizontal axis of which the values of the average human step are plotted, and on the vertical axis - half of this value.
Important! With this calculation, you need to choose a suitable scale, otherwise the drawing will require too large an area.
If the average human step is taken to be 620 mm, and the scale is chosen to be 1:10, then segments of 66 mm are plotted on the horizontal axis, and 31 mm on the vertical axis. The number of segments on each axis must be equal to the number of steps.
Having axes with marks, draw lines connecting the first mark on the horizontal axis with the first mark on the vertical, the second – with the second, the third – with the third, etc. Having received a series of parallel inclined lines, a straight line is drawn from the center of coordinates, indicating the steepness of the stairs. Now, from each point of intersection of a straight line with inclined lines, two segments are drawn:
- the first - to the left, parallel to the horizontal axis;
- the second - upward, parallel to the vertical axis.
As a result, the boundaries of the steps should be outlined. Their width and height are determined by simply measuring the resulting lines on the graph. The final dimensions are obtained taking into account scaling (for example, multiplying by 10 if the scale was 1:10).
Online calculator
The most in a simple way calculating the parameters of stairs is an online calculator. No special knowledge or skills are required here. In addition, online calculators allow you to calculate the parameters of not only simple single-flight staircases to the second floor, but also spiral staircases, as well as staircases with winder steps. The calculation can be made with different initial data. In one case, to receive required sizes The floor height and room area are entered into the program. In another case, calculations are made based on the height of the steps and the angle of inclination of the structure. Online calculator for stairs and others construction work
Online calculators that calculate the parameters of stairs are developed, as a rule, in compliance with the standards specified in GOST. Using such programs can benefit not only beginners, but also professionals.