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 clarity.
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 supposed 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 miscalculation 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.
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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 area of the roof, we need to know the length of the slope and its width, which should be multiplied among themselves 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, each particular case requires an individual approach, careful analysis and competent calculation. 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 a similar 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;
- slope length (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 Unikma soft roofing 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.
You need to know the exact areas of roof slopes not only in order to correctly calculate the amount of material purchased, but also the amount of work for which you will have to pay when hiring a team. The dimensions of the roof, as well as the volume of work performed on it, are always calculated in square meters. The only difference is that when buying a material, some corrections and coefficients are taken into account.
Table 1. Nuances in the calculation of coverage.
| Nuances in the photo | What you need to take into account: instructions |
|---|---|
| Whatever material you buy, when calculating it, you should always take into account the total area of \u200b\u200bthe roof according to the existing project (or your own calculation). Important! At the same time, it is impossible to subtract from it the areas occupied by superstructures: a chimney, a dormer or dormer window, a mezzanine. And even vice versa, if they need to be lined with the same material, you should calculate how much it will take and add to the total amount. |
| When measuring the parameters of the slope, it must be remembered that this is the size not between the ridge and the fulcrum on the wall, but between the ridge and the most extreme line, taking into account the overhang. |
| When calculating the material, the location of the gutter is also important. If it is not on the wall, but on the cornice, then 7 cm is added to the slope area. |
| The area of the walls of the parapets on the roof, which require coating with the same material, is calculated separately. |
| When roofs are covered with galvanized steel sheet, chimney bypasses are usually performed by arranging folds that extend onto vertical surfaces. They do not need to be taken into account when measuring the area of \u200b\u200bthe slopes. |
| Roof sections in those places where it adjoins vertical structures do not need to be taken into account separately. |
note and on such a very important nuance. When the roof has an overly complex configuration, which makes the measurement process difficult, the area can be calculated not from the slopes themselves, but from their projection, using correction factors. But for this you need to know the exact parameters of the slope.
Table 2. Slope parameters.
| Slope degree | Correction factor |
|---|---|
| 7 | 1,014 |
| 8 | 1,02 |
| 10 | 1,031 |
| 13 | 1,054 |
| 15 | 1,077 |
| 18 | 1,118 |
| 22 | 1,202 |
| 30 | 1,41 |
On a note. If the roof has several sections that lie in different horizons, but are not interconnected by the roofing material, the area of each of them is calculated separately.
Prices for metal tiles
metal tile
Calculation of areas in the traditional way
Now that the general requirements and amendments have been agreed, you can proceed directly to the calculations. Actually, they come down to determining the area of a particular geometric figure, which is any slope. Many can remember the principles of calculations from the course of school geometry, you just need to use the tape measure and the calculator correctly.
Pyramid and arched roof elements
Depending on the configuration of the roof, you will most often deal with a rectangle or a parallelogram, triangles or a trapezoid. Irregular quadrilaterals can always be divided into a regular rectangle and one or two triangles, and each one can be calculated separately. Those who are good friends with mathematics may find it easier to use the formulas shown in the picture below.
Before you start direct calculations, you should have a ready-made plan and sections of the roof in front of you, indicating horizontal and vertical dimensions. Lucky for those who have construction documentation, and in its absence, they will have to climb onto the roof with an assistant, armed with a notebook with a pencil and a tape measure.
We understand in which case and what exactly needs to be measured, and how to make calculations.
Roof with one slope - or two identical
If you were able to measure the full length of the slope, which, as already mentioned, is the distance from the ridge to the edge of the overhang, then multiplying the result by the width, you will get the area. Alternatively, to determine the length of the slope, you can use the projection method, for which you need to know two of the three dimensions of the triangle formed by the slope. The formulas are shown below.
When calculating the length of the slope according to the projection, do not forget to add the length of the overhang to the total. By the same principle, you can calculate the gable roof. If her slopes are the same, it is enough to calculate the area of one and double the result.
Hip and hip roofs
The peculiarity is that it does not have rectangular slopes, but there are triangles and trapezoids. There are only triangles in hipped roofs, since there is no ridge in such roofs, and the rafters are connected at one central point. Therefore, the principle of calculating the areas of one- and two-slope structures is not applicable here.
