Formula for calculating a pitched roof. Calculation of the roof area of ​​a house: main types of roofs, formulas

Often they try to order work on measurements from roofing companies for fear of making some kind of mistake. However, if you know a few simple rules, you can take competent and accurate roof measurements yourself.

Draw a diagram in a plane

First of all, you need to draw a diagram of your roof in a plane. “Quite often clients try to draw all sorts of 3D projections, but in reality, in order to correctly calculate the amount of material, the most basic drawing is needed, representing the view from above,” comments Andrey Opuk, general manager LLC "First Roofing" – Such a drawing does not even have to be done to scale.

When you arrive at the company’s office for the final calculation, the manager will simply ask you clarifying questions from the series “Do I understand correctly that you have a connection here?” etc. You just give the necessary comments.

Even a computer program that automatically calculates the material divides the roof into segments, which are triangles, trapezoids and other elementary shapes.”

Let's start taking measurements

To make it easier and faster to measure the roof, it is best to do it together. You don't need any special devices like a laser rangefinder.

As practice has shown, a long tape measure is enough, which is sold in any construction supermarket. With its help, you need to fix the sizes of all the edges.

Typically measurements occur as follows: one person comes closer to the edge of the roof and fixes the end of the tape measure at the place where the rafter leg ends, and if the roof is old and it is to be dismantled, where the roof covering ends.

The second person fixes the tape measure on the top of the roof (on the ridge).

There is one rule that must be followed: in addition to the ribs, it is necessary to take measurements of all slopes. The fact is that often the sizes of the slopes do not match perfectly. There may be slight displacements that are not noticeable to the naked eye. There is nothing fatal about this, but they should be taken into account when making calculations, so measure each slope separately.

No way no need to take all measurements from the attic side, from the inside. Otherwise you will get very approximate measurements.

Ilya Bykov, key account manager at Pervaya Roofing LLC:

Firstly, it is best to take measurements of the roof already after the sheathing is ready. Having only a rafter system, measurements are also possible, but using lathing they will definitely be more accurate.

Secondly, it is necessary measure the roof perimeter, where it is then assumed cornice strip. This size is also necessary to count the number of sheets of metal tiles (or corrugated sheets).

Thirdly, do not forget that the metal tile does not end with the rafter leg. As a rule, a release of 5-10 cm is made so that the roof has a decent appearance. When the final calculation is made to you, be sure to express to the manager your wishes for the release.

Fourthly, you should measure the perimeter of the pipe outlets from the outside. This is necessary to order the junction strips that are needed to protect against leaks.

If skylights or dormer windows are planned, also measure them and indicate their location on the drawing. This will save several meters of tiles.

If the calculation is carried out without taking into account the skylights, no problems will arise: the installers will cut the material to size. If any buildings are adjacent to your house, this should also be reflected in the drawing.

Metal tiles out of stock or to size?

Sometimes people prefer to order large sheets of metal tiles, for example, 6 or 7 m wide, so as not to install them with overlaps. We especially note that overlaps do not cause leaks, since this is structurally impossible.

Regarding savings in this case, we note the following.

Firstly, by “fighting” for size, you get quite long production times(during the season up to two weeks). Naturally, this is not a problem if you are not in a hurry.

Secondly, if the area of ​​your roof is about 200 sq.m., then saving due to large sheets may be a maximum of 4-5 square meters, however this benefit is most likely will fade away, when the cost of delivery and packaging will be calculated for you. For delivery of metal tiles, for example, 7 or 6 meters long, the gazelle is no longer suitable.

In addition, manufacturing plants are required to supply roofing materials in packaging, and it is sold linear meters. It turns out that delivery and packaging standard sizes may cost less.

We also note that when ordering large sheets of metal tiles, the installation process may become more complicated. Lifting a sheet 7 meters wide to the height of a two- or three-story house with two people is quite difficult. In addition, there is a risk of damaging polymer coating, scraping a sheet of metal tile against a staircase or rafter.

The article was prepared by experts from First Roofing.

