How to calculate the area of a pitched roof. We calculate the roof area correctly
Calculating the roof area is a simple geometric task for people involved in construction. However, novice builders may have some problems in order to do all the operations correctly. Especially if such calculations are made by a person for the first time. Any small mistake here can lead to the loss of a considerable amount of money. Therefore, in order to answer the question of how to calculate the area of the future roof correctly, it should be understood that the material is more important than the type of roof. The figures obtained by the theory, in the final analysis, differ somewhat downward from the real state of affairs. Accordingly, the material should always be purchased more than calculated by the formulas.
In this article
Necessary preliminary preparation
Let's take a look at what you need to have on hand:
- Calculator, formulas. It will significantly free you from unnecessary gestures, because you just need to drive in ready-made measurements there. You can find such calculators on the Internet.
- Roof plan. At least approximate. Needed to know which type will be built. The plan must contain the angle of inclination, the length of the ridge. Based on the finished plan of the house, mark the width and length of each slope. In calculating almost every type of roof, you also need to know the height of the entire structure. Often a constant is introduced - a design coefficient that depends on the angle of inclination. Here is a list with the angles of inclination that are most common:
- 9, 14, 18 deg. – r.k = 1.01 and steps in 0.02
- 23 deg. – r.k = 1.08
- 27 deg. - r.k. = 1.12
- 34 deg. - r.k. = 1.20
The general calculation technology for any type of roof comes down to the fact that complex geometric shapes are divided into simple two-dimensional ones: triangles, parallelograms. To simplify, even all parallelograms are often divided into triangles, rectangles, trapezoids.
Shed
First, measure the length of the slope (A). To do this, add to the length of the building (ap, it is also the length of the larger wall of the house) the length of the overhangs (ac).
Width (B) is calculated according to the school curriculum (t. Pythagoras), do not forget to add the length of the slopes (bc). We use the projection of a triangle, where the legs are the height of the roof (h) and the width of the building (bp, it is also the length of the narrow wall of the house).
B \u003d bc + √ (bp 2 + h 2)
In total, the roof area can be easily calculated: S = A * B
gable
We apply the same formulas as for a single-sided one, with the exception that ap will be equal to the length of the ridge, and the second leg, when calculating the width of the slope, will already be half the length of the narrow wall (bp).
Roughly speaking, we again calculate the pitched roof. You should remember about overhangs. If you plan to install a window, a chimney, then you don’t need to take away the area they occupy: it’s too easy to make a mistake and, as a result, there may not be enough material.
The area of the roof of the house will be equal to the sum of the areas of the slopes: S \u003d S1 + S2.
Calculation of the hip roof area
The elementary form is also called a four-slope or tented form for a reason: here again we just have to sum up the areas of all the slopes. But, if the previous simple figures were rectangles, then here we are dealing with four triangles. The most effective option is to count pairs of triangles using the same school geometric formulas. In any case, all triangles will be isosceles. This means that the area of each is calculated by the formula:
St \u003d (m * h) / 2, where m is the base, and h is the middle line of the triangle.
Or: St = √p*(p-m)*(p-n)*(p-c), where p is the sum of all sides of the triangle (m, n, c) divided by 2:
As a result, we get the calculation of the entire roof area:
S = 2*St1+2*St2
Complex hip, structurally divided into two trapezoids and two triangles. We also consider the sum of the areas of triangles. We consider a trapezoid as follows:
Strap \u003d (m + b) * j / 2, where m and b are the lengths of the two bases of the trapezoid, and j is the distance between them. If we represent j as a line, then it is perpendicular to both sides.
Calculation of the areas of complex roofs
Produced in a similar way. If the shape formed by the slopes is not a triangle, rectangle or trapezoid, then it is divided on paper into these simple ones. Further, they are already calculated on the basis of their above geometric properties. For example, parallelograms are usually divided into trapezoid, triangles, rectangles.
Roof surface
In order not to be mistaken, the right decision would be to take more material. For such a popular material as slate, there is even a special calculation formula:
S \u003d (2 x ap + ac) x (2 x bp + bc) x cos (c.u.). S - the area of the required coverage, the index "c" - overhangs, "p" - the length of the wall surface, a - the length of the slope, b - width. This area usually exceeds the "empty" roof area by 12%.
Metal tile is considered more complex in calculations: we take into account the ridge, valley, cornices. Often exceeds the "empty" area by 20%. To understand what area you need to collect material, you need to know its consumption.