Your task is to calculate the area of each slope, which differs in configuration, separately, using the appropriate formulas. For triangles, they are one, and for trapezoids, they are different - moreover, there can be several ways to calculate.
If the house is square in plan, then at the hipped roof all four slopes will be equal. If such a roof is made over a rotunda (a building with spherical walls), there can be 6 slopes with the same proportions. Therefore, having calculated the area of one, multiply the result by 4 or 6.
You can determine the area of \u200b\u200ba trapezoid slope in three ways indicated in the photo below.
Roofs, most often attic, can also have a half-hipped design. They differ from the hip ones in that, due to very small side triangles, large slopes do not have a trapezoidal shape, but an irregular hexagon configuration. Its area is calculated by dividing it into two shapes: a rectangle and a trapezoid. In the picture, this division is shown with a red line.
Calculate the area of each figure separately, and then summarize.
Roofs with spherical configurations
The most aesthetically pleasing from the point of view of architecture look combined, in which there are elements of different shapes. As a result, they make up a coverage of a rather complex configuration, each section of which must be calculated separately. Including, on the roof there can be not only planes, but also spherical surfaces: a cone or a hemisphere, which are usually designed over rounded walls or extensions in the form of turrets.
In any case, the calculation of their area is also determined by mathematical formulas.
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Construction is often called an exact science. One cannot but agree with this, because in fact, any building does not begin with the preparation of the foundation for the foundation, the erection of walls or the purchase of the necessary building materials. First of all, it is “built” on paper - a project is prepared, which includes sketches, drawings and all kinds of calculations.
One of the conditions for the "correct" construction of the roof is the choice of building materials and a well-compiled estimate for their purchase. Therefore, it is so important to know how to calculate the area of \u200b\u200bthe roof. For this, many resort to online calculators, which are widely presented on various sites on the Internet. Nevertheless, professionals recommend performing calculations "manually" taking into account the characteristics of a particular object.
If you know how to calculate the roof area correctly, and adhere to the required scheme when preparing project documentation, then the roof will undoubtedly turn out to be quite strong and reliable. Moreover, this will avoid unnecessary financial costs when buying building materials and its installation.
What determines the calculation of the roof
The roof calculation scheme depends primarily on the architectural features of the structure. For example, for outbuildings, they mainly use the easiest option for calculations - flat, attic - are more diverse:, and others, and each of these types involves its own calculation methodology.
Among the defining parameters should also be noted:
In almost any formula, the so-called design coefficient is used in calculations, which is selected based on the angle of inclination of the roof slope.
geometric shapes
Upon closer examination, it becomes obvious that the range of the most common forms of individual slopes is limited to elementary geometric shapes, such as:
- rectangle/square;
- trapezoid;
- parallelogram;
- isosceles triangle.
Of course, the design of modern roofs is much more diverse and, as a rule, it cannot do without a serious complication of the roof structure: its shape and dimensions change. However, even in this case, the "three pillars" on which the calculation is based remain elementary figures. The area of any complexity for calculating the area is divided into a number of simpler ones. The desired area, therefore, is nothing more than the sum of the areas of the constituent elements.
That is why, even if you have already graduated from school a long time ago, but are still at odds with elementary geometry, it will not be difficult for you to calculate the roof yourself.
Just in case, we recall the formulas for the areas of the main figures:
How to measure slopes and calculate roof area
When there is no roof plan with the exact dimensions at hand, they are removed independently. You will need a tape measure, calculator, and other tools needed when working at height.
For roofs with symmetrical slopes, it is enough to measure only one.
shed roof
To calculate the area, use the formula for a rectangle:
S=K x L, where K is the length, L is the width.
You can also measure the slope without climbing the roof - it is enough to measure the length and width of the house, taking into account the size of all overhangs:
- the width of the slope will be equal to the resulting length of the building;
- length - calculated according to the Pythagorean theorem, taking the height of the roof and the projection of the slope as the legs.