What data is important and where to start calculations

1. Calculation of the area of ​​a lean-to structure
2. Calculation of the area of ​​a gable structure
3. Calculation of the area of ​​hipped structures
4. Mansard roofs and features of complex calculations
5. Help from online calculators

The construction of any house, regardless of its size, number of storeys and luxury, begins not with a foundation pit and foundation, but with the preparation of a project and calculations, among which the roof is one of the most significant and requires increased accuracy. It is also considered one of the most important elements of the building, and performs two important functions at once:

• protective, because it is it that will protect your home from moisture, precipitation, cold, i.e. will provide warmth and comfort in the room;
• aesthetic, giving completeness and expressiveness to the exterior, making the structure interesting and presentable. Even the most primitive “box” of a house, with walls that don’t stand out in any way and without original additions ( beautiful porch, fashionable terrace) well-chosen roof interesting design can easily turn into a real masterpiece of design art.

But it will only turn out this way if you have chosen the most suitable form, know how to calculate the area of ​​the roof of a house and perform other calculations, have not made any inaccuracies in measurements and mathematical operations, and have professionally implemented your wishes.

What you need to consider when calculating the roof area of ​​a house

Understanding how to calculate the roof area of ​​a house, knowing the area of ​​the house, will be useful to you, first of all, in order not to make a mistake in the amount of material needed for construction. The more accurately they are performed, the higher the chance of avoiding unnecessary financial costs.

First, decide on the type of roof to be constructed, because there are many modern architectural solutions: there are simple and complex, of the same type and combined - for every taste, as long as the appearance of the building is unique and irresistible. Today there are different forms:

• single-pitched;
• gable;
• hipped;
• attic;
• hip;
• tent

The shape chosen for the roof arrangement is always reflected in the construction project. When performing calculations, they also pay attention to what roofing material will be used to cover it (slate, metal tiles, etc.).

Directly to determine the general quadrature you will need to take the following data:

• the height of the ridge girder (ridge);
• slope length;
• angle of inclination of pitched planes;
• house parameters (width, length);
• the size of overhangs (pediment, cornice).

How to determine the quadrature of the simplest type of roof

The easiest way is to find out the area of ​​a lean-to structure, which is usually chosen to cover outbuildings (barn, garage, buildings for breeding pets).

The shape of the pitched plane is the simplest - it is a regular rectangle, respectively, the area is equal to the length multiplied by the width, and to each side you need to add the value gable overhang and cornice (you can take a standard one of half a meter).

How to calculate the roof area of ​​a house: gable structures

For residential buildings and cottages, gable structures are most often chosen; this option is often called “classic”. There will also be no problems with how to calculate the roof area of ​​a house with a calculator, because... all calculations are based solely on the simplest basics from the trigonometry course studied in high school. Initially, the area of ​​the pitched plane is determined, and then the resulting value is multiplied by “2”, because There are two slopes in the design. But if the project provides for the construction of sloped planes with different sizes, then the areas of each of them are calculated separately and summed up.

For a visual representation, we can consider one of the calculation examples; for it we will need the following initial data:

• the length of the house (let’s say it is 10 meters);
• the length of the slope (it is also equal to the length rafter leg and, suppose, was 5 meters);
• the size of the pediment and cornice overhang (let’s take standard ones, 0.5 meters each).

Substituting all the values ​​into the formula, we find that the area of ​​one pitched plane is equal to:

S=(10+2*0.5)*(5+0.5)=66 sq. meters.

Considering that there are two slopes, we double the obtained value, as a result we determine that the roof area will be 132 square meters. meters.

As a rule, any structure contains chimney pipes and ventilation duct outlets, and can be equipped with windows. But their sizes do not subtract from the resulting area.

How to calculate the roof area of ​​a house: features of hipped structures

Today, for the construction of the roof of a residential building, it is fashionable to choose hipped structures. Most often, if the dimensions of the building are proportional and square, the roof is made in a pyramidal shape. This variety is called “tent”, in this case each slope is an isosceles triangle, they are all connected at the top at a single point, and the base is a quadrangle. In this case, how to calculate the area of ​​a hip roof of a house with a calculator will not cause difficulties, because you can apply a formula that involves calculating the area of ​​the triangle, then multiplied by “4”. To find it, you need to multiply the width by the height and divide the result by two. Let's say we have the following data:

• the width of the base of the triangle is 8 meters;
• the height of the slope is 5 meters.