The main thing to remember here is: the more complex the roof is in the device, the more expensive the construction is.
The strict geometry of roof coverings determines the method of calculating the total roof area as an arithmetically simple task. But the mass of various types of roof construction and the personal preferences of the owner of the dwelling leave many questions and doubts about the correct choice of the method for calculating the area.
The desire to organically fit the house into the surrounding landscape is dictated by the most elaborate roof designs. Tent, attic, multi-gable projects complicate the calculations. So how to reliably calculate the area of \u200b\u200byour roof? We will cover this issue in detail from the point of view of the end user of roofing.
In this article
Classification of roof types
The choice of roof type depends on how the under-roof space will be used. In the case of an auxiliary, technical room, the choice is usually stopped on a pitched roof. In the case of a residential attic, a mansard-type structure is chosen, or, given the presence of natural light, a complex multi-gable roof is built.
Naturally, the roof area will increase significantly, and it will be more difficult to calculate it. Before you start designing a roof, you need to know what they are.
According to the signs of the shape and number of slopes, the roofs are divided into the following main types:
- shed roofing is used for baths and utility rooms, less often for residential buildings, which at the same time acquire an original and non-standard appearance;
- gable roofing, one of the most popular solutions in suburban construction, is practical, easy to install and maintain;
- the attic type of roof has certain advantages due to the presence of an additional residential attic space;
- the hip roof is a four-pitched roof, which consists of two trapezoidal and two triangular slopes and is characterized by increased resistance to wind loads;
- the hipped roof has four or more triangular slopes, it is used in the construction of both residential premises and all kinds of arbors;
- multi-gable roof - a complex broken structure that has an attractive appearance and allows you to use the under-roof space for housing;
- the domed roof is used as an architectural element or as a roof of places of worship.
Such a variety of designs gives a wide scope for the owner's imagination and the ability to combine different types of roofs in one structure. Determining the area of a sloping roof is a rather difficult technical task, but we will try to simplify it.
Calculation of the area of a simple roof
Before calculating the roof area, it is necessary to know in advance not only the dimensions of the roofing, but also the dimensions of the overhangs on the gables and cornices. Otherwise, it will not be possible to optimally arrange the sheets and calculate the required stock of material.
Buying additional coverage in case of its shortage, you run the risk of purchasing it from another batch, which can lead to inconsistency in colors.
When determining the area of \u200b\u200bthe roof of a house, it is necessary to prepare a number of tools and fixtures in order to draw up a detailed drawing. Based on it, the true area is found, which may differ from simple rectangular shapes. For measurements you will need:
- construction roulette;
- trusted level;
- square to determine the squareness of the slope;
- pencil and notepad.
The area of the slope, subject to its rectangularity, is calculated by simply multiplying the length by the width of the roof. The parameters are fixed taking into account the gable and eaves overhangs, then the amount of the required roofing material is calculated, without losing sight of the correction for the overlap of the sheets.
The length of the slope can also be calculated using the Pythagorean formula, by measuring the height of the ridge and the width of the house, taking into account the cornice overhang. If the roof is not strictly rectangular, we calculate the area by summing the area of the rectangle and two triangles.
When a house has a gable roof, it is necessary to calculate the quadrature of each slope separately and sum them up to calculate the overall result.
Calculation of hip roof area
Complex roofs include multi-gable, hip and domed types of structures, the quadrature of which is the sum of the area of various geometric shapes. As an illustration, you can consider the calculation of the quadrature of the hip roof. It consists of two isosceles triangles and two trapezoids.
The area of a triangle is calculated using the following formula:
S 1 \u003d (a x h): 2,
where S 1 is the area of the triangle, a is the length of the base and h is the height of the triangle.
The area of a trapezoid is calculated using the following formula:
S 2 \u003d [(a + b) x h]: 2,
where S 2 is the area of the trapezoid, a and b are the bases of the trapezoid, and h is its height.
Thus, the total quadrature of the hip roof will be equal to:
S total \u003d (S 1 + S 2) x 2
Calculation of roof area of complex configuration
In the case of calculating the quadrature of more complex roofs, the method of breaking down into simple geometric shapes also fully justifies itself. The drawing made after the measurement will allow you to accurately calculate the quadrature of the fragments and, by addition, get the overall result. If the slope or fragment of the roof has the shape of a parallelogram, you can calculate the overall result using the formula:
where S is the area of the fragment, a is the length of the side, and h is the height of the parallelogram.