During construction, people face a lot of different problems. One of them is the arrangement of the roof and the calculation of the amount of material necessary for its construction. It can be recognized only if the area to be covered is correctly calculated.
Peculiarities
It will not work to calculate the roof area using some universal formulas. For a simple shed roof, such calculations are the simplest, but there are always nuances, ignoring which leads to sad consequences.
The calculation of the area always implies:
- accurate height measurement;
- determination of the degree of inclination;
- determination of the volume of the necessary building materials and fasteners to them (as the final stage).
Construction forms
The area of a pitched roof is calculated depending on which geometric figure the proposed roof corresponds to - most often these are isosceles triangles, trapezoids, rectangles and parallelograms. But it is important to consider that almost all roofs still consist of several slopes.
The single-sided option is calculated according to the formula for a rectangle.
If there are two slopes, you only need to apply the same formula to each of them and summarize the results.
A roof of four slopes is calculated as the sum of a pair of trapezoids and a pair of triangles with equal sides.
If the form is very complex, more time will have to be spent but the basic principles remain roughly the same. The first step is a breakdown into the simplest geometric shapes. Then the same formulas are applied to calculate the area of any of them as in the standard case. We must not forget that the length of the slopes is measured from the final lines of the cornices to the ridge elements.
When the area is irregular in shape, it is advisable to divide it into even smaller fragments in order to drastically simplify the calculations.
Chimneys and ventilation ducts should not be subtracted from the results obtained., windows built into the roof and other similar elements. When calculating the area of a flat roof for laying welded roll materials, the area of parapets is taken into account separately. It is necessary to take into account how the overhang will be located - along the perimeter, with a closed parapet or with a lower overhang and a three-sided parapet.
In its simplest form, the area of a flat roof can be taken equal to the total area of \u200b\u200bthe building, with the addition of overhangs and other elements that go beyond the contour. But such a calculation scheme is acceptable only if there are actually no corners.
With due diligence, it will not be difficult to calculate the area of \u200b\u200bthe pediment on your own. For this, there will be no need to even turn to the help of online calculators. The configuration of the gables is closely related to the geometry of the slopes: for example, triangular options most often accompany the formation of roofs with two slopes. When installing the structure before preparing the truss frames, it is necessary to calculate the area and height of the gables with special care.
To make the necessary calculations, as always, the use of "school" formulas helps. It is advisable to use electronic calculators only for self-examination.
The lengths of the walls of the ends, divided in half, are multiplied with the tangent of the angle that creates the slope and the base of the roof. For non-residential premises under the roof, the height will be much less than for actively used by people. The triangular wall is calculated by multiplying the height of the pediment itself and the length of the roof base. This result should be reduced by 50%. In the case of a “trapezoid” wall, take ½ of the total length of the bases, multiply it by the height. The pentagonal pediment is conditionally divided into an upper triangle and a lower trapezoid - this simplifies the calculation.
Calculating the area of \u200b\u200bthe L-shaped roof with a different slope is also not difficult. By its nature, it is formed from a pair of typical gable structures, joined at right angles. The general configuration is divided into four similar rectangular trapezoids to simplify calculations. The calculated areas are summed up and the final result is obtained.
You can simplify the work (refuse to measure individual slopes and planes) if you have a carefully prepared plan on hand.
Calculation method
It will not work correctly to calculate the quadrature of the roof of a house if you do not figure out exactly what its shape is. In the absence of clear and unambiguous plans, you will have to prepare them yourself by drawing all the necessary drawings by hand. An isosceles trapezoid is calculated taking into account not only the width of the slopes, but also the lengths of the bases and height. The prepared roof plan should reflect all lengths, widths and heights with an error of no more than 1 cm. If you can measure more accurately, you should definitely take this chance.
It is advisable to prepare a plan in several projections at once, and recheck each measurement and each calculation step. A mistake can be very expensive, literally. You can determine the number of square meters from the ground, from the roof itself, and from the attic.
To improve the accuracy of measurements and calculations, it is recommended to pay attention even to the asymmetry of the edge, to the excessive width of the ridge, to changes in the angles of inclination in different places. A 9 degree pitched roof is 10% larger than an identical flat roof.