It is very important to take into account for this calculation that measurements are taken not along the perimeter of the structure, but along the eaves overhangs. Also, do not forget that the height of the slope must take into account the angle of inclination of the slope planes.

Understanding how to calculate the roof area of ​​a house hipped roof, you may be faced with the need to select calculations for a more complex design type called “hip”. This is also one of the popular solutions used today for the design of residential buildings, country cottages. This design consists of two end sides, shaped like isosceles triangles, and two side sides, made in the form of trapezoids. The calculation principle is based on determining the areas of a triangle and trapezoid, multiplying each obtained value by “2” and then summing it into the overall result.

As already discussed, to find the area of ​​a triangle, you need to multiply the width by the height and divide the result by two. In the case of a trapezoid, it is also necessary to use the provided formula, in which the bases are summed up, the resulting result is divided by “two”, and then everything is multiplied by the height of the pitched plane.

For hip design It is imperative to pay attention to the presence and size of windows, chimneys, overhangs, and parapets.

How to calculate the roof area of ​​a house: features of attic structures

Among the undisputed leaders in popularity is attic type. It is characterized by a sloping “broken” roof, which consists of two parts. In this case, the top is flat and the bottom is steep, which allows you to create a spacious and roomy attic space, which is usually called an “attic”.

When figuring out how to calculate the roof area of ​​a mansard roof house, at first glance it may seem that it is too difficult to do, but in fact the principle will be clear even to a non-specialist. First, you need to draw up a design plan with a clear indication of all known dimensions, and then simply break it down into the simplest geometric figures, the determination of the areas of which is carried out according to the school curriculum in geometry lessons:

• for a square S = a*a, where a are the sides;
• for a rectangle S = a*b, where a and b are also sides (length and width);
• for a triangle S = a*h/2, where a is the size of the base, h is the height of the figure;
• for a trapezoid S = (a+b)*h/2, where a and b are the upper and lower bases, h is the height.

Having received the values ​​of simple figures, they are summed up, and the final result will be equal to the total area of ​​the roof. Do not forget that there are two pitched planes, and it is necessary to sum up the quadrature of the simple figures of both sides.

Also, always remember that all measurements must be taken from the extreme point of the eaves to the ridge. When measuring the bases, always add at least half a meter to the eaves and gable overhangs.

Construction online assistants

Thanks to the limitless possibilities of the Internet, nowadays you can cope with the task much easier and faster, because... this one was invented handy tool, How online calculator, and anyone can calculate the roof area of ​​a house with its help.

To perform calculation actions, just go to the website and enter the data requested for calculation operations in a special form. Then the system itself performs the calculations and produces the finished result.

Online construction programs are offered paid and free; there are those designed for the most primitive calculations and more complex ones, working online or requiring installation on a computer. Of course, if you have to build a simple structure, then such a calculator will provide invaluable assistance in drawing up cost estimates for the purchase of materials.

When constructing more complex, combined forms, which are complemented by roof windows, necessity, hatches, chimney pipes, ventilation outlets, you can seek advice from a specialist (their services are also offered online). In addition, we should not forget that consumption depends on the type of selected roofing material.

Only 100% correct calculations of the roof area of ​​a house will allow you to avoid extra costs when purchasing materials for roofing and at the same time will not allow you to encounter shortages during the work process, which means that nothing will prevent you from finishing the roofing on time and moving into a new cozy and beautiful home as quickly as possible!

Information to note: , .

Construction of any kind is impossible without preliminary calculations, so this preparatory stage should not be neglected under any circumstances. You need to calculate the parameters of the roof itself, its angle of inclination and other aspects, as well as the amount of roofing material that will be required for the surface of the entire roof. We will tell you how to do this in this article.

The calculation of the roof area depends on the type of roof itself. If the roof is simple, i.e. single slope, then special problems should not be included in the calculations. But there are other cases when there are certain difficulties in this matter.

Any construction is a rather expensive undertaking, so the owner is glad of any opportunity to save money somehow.