When calculating the total amount of coverage, it must be borne in mind that in triangular and trapezoidal sections of the roof, material losses can reach 20% or more.
Hip roofs consist of four isosceles triangles, the quadrature of which is summed up to obtain a common result. Domed roofs may consist of separate sheets of complex shape, but nevertheless they are calculated by reducing to individual geometric components for a simple calculation of the amount of coverage. It is necessary to say separately that in the case of using combustible roofing materials, it is necessary to provide the workplace with fire protection equipment.
By calculating the required amount of roofing material, it is not necessary to take into account ventilation outlets, chimneys and window openings, this way we reduce the risk of a shortage of coverage, since on complex roofs waste can be from 8 to 30%.
On a detailed drawing of a multi-gable roof, individual geometric figures should be carefully measured, which can be:
- parallelogram;
- trapezoid;
- triangle;
- rectangle.
The position of these figures on the roof must be clearly and unambiguously fixed on the drawing, which will later make it possible to draw up a scheme for cutting the coating in relation to its overall dimensions. This will avoid large financial losses and optimally lay the roof.
Additional elements of the roof are calculated separately, it is best to do this with the participation of a qualified seller who can check your roof square calculations and give additional recommendations. In addition, there are special calculators on the Internet for calculating the area of \u200b\u200bcomplex roofs.
Conclusion
Thus, we talked about the correct calculation of the area of \u200b\u200broofs of various types. Attentiveness and thoroughness of measurements, as well as a compiled installation scheme, will allow you to avoid miscalculations and gross errors. And then roofing work will take place without financial losses and will bring joy.
Introducing a free calculator for gable roof calculations. Online calculation of the crate, the angle of the rafters and the required amount of materials.
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos-cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos-cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bituminous (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated board (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roof (6 kg/m2) Polymer-sand tile (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tile (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter roof parameters:
Base Width A (cm)
Base length D (cm)
Lift height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafter:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working section of the side rafter (optional) (cm) ">
Lathing calculation:
Purlin board width (cm)
Lathing board thickness (cm)
Distance between decking boards
F(cm)
Snow load calculation:
Select your region using the map below
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to building ridge
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof pitch: 0 degrees.
The angle of inclination is suitable for this material.
The angle of inclination for this material is desirable to increase!
It is desirable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulation material with 10% overlap (1x15 m): 0 rolls.
Rafter:
Load on the truss system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs
Lathing:
Number of rows of lathing (for the entire roof): 0 rows.
Uniform distance between the boards of the crate: 0 cm
The number of boards of the crate with a standard length of 6 meters: 0 pcs
Volume of boards of an obreshetka: 0 m 3 .
Approximate weight of the boards of the crate: 0 kg.
More information about the calculator
The online gable (gable) roof calculator will help you calculate the angle of the slope, the size and number of rafters, the number of sheathing, as well as the amount of materials needed online. Such common roofing materials as metal tiles, slate, ondulin, tiles made of ceramics, bitumen, cement and other materials are pre-made in the calculation base.
Note! Calculations are made on the basis of SNiP "Loads and Impacts" and TCP 45-5.05-146-2009, taking into account the standards contained in these documents.
Gable roof (there are also spellings "gable roof", "gable roof") - a variant of the roof with two slopes going from the ridge to the outer walls of the building. Today it is the most common type of roofs, due to the ease of execution, low cost and attractive appearance.
The rafters in the construction of such a roof in pairs lean against each other and are connected by a crate. The end sides of a structure with such a roof are triangular in shape and are called pediments (sometimes tongs). Usually, an attic is arranged under a gable roof, and small attic windows are made on the gables for lighting.
When filling out the fields of the calculator, pay attention to the icon "Additional Information", under which explanations are hidden for each item.
The calculation results are also accompanied by explanations, which you can find below.
Explanations for the calculation results
Roof slope
This is the name of the angle at which the slope and rafters are inclined to the plane of the ceiling. The calculations are made taking into account the fact that it is planned to build a symmetrical gable roof. By entering an angle, you can not only calculate the required amount of materials for a given angle, but also check whether it is possible to build a roof at this angle from the materials you have chosen. You can reduce or increase the angle by changing the width of the base or the height of the lift: these parameters are tightly interconnected.
Roof surface area
The total area of the roof slopes, including the area of overhangs of a given length. Determines the amount of roofing and subroofing material required in the construction of the roof.
Approximate weight of roofing material
The estimated total weight of the roofing material.