If the slope increases to 56 degrees, the conversion factor already reaches 1.8, and the approximate change in it with an increase in the angle by 10 degrees is 15%. The slope angles of the slopes in houses covered with symmetrical gable roofs are determined depending on the length of the base of the isosceles triangle formed by the slopes. To calculate the overlap, you need to multiply the length of the house by the length of the rafters.
The area of all slopes is individually determined as the length of the house with the addition of the front and cornice overhangs, multiplied by the length of the rafters + the length of the overhang. If the roof is shed, doubling the resulting number is not necessary.
For the most accurate calculation of the footage of a triangle or any other geometric figure, the results obtained from the formulas must be increased by 10-15%. This will compensate for possible errors and defects when laying roofing material. It will be somewhat more difficult to calculate the roof area for subsequent fire retardant treatment and for impregnation with antiseptic compounds. The methods are approximately the same, but it will also be necessary to take into account the coefficients recommended by the fire department. They will make it possible to compensate for both calculation errors and the overconsumption of impregnating mixtures.
The problem is that special impregnation is not applied to the roof, and on the crate and the upper parts of the floors, rafters, trusses and crossbars. But rafters, beams and other similar elements have a much smaller area than the roof itself. And therefore, in most cases, to accurately predict the need for flame retardant treatment, you will have to enter a factor of 1.2. He will successfully “absorb” all the bumps.
The angle of inclination of the roof is calculated between the inclined rafters and the ceiling. When calculating the surface area that sheets of metal, slate or corrugated board will have to occupy, we must not forget that one of the waves is spent on connections with neighboring sheets. Therefore, you will have to add another 10% to the resulting area after all calculations and adjustments. It is also taken into account that sheet materials are measured in linear meters, which must first be converted into square ones, and only then compared with the dimensions of the roof. Additionally, you can check yourself using specialized online calculators directly from major providers of selected coverage.
If the roof does not have a wall gutter, add 7 cm to the slopes above the cornices. And in the case when there is a gutter, and a cornice, and an overhang, the length can be reduced by 70 cm. It is necessary to additionally calculate the area of parapets, a firewall wall and other structures that are not physically connected with the main coating. It is not necessary to take into account standing seams if single parts are covered with roofing steel.
You can also ignore the bypass of the base beam with rolled covers. Essentially, it does not play a role, as does the arrangement of aprons.
And about the ignored details: there is no need to calculate the roof connections to:
- parapet;
- antiaircraft lamp;
- thermal seam;
- pipe;
- ventilation shaft;
- wall.
Coverings of parts of the same roof, located in different planes and separated by other materials, are calculated each separately. If there is no building project or it raises certain doubts, it is better to measure all quantities in fact. The effort expended will turn a hundredfold, it will be much easier to repair or build from scratch. Moreover, centimeters unaccounted for on large-scale plans and diagrams in reality turn into whole meters of error.
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.
The correctness of the calculations when planning a new construction or carrying out repairs can significantly save on basic and consumable materials. Roofing cake is one of the key components of the house. In the process of its design, you need to know how to calculate the area of \u200b\u200bthe roof, be able to calculate the area of each of its elements. There are special computer programs for this. But, unlike the machine, the calculation "manually" gives a more accurate result, since it allows you to take into account the nuances of further laying of the roofing material.
Geometric roof shapes
The variety of geometric shapes of the top of the house determines the complexity of the calculation of its area. The most common stingray figures:
- rectangle,
- trapezoid,
- isosceles triangle,
- parallelogram.
It is quite simple to calculate the roof area if it has one, two or four slopes. The more elements - the more difficult, the more measurements and mathematical operations need to be done.
The calculation can be done in two ways:
- Make calculations based on the plan of the top of the cottage. All linear dimensions of each slope are necessarily prescribed on it. It remains only to calculate the area of \u200b\u200beach element and find their sum.
- Take "live" dimensions from the finished roof and perform mathematical operations. This option is more accurate, since an absolutely exact match between the real dimensions of the top and its plan is very rare.
In both cases, you need to pay attention to symmetrical slopes. First of all, this applies to the elements of a two- or four-pitched roof.