Determining the roof area involves quite a lot of calculations, including finding the height, angle of inclination of the roof, as well as the volume of those building materials that are necessary to build the roof. If everything is done correctly, then you will not have to overpay for building materials by buying more than you need, and you will also save on transporting the material to the construction site.

The complexity of the calculation will directly depend on the type of roof used, of which there are a sufficient number.

How to calculate the roof area of ​​a house: online calculator

How to calculate the square footage of the roof of a house and not make mistakes in the calculations? Our construction calculator will help you with this, which calculates not only the square footage of the house, but also calculates the angle of inclination, the amount of roofing, rafters and much more.

This calculator calculates the coverage for a gable roof. Before starting the calculations, In the upper right corner of the calculator you need to select a roofing covering.

Below are calculators for other types of roofs:

Designation of fields in the calculator

Calculation results

The most popular types of roofs

The construction of a roof is a rather complex process in which it is necessary to take into account not only the roofing material, but also hydro- and thermal insulation. You also need to decide on the type of roof. So, Builders distinguish several types of roofing:

If the roof has a fairly simple shape, without unnecessary kinks, then calculating its area will not be difficult. If the roof is more complex configuration, with many slopes, then you will have to arm yourself with all your knowledge in geometry. This is explained by the fact that we will have to calculate the parameters of the geometric shapes included in the conventional roof pattern, and the difficulty will lie in the type of these same shapes.

In most cases, the roofs of private buildings are as follows: geometric shapes. Square pitched roofs calculated using these formulas:

1. Trapezoid. Calculation formula (A+B)*H/2.
2. Rectangle - A*B.
3. Parallelogram - A*H.
4. Triangle with equal sides - (A*H)/2.

Shed roof area

Calculating the area of ​​a pitched roof seems to be the simplest, because it does not require a detailed roof plan.

It is calculated using a very simple formula:

S- this is the area of ​​the roof itself (in this case, a rectangle).

A- this is the width of the roof.

B- this is the length.

Let’s say the length of a pitched roof is 7 meters and the width is 4. We calculate:

S = 4 * 7 = 28 meters.

How to calculate the area of ​​a gable roof?

This type of roof consists of two pitched roofs with different sides, therefore the calculation will occur according to a similar algorithm. All that remains is to add the resulting values ​​together.

Let us take for the calculation the same parameters as in the previous example, i.e. the width will be 4 meters, and the length will be 7. We make the calculation:

S = (4*7) + (4*7) = 28 + 28 = 56 meters.

Square hipped roof

If you look at such a roof from above, you can see that it consists of four geometric shapes, the areas of which we need to calculate. In other words, we need to calculate these values ​​for two trapezoids and two equilateral triangles. All the resulting indicators will need to be added up.

Let's take the same values ​​as the length and width, i.e. 7 (value A) and 4 (value B) meters, and the height will be equal to the conditional 3 (value H) meters.

We calculate using the following formula:

S = A*H/2 = 7*3/2 = 21/2 = 10.5 meters. The value of the second triangle will be the same, so we add these values: 10.5 + 10.5 = 21 meters.

Calculating the area of ​​a trapezoid:

S = (A+B)*H/2 = (7+4)*3/2 = 11*1.5 = 16.5 meters. We add the value of the second trapezoid: 16.5 + 16.5 = 33 meters.

Add up the resulting values: 21 + 33 = 54 meters. This will be the final area of ​​the hipped surface.

How to calculate the roof area of ​​a complex shape?

In principle, calculating the roof area of ​​a complex configuration is not much different from previous methods. Of course, you will have to spend a little more time, but the calculation rules are common for everyone:

• We divide the space into separate geometric elements. As a result, we get various rectangles, triangles, trapezoids and other shapes.
• Next you need to use mathematical formulas, already familiar with school curriculum, thus calculating the area for each figure.
• Remember that The length of the slope is taken from the extreme line of the eaves and ending with the ridge of the roof.
• We calculate the indicators for all the resulting figures, and then add all these values ​​together.
• If you see that the roof slope is of irregular shape, then it is better to break it into two simple shapes, because it is much easier to calculate the area of ​​two trapezoids than the area of ​​a polygon. This way you will save yourself time and nerves.