Number of rolls of insulating material
The required amount of roofing material, taking into account the required overlap of 10%. In calculations, we proceed from rolls 15 meters long and 1 meter wide.
Load on the truss system
The maximum possible load, taking into account wind and snow loads, attributable to the rafters.
Rafter length
Rafters are measured from the base of the slope to the ridge of the roof.
Number of rafters
The total number of rafters required for a roof truss system at a given pitch.
Minimum section of rafters
To provide the roof with sufficient strength, it is necessary to choose rafters with the section options proposed here.
Number of rows of battens
With the parameters you set, this number of rows of crates will be required. If you need to determine the number of rows for one slope, then this value must be divided by 2.
Uniform spacing between boards
To eliminate the overspending of materials and save yourself from unnecessary trimming work, you need to choose a given distance between the boards of the crate.
The volume of boards of the crate
The number of boards required for the sheathing of the entire roof (in cubic meters).
Before calculating the area of the roof, it is necessary to draw up an accurate plan with the application of all sizes in uniform digital indicators. In addition, you need to know what roofing material will be used for roofing, waterproofing, vapor barrier, thermal insulation. Having a calculation of the roof area, each developer will be able to economically build his roof.
Roofs can have a different shape:
- one, two or four
- hip or semi-hip
- forceps;
- multi-pitched
The easiest way to calculate roofs that do not have kinks on the slopes and are regular triangles or trapezoids. But modern builders are increasingly using multi-pitched or hip roofs, where, along with triangles, there can also be irregular rectangles, rhombuses and other geometric shapes.
Therefore, if school knowledge of geometry is still fresh in memory, you can calculate the roof area yourself, and if you have been at odds with geometry for a long time, then it is better to order the calculation of the roof area to a knowledgeable specialist or use special online tools. We will talk about this in our article.
Drawing up a roof plan
If the rafter system is already ready, and there is no house project where the roof plan should be, then you will have to draw up a roof plan yourself.
drawing up a roof plan
The entire roof is measured and a drawing is drawn up, which will show the roof in plan. In addition, you need to measure the height of the roof, from the ridge to the ceiling. If the roof is multi-level and has different heights, everything is measured and marked on the drawing, where is the height of the roof. If you have the ability to draw, it is better to make an additional drawing of the roof in projection, for better visibility.
With such a drawing, it is easier to imagine the appearance of the future roof, decompose it into its constituent geometric elements and calculate the roof area . The dimensions of the future roof are not limited to the dimensions of the perimeter of the house. To them, you need to add the values \u200b\u200bof the roof overhangs, where they are expected.
Examples of calculating the area of various roofs
A shed roof is easy to calculate - you need to measure the width and length of the building, add the values \u200b\u200bof the estimated overhangs and multiply the resulting numbers. But with pitched roofs, this approach will be wrong, because here you need to take into account the angle of inclination of the roof and all individual elements (dormer windows and other similar structures).
- Before calculating the roof area, all the complex elements of the roof are divided into separate components - triangles, squares, etc.
- When calculating the area of a gable roof, you need to multiply the area of \u200b\u200beach slope by the cosine of the angle of inclination of the roof. This refers to the angle that is formed by the slope and the overlap.
- the length of the slope is taken from the ridge to the extreme line of the cornice
- In the same way, all other roofs with several slope planes are calculated. The area of \u200b\u200beach slope is found separately and multiplied by the cosine of the angle that is formed by the slope and a straight line parallel to the ground.
- After that, all the obtained values \u200b\u200bare summed up, and the total area of \u200b\u200bthe roof of the house is obtained. .
- If the roof slope is an irregular rectangle, it should be divided into regular geometric shapes and calculated separately for each , and then sum up all the data obtained.
Let's give an example of calculating a gable roof for a house (8 x 6 m), the length of the rafter leg is 3.68 m, the length of the overhang is 0.5 m, the gable overhang is 0.5 m.
We calculate the area of one slope - Sabcd \u003d Lcd x Lbd \u003d (8 + 0.5 + 0.5) x (3.68 + 0.5) \u003d 37.6 m2.
The area of the entire roof S \u003d 37.6 x 2 \u003d 75.2 m2.
When calculating, roofing elements such as chimneys and ventilation ducts, dormers, dormer windows or skylights, parapets are not deducted from the total area. If the shape of the roof is very complex or the developer is not able to make calculations on his own, you should contact specialized web resources where they offer to calculate the roof area online .
roofing factor
In addition to the fact that the roof area is calculated, it is also necessary to make calculations of the roofing material that is required to cover this area. At the same time, the figures for the area of \u200b\u200bthe roof and the area of \u200b\u200bthe required roofing material will differ significantly. The fact is that individual roofings are laid with overlaps, and therefore the consumption of materials increases. When calculating the roofing material required to cover complex roofs, it is better to use the roof area calculator.