Calculation of the area of \u200b\u200bone- and gable roof
These two types are the simplest, since the slopes of the single-slope and gable tops of the house usually have a rectangular shape. The calculation of their area can be performed even without a detailed plan. It's also fairly easy to take measurements.
The area of \u200b\u200ba shed roof is equal to the area of one roofing rectangle:
A and B are the width and height of the slope, respectively.
These parameters can be found even without climbing to a height. It is enough to find out the length and width of the house and add the overhangs of the top of the house to them. Next, you need to measure the height of the roofing pie itself and, using the Pythagorean theorem, calculate its length. Now you can multiply the obtained parameters and get the desired result.
According to a similar scheme, the area of \u200b\u200ba gable roof is calculated. It can always be imagined as two sheds. Accordingly, and similarly, the dimensions of this type of roof are taken. If the slopes are symmetrical, you can remove the parameters of only one of them. Knowing the length, you can calculate the area of \u200b\u200bthe pediment of a gable roof, especially if it is planned to be lined with wall decking or siding.
The result for each roof element is determined by the same rectangle area formula:
Having known the area of both elements, by simply summing them up, the total value for a gable roofing surface is calculated.
Calculation of the area of hipped, hip and semi-hip roof
These roof options have a more complex configuration, so it takes more time to calculate the area of \u200b\u200bthe mansard roof. All of them are four-slope, which means that more measurements need to be taken.
A kind of roofing surface, composed of two trapezoids and two triangles, is called a hip. In most cases, its opposite sides are equal, and the triangles are isosceles. For such a symmetrical hip roof, it is enough to calculate the value for only two adjacent elements and multiply the result by two. If the dimensions of each of them are different, you will have to measure the entire roof.
After the measurements, you can calculate the value for each element. For trapezoidal elements, you need to use the following formula:
a - width along the lower overhang,
b - ridge width,
h is the height.
For triangular elements, the formula is applied:
a - the width of the slope along the lower overhang,
h is the height of the slope.
Well, at the end, as in the previous cases, the sum of the results of the calculation of all elements is calculated.
The half-hip design differs from the hip design in that instead of trapezoidal elements, it has hexagonal elements, the lower part of which is in the form of a rectangle, and the upper part is a trapezoid. Accordingly, the measurement process is slightly different. In a hexagonal element, you need to measure its two components separately, and also do the calculations separately. The formulas can be viewed a little higher in this article. Again, the total area of the half-hip roof is the sum of the results of the calculation of all its elements.
The traditional tented top is made up of four isosceles triangles. Usually it is symmetrical, so measurements can only be taken on two adjacent elements. It is only necessary to find out the height of each of the slopes and their width along the lower overhang. Further, according to the formula given just above, each element is calculated and the final calculation of the hipped roof is made.
Calculation of roof area with slopes with complex geometry
Multi-pitched roofs with elements with complex geometry no longer surprise anyone. These are the so-called dome and multi-gable structures. These solutions for the top of the house are very attractive. It is much more difficult to calculate the roof area of \u200b\u200bsuch a configuration than in the case of conventional four-slope options. But an accurate calculation is necessary, since there are a large number of slopes, each of which has a different shape. The construction of such structures is quite expensive and the slightest mistake will inevitably lead to additional expenditure of money and time.
The main difficulty in the process of calculating a multi-pitched roofing surface is the sizing stage, and the more elements in the structure, the more difficult it is to make measurements. Here you can not do without lifting to the roof. In any case, it is necessary to make a drawing of the roof and measure each slope. For each of them separately, it is necessary to calculate the area using the formulas given above, then, summing up the data obtained, find the total roof area.
The issue of calculating the area of \u200b\u200bthe roof must be approached very scrupulously. After all, roofing materials are quite expensive and errors in calculations will lead to unnecessary costs. It must be remembered that when buying roofing materials, it is necessary to make a small margin, since they are overlapped, and it is not taken into account when calculating the roof area.
We calculate the roof area correctly
How to calculate roof area: Rules and formulas.
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 a similar 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.
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,
- slope length (between the ridge and the cornice),
- 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.
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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.