Calculation of roofs of complex shapes

Dependence of area on type of roofing material

We have already said that calculating the roof area is necessary for in order to calculate the approximate amount of roofing material.

But even if we carried out all the calculations correctly, the material still needs to be purchased with a small reserve so as not to encounter a shortage during the installation process. The type of roofing material also plays an important role, because the technology for laying it can be different.

Slate, metal tiles and corrugated sheets. Each of these materials is sold in the form of sheets, and they need to be laid overlapping. There is such a thing as " usable area» material, so you need to take it into account, and not the actual indicators. If the manufacturing company high level, then it must display such information on the packaging.

• The length of the building is divided by the width of the sheet of material. To the resulting value you need to add another 10%, which will be used for pruning. This is how we find out exact number sheets covering the entire width of the roof.
• Divide the length of the slope by the length of the sheet of material. Then you need to add 13%, which will be used for overlap when installing sheets.
• Then we multiply the number of sheets by the width of the roof and total number rows to the eaves. The required figure will be the total number of sheets of slate or metal tiles for a particular roof.

Calculation of a complex roof

In principle, the calculation of all parameters turns out to be not so complex process if you follow the above recommendations.

Our construction calculator can do all the calculations for you. All you have to do is enter the data on the length, width, height and other indicators of the building, as well as the roofing material used.

Conclusion

Correct calculation of roof parameters is necessary to purchase the required amount of roofing material. If you don't have detailed plan at home, then all measurements will have to be carried out independently, using a tape measure, a ladder and other related tools. Also, do not forget that the type of roofing material also plays an important role, so each calculation should be carried out individually.

If you are not confident in your abilities, then you can entrust this matter to professionals who will do all the work for you. It's practically win-win, only if the price of the issue does not bother you much.

In any other case, you can think a little and make individual calculations. As you can see, this is not so difficult to do, but you can save money, which will then be spent on the same materials and more.

Roofing calculator

Construction of a house requires competent calculation of the estimate. The choice depends on it building material, the process of constructing a building or structure. You can independently calculate the cost of the roof using a special program.

The amount of required material and the number of additional elements. The more complex the roof, the more basic and consumables will be required.

Take measurements and enter data. If the roof structure is complex, then it is divided into separate planes and all distances for cutting the material and geometric construction are measured. When calculating, special attention should be paid not to the roof area, but to the size of each slope.

Each material has its own installation features, different additional elements and fasteners. Therefore, before making calculations, you need to decide directly on the material.

Above the roof layout there are switches for product profiles; they will allow you to select the required profile, taking into account its working width and restricted lengths. To view the layout of sheets on a ramp, select the ramp by clicking on it. Use the arrows to change the length of the sheets according to your needs for the selected slope.

Below are the parameters of your roof and the amount of material required, taking into account the prohibited lengths and overlaps of the sheets. You can then add the item to your cart and, if necessary, cancel any items in your cart.

Calculation of roof covering

An easy-to-use roofing calculator will allow you to find out the amount of material required per square meter, the number of additional and component elements. If you find it difficult to complete the calculation, request a call back. Grand Line managers will provide you with detailed technical information about various types roofing coverings, prices, terms of payment, delivery and will create an accurate estimate.

The roof calculation is carried out after taking the necessary measurements. The resulting dimensions must be entered into the appropriate fields of the calculator. When measuring, it is worth considering the following parameters:

• roof slope and geometry (single/gable, hipped, mansard, hip);
• the presence of hatches and other elements that are left without roofing.

Dimensions of drawings and building plans may differ significantly from actual dimensions. The most accurate calculation will be made only by a highly qualified specialist.

When calculating complex roof the roof is divided into separate planes and each element is measured. Special attention pay attention to the size of the slopes.

Before making calculations, you must select a material (corrugated sheeting or metal tiles). Each type of coating has different features installation work, additional elements, fasteners. For roofs with a slight slope, seam roofing is used. Fold is a special seam with which metal sheets connect with each other.