If it is planned to cover the roof with slate, then the calculation is as follows: S= (2 x A+B) x (2xA+C) X cos 30,
where S is the total area, A is the width of the overhang, B is the length of the house, C is the width of the house. 30 * - the angle of the roof. If the length of the house is 15m, the width is 10m, the width of the overhang is 0.5m, the cosine of 30 degrees is 0.87, the total roof area is 202.2 kV m.
- How to find the roof area if a metal tile is used as a coating?
useful formulas for area calculation
It is necessary to take into account such nuances as the total length of the skates, valleys, overhangs, cornices. When using metal tiles or profiled metal for complex roofs as a covering, it must be borne in mind that inevitable and very significant waste will follow.
If, with less complex roofs, experts recommend buying roofing material with a margin of 7-15%, then for complex roofs, the margin of material should be increased to 20%.
The calculation of a soft roof is made according to the same formula as for a slate roof. The consumption of roofing material depends on its type and laying technology. The areas of skates, valleys are considered separately and ordered separately, because they are no longer measured in square meters, but in linear meters.
Before calculating the area for any structures and roofing materials, a calculation is made for the connection of individual elements, which are almost always overlapped. At the same time, material consumption increases depending on the size of the overlap, the angle of the roof. Since, the greater the angle of inclination, the smaller the overlap of the roofing material is allowed.
roof pitch table
When calculating the area for complex roof configurations and a large number of drops, you can perform a calculation by applying slope correction factors from the table to the area of the horizontal projection (or individual sections)
You should not start laying roofing material without having it laid out on paper before your eyes. In this case, the error in the installation of the roofing will be minimized, and you will not have to buy the missing material to replace the damaged one.
- 9 degrees - coefficient. 1.01;
- 14 degrees - coefficient. 1.03;
- 18 degrees - coefficient. 1.05;
- 23 degrees - coefficient. 1.08;
- 27 degrees - coefficient. 1.12;
- 34 degrees - coefficient. 1.20.
Naturally, there is an overhang.
Calculation for a hipped roof
For a square: a x a.
a is the length of the side.
b is the width of the figure.
a - the base of the figure,
h is the height of the figure,
How to calculate the roof area of a house
At the beginning of construction, the question always arises, how to quickly and correctly calculate the roof area? This operation seems simple only at first glance. In practice, it turns out that the calculation can be quite difficult even for experienced craftsmen. Since the total amount of money spent on the construction of the roof directly depends on its correctness. Given the high cost of building materials and the cost of installation work, you can try to reduce the cost of the entire project. Let's try to figure out what is needed to perform the correct quadrature calculation.
Friends, U-ra, it happened and we are pleased to present you an online calculator for calculating the roof area, now you don’t need to figure anything out on a piece of paper or in your mind, everything just indicated your parameters and received an immediate answer. Now you will know exactly how much material you need to cover the roof. Here is a link to the calculator -> Roof area calculator, online roof calculation. In addition, we have many other construction calculators, you can see a list of all of them on this page: Construction calculators
Main stages of work
The calculation of the roof area should always start with:
- getting acquainted with the future project of the roof of the house and remembering the most key parameters: ridge length, slope angle, height, width and length;
- determining the type of roofing material to be used.
One of the most important characteristics is a special calculation coefficient, which is present in absolutely all formulas. Its value depends on the angle of the roof slope and is determined by the following relationships:
- with a slope of 9 ° slopes, the coefficient will be 1.01;
- for 14° - 1.03;
- for 18° - 1.05;
- at 23° - 1.08;
- at 27° - 1.12;
- for 34° - 1.2.
The specified range of roof slope angles is the most popular options used in construction in our latitudes. It is possible to determine the parameters of a structure with a complex geometric shape by breaking it down into separate small figures, which can be easily calculated by summing up the obtained values at the end. Experts recommend adding about 10% to the result, which is the standard margin in construction.
Formulas and definitions
The simplest calculation option is to determine the area of \u200b\u200ba shed roof with any slope. Houses with this kind of roof are usually covered with simple materials, and the most common shape is a rectangle. To calculate the roof area, we need to know the length of the slope and its width, which should be multiplied together with a predetermined calculation coefficient.
It should not be forgotten that the value of the slope overhang area, which is mandatory for roofs of this type, should be added to the area of \u200b\u200bthe shed roof of the house.
To calculate the area of \u200b\u200bthe gable roof of a house, it is necessary to take into account much more values and factors. So, for a slope with a length of 6 linear meters and a ridge of 9.5 linear meters, the calculation formula will take the following form: the length of the ridge should be multiplied by the length of the slope and multiplied by the number of slopes (in our case 2). If you need to calculate the amount of metal tiles for this roof, then you should first determine the dimensions of one sheet of roofing material. The formula that will allow you to calculate the number of sheets of metal tiles is as follows: the length of the ridge is divided by the width of the roof sheet and rounded up. To carry out such calculations, it is important to know well the geometric parameters of the roof of the house and the geometric parameters of the roofing material.
Final Conclusions
The area when using other materials can fundamentally differ. For this reason, for each particular case, an individual approach, careful analysis and competent calculation are required. The most difficult situation arises when it is necessary to calculate the quadrature of roofs of complex shape. To get a reliable result, you should follow a few simple rules.:
You should be aware that when calculating the area, it is important not to forget to take into account ventilation ducts, skylights, chimneys, parapets, hatches and other elements. In case of violation of this rule, there is a high probability of a shortage of building materials during the arrangement of the roof. Correct and competent calculation of the area will provide all the conditions for the optimal use of funds associated with the purchase and cutting of material during the construction of the roof of the house.
How to calculate the roof area of a house. Formulas, schemes and calculation
Calculating the area of the roof, for those who know how to use a tape measure and a calculator, will not be difficult. Because the whole calculation comes down to calculating the areas of individual slopes, and if the roof of the house is not complicated, but the usual two- or four-slope, then it will be even easier to calculate the area.
There are a huge variety of types and geometric shapes of the roofs of private houses, but the roof slopes themselves, as a rule, come in four geometric shapes:
- rectangle
- trapezoid
- equilateral triangle
- parallelogram
In this article, we will only consider the area of pitched roofs, we will not calculate the area of flat and inverted roofs, because the area of such roofs, in most cases, will be equal to the area of the house or part of it under this roof.
And if you learn to calculate the area of \u200b\u200beach such slope separately, the formulas of which are presented below in the diagrams, then it will be very easy to calculate the total roof area.
It must be remembered that the more slopes on the roof, the more difficult it will be, not only in terms of construction, but also roof insulation, its decoration and maintenance. And during the construction itself, there will be a lot of unused scraps, which will become unnecessary financial costs.
And so, before you get a calculator and start counting, you need to have a roof plan on hand. If there is none, then you will have to take a tape measure, a sheet of paper, a pencil and start measuring the slopes.
What sizes of slopes are needed, and what exactly to measure, depends on the type of roof of a private house, which are described in detail in one of the previous articles, and here I will tell you how to correctly apply the area calculation to a specific type.
Calculation of the area of \u200b\u200bshed roof
This is the simplest calculation that can be done without a detailed house roof plan.
It is necessary to measure the length C and the width D of the slope.
It is not difficult to calculate the length of the slope, it is necessary to measure the length of the building and do not forget to add roof overhangs on both sides. If for some reason it is not possible to measure the width of the slope, then you will have to measure the height of the roof B and the projection of the slope A (according to the diagram). After we apply the Pythagorean theorem and find the width of the slope C.
Calculation of the area of \u200b\u200ba gable roof of a house
The calculation of such a roof, I think, is also not difficult.
Calculation of the area of the hip, semi-hip and hipped roof of a private house
For the calculation, it is necessary to mentally break the hip roof into four separate slopes, as shown in the diagram, and then count each slope separately.
After splitting, you should have two trapezoids and two equilateral triangles if the opposite slopes are equal.
Now we calculate the areas of these geometric figures using simple geometric formulas, then add the resulting areas of the figures. This completes the calculation, as you have seen, there is nothing complicated here.
Half-hipped roof area a private house is considered exactly the same, except that the triangular slopes will be smaller than those of the hip, and the main large slopes must be divided into two geometric shapes, a trapezoid and a rectangle, calculating their area separately.
Counting technology hipped roof area the house is no different from the hip, we also break the roof into four slopes, only here we should already get four equilateral triangles. The area of these triangles is calculated in the same way as in the previous examples.
Calculation of the area of a complex roof with numerous slopes
Such roofs, as a rule, include domed and multi-gable roofs of private houses, containing a large number of different slopes.
Although the formulas for calculations are very simple, it will still not be easy to calculate the area of \u200b\u200bsuch a roof. The whole difficulty will lie in a large number of measurements, because each slope will have to be measured separately, and the more complex the roof, the more difficult it will be to do. The task can be made easier by having an accurate roof plan.
Complex roof area calculation technology
To begin with, we break the roof into separate flat slopes. As already mentioned at the very beginning, the slopes of a complex roof can be in the form of three geometric shapes:
- equilateral triangle
- rectangle or square
- trapezoid
- parallelogram
Calculation of material for the roof of a private house
Calculating the material for the roof is much more difficult than calculating the area of the roof itself. Sometimes the roof area is half the area of the ordered material. In order not to make mistakes in the calculations and not to buy too much, and it happens even worse when there is not enough material, you need to contact the specialists from the company from which you will order the material. For most organizations, this service is free. They will very accurately count the number and size of the sheets and give you a layout of them on the roof.
Since roofing materials are usually rectangular in shape, and roof slopes are not always, sheets will have to be cut and adjusted to the angles of the slope. And the more complex the roof, the more unnecessary scraps you will have. It must be remembered, no matter what material you choose for roofing, during installation, the layout of the sheets should always be at your fingertips so that you do not cut off the wrong sheet when cutting.
How to correctly calculate the area of \u200b\u200bthe roof
The construction of each house does not begin with digging pits and not with pouring foundations.
Construction begins with the development of the project and the execution of calculations.
With the roof, everything happens in the same way: before proceeding with its installation, a careful calculation of the height, the size of its surface is performed, the number of structural elements and the amount of material for the roofing pie are determined.
The strength and reliability of the roof, as well as the amount of financial resources that will be spent on its installation, depend on the correctness of the calculation performed.
The surface calculation always starts with:
- measurements of the main parameters of the roof: the angle of inclination, the length of the ridge, the length, width and height;
- determining the type of roofing material that is planned to be used in the future when installing the roof.
One of the most important characteristics is the calculated coefficient used in almost all formulas in calculations.
The value of this coefficient depends on what is the angle of inclination of the slopes on your house.
For the most popular tilt angles, the coefficient is:
- 9 degrees - coefficient. 1.01;
- 14 degrees - coefficient. 1.03;
- 18 degrees - coefficient. 1.05;
- 23 degrees - coefficient. 1.08;
- 27 degrees - coefficient. 1.12;
- 34 degrees - coefficient. 1.20.
If the shape of the roof is complex, irregular in shape, then during calculations its surface is divided into separate regular figures, the area for which is considered elementary.
And at the end the results are summarized.
The order of calculations for a pitched roof
This is geometry from a school course.
Houses on which a shed roof is arranged are usually covered with simple materials.
And rectangle is the most common shape.
Therefore, it is enough to measure the length and width of such a rectangle and multiply them.
Also, do not forget the coefficient mentioned above.
We calculate a gable roof
Calculations for the surface of a gable roof are more complicated.
Yes, and there are many more factors to consider in such calculations.
To begin with, we decompose all complex elements into separate simple shapes: rectangles, squares, triangles.
Indeed, on the roof, each corner is formed only by an overlap and a slope.
Therefore, in order to calculate the roof surface, it is necessary to multiply the area of \u200b\u200beach slope by the cosine of the angle of inclination.
With this calculation, the length of the slope is the distance from the ridge to the cornice line.
In exactly the same way, any roof with any number of slopes is calculated.
You just need to sum the resulting surfaces of all the slopes, multiplied by the cosines of their angles.
If the roof element has a complex irregular shape, then it is also divided into several simple geometric shapes and the area of \u200b\u200beach of them is considered.
Then all surfaces are summed.
Let's look at how this is done in the following example: the house has dimensions of 10 x 8 meters.
The rafters are 4.5 meters long.
Naturally, there is an overhang.
The length of the overhang is standard - 50 cm.
First, we calculate what surface one slope has:
S = (10 + 0.5 + 0.5) x (4.5 x 0.5) = 55 square meters.
Since the building has two such slopes, the total area will be 55 x 2 = 110 square meters.
Despite the fact that on any roof there are ventilation ducts, chimneys, dormers and skylights, parapets, they are not taken away from the resulting area value.
We consider a hipped roof
Then you should determine how difficult each of them is.
The simplest hipped roof has a pyramidal shape.
Therefore, when calculating its surface, the formula for the pyramid is used.
If all the slopes are the same size, then it is enough to calculate the area of \u200b\u200bone of them and then multiply by four.
In the case when the hipped roof has a complex shape, then it is divided into simple figures and the surface of each of them is calculated separately.
Indeed, for such a roof for different slopes, the angles of inclination can differ significantly.
It should also be remembered that dimensions are taken not along the perimeter of the building, but along the overhangs of the cornices.
We calculate the hip roof
In order for the calculation of the hip roof to be performed correctly, it is necessary to take into account the following:
- window size and chimney size;
- the length of the slope (between the ridge and the eaves);
- details that are not included in the roofing (overhangs, parapets, etc.);
- when performing the calculation, the adjoining roofing slabs, block ledges, standing folds are not taken into account.
Calculating the surface of a hip roof consists in finding the area of two end triangles and two trapezoids.
In any case, if the hip roof has a complex shape, it is divided into several simple figures and calculations are made separately for each of them.
And then the calculation results for each figure are summarized.
You should know that even though the hip roof is the best roofing solution, its installation is not cheap.
Calculation for a hipped roof
A hipped roof is one of the varieties of a hipped roof.
So let's say this is a classic roof with four slopes.
The basis of this design is a quadrilateral.
And the slopes are isosceles triangles converging at the central upper point.
Such a roof is the most economical, since there are no gables in it.
More about the construction of a hipped roof with your own hands.
About soft roof Unikma here. The entire range of the Unikma construction company is presented.
Since the slope is equal to an isosceles triangle, then:
b is the length of the base of the triangle;
S is the area of the triangular slope.
Calculation of a broken mansard roof
The area of a broken mansard roof, despite the apparent complexity, is quite simple to calculate.
To do this, first of all, make a roof plan indicating all dimensions.
The entire roof will be a set of simple geometric shapes: triangles, squares, rectangles, trapezoids.
For a square: a x a.
a is the length of the side.
b is the width of the figure.
a - the base of the figure,
h is the height of the figure,
a and b are the dimensions of the upper and lower bases.
After the area of \u200b\u200beach of the simple figures into which the broken mansard roof is divided is calculated, the results are summarized.
Video about the construction calculator for calculating the roof.
Sergey Novozhilov is an expert in roofing materials with 9 years of practical experience in the field of engineering solutions in construction.
A gable roof is a complex, large building structure that requires a professional approach to design and work. The biggest costs go to building materials for rafters, battens, insulation, waterproofing, roofing material. Our gable roof calculator will allow you to calculate the amount of material.
Using a calculator saves roof design time and money. The final 2D drawing will guide the work, while the 3D visualization will give you an idea of what the roof will look like. Before entering data into the online calculator, you need to have an idea about the elements of the roof.
Rafter parameters
To calculate the truss system of a gable roof, you need to consider:
- roof load;
- step between rafters.
- type of roofing
- 100-150 mm with a span of no more than 5 m, and with additional props .;
- 150-200 mm with a span of more than 5 m, with a step of more than 1 m, and if the angle is not large.
Important! The distance between the rafters of a gable roof is usually set to 1 m, but with a roof slope of more than 45 degrees, the pitch of the rafters can be increased to 1.4 m. With flat roofs, the pitch is 0.6-0.8 m.
Rafter legs are attached to the Mauerlat, which runs along the perimeter of the house. For him, either a board with parameters 50x150 mm, or a bar 150x150 mm (for load distribution) is taken
Lathing parameters
For a metal tile, a sparse crate is created with a board, the width of which is 100 mm, and the thickness is 30 mm. The board is stuffed with a step that should correspond to the longitudinal axis of the metal tile module - 35 cm (supermonterrey).
For flexible tiles, the crate is carried out with a large step, since OSB or plywood will be laid on top of it with a continuous carpet.
Important! When choosing materials, pay attention to indicators of moisture resistance and minimum thickness.
When constructing warm roofs, a counter-lattice is made between the waterproofing and the roof with a bar, the thickness of which should be 30-50 mm.
Roofing parameters
- To calculate the roof of a gable roof, you need to know the dimensions of the roofing material and the size of the overlaps.
- A metal tile for a hard roof is produced with a width of 118 mm (working 110), but the length can be different. The manufacturer under the order can cut any length.
- Flexible tiles for soft roofs have different sizes, so you need to look at the specific material
- As for the choice of insulation, for Russia a minimum thickness of 100 mm is recommended, and the correct one will be 150-200 mm.