The program allows you to select the thickness of the metal and the color of the coating. Thanks to the wide color scheme you can pick up best option for your home.

Our calculator will allow you to cope with this task online. Soffits are calculated automatically taking into account the material (metal / PVC). Soffits are used to cover eaves and gable overhangs.

If necessary, you can refuse to calculate screws, insulation, additional elements and components. This will reduce the order cost. The calculation is made taking into account the prohibited lengths and overlaps of sheets.

Once payment is complete, add your order to your cart. Delivery of roofing material is possible to any region of the Russian Federation.

When independently designing a three-gable roof and preparing for its installation, it is necessary to calculate in advance many important parameters, one of which is the total area of ​​the roof being created. Importance exact value area is large, since you will have to plan to purchase not only the selected roofing material, but also waterproofing and windproof membranes, thermal insulation, materials for creating sparse or continuous sheathing.

Calculator for calculating the roof area of ​​a three-gable roof

It would seem that there is nothing complicated, since the roof slopes are ordinary flat geometric figures, the formulas for calculating the areas of which have been known since school. However, the rules can be forgotten, and the features of a complex design with the intersection of planes can confuse an inexperienced novice designer or cause an error. To simplify the calculation process, a calculator for calculating the roof area of ​​a three-gable roof will be helpful.

A number of necessary clarifications will be given below.

Calculator for calculating the roof area of ​​a three-gable roof

What is the basis for calculating the roof area?

The roof of a three-gable roof is a combination of rectangles, triangles and trapezoids.

Total area roof is the sum of the areas of the rectangles, triangles and trapezoids that form it.

The slopes of the main building are rectangular, but a triangular section is “cut out” on one of them, bounded by slanted rafter legs. Above an extension, the slopes are usually trapezoidal, but in the case where there is, in fact, no extension, and an additional gable (pediment) is created only to form a dormer window, these slopes become triangular.

So, to enter data into the calculator you need to know:

• The overall length and width of the main building are easy to measure.
• Length and width of the extension. If there is no extension, as such, then the length is indicated “0”, and the width is the width of the created tong (“cuckoo”).

The extension itself may not exist - an additional gable (often called a “cuckoo”) is erected only to expand the useful functionality of the attic space

• The lengths of the main rafters of the building and extension. In this case, the elongation of the rafters to create a cornice overhang is also taken into account.

Where can I get the size of the main rafters with the extension for the eaves overhang?

Nothing complicated - if this shelf parameter is unknown, then it can be quickly and accurately calculated. For this purpose, the portal contains calculators, one of which is intended for calculating the length of the main rafter legs, and the second – to determine the necessary lengthening the rafters to form a cornice overhang.

Important - for the main building and for the extension (additional gable), calculations of the length of the rafters are carried out separately, since both the slope angle of the slopes and the dimensions of the rafter leg with the same ridge height may vary.

Prices for corrugated sheets

• And finally, it is necessary to indicate the planned width of the eaves and gable overhangs of the roof. This refers to their width in plan, that is, the horizontal distance from the surface of the wall to the edge of the overhang.

The calculator will calculate everything else itself. Accurate result will be issued in square meters. Well, with the further purchase of roofing and other materials, it is already possible and necessary to lay down a certain reserve - for different types coatings it can vary significantly.

Multi-gable roofs - how is their rafter system designed?

More details about the device rafter system multi-gable roof, the procedure for its calculation and construction can be found in a special publication on our portal, to which the recommended link leads.

How to calculate the roof area depending on its type?

The construction of a roof begins with choosing its type and calculating the required building material. Many people have problems with the latter: either they have purchased less, they have to visit markets or stores again, or they have more - they are left with material that has nowhere to be used. Therefore, calculating the roof area is a mandatory procedure for a thrifty and economical owner. So, let's figure out how to calculate the roof area of ​​a house.

Types of roofs

The most commonly used designs:

• single slope;
• gable;
• hip;
• half-hip;
• tent.

Roofs are rarely assembled in the form of multi-gable structures, domed or arched. Regarding the shape of the roof, it is necessary to indicate that its elements are geometric shapes. This means that calculating the roof area is the calculation of this parameter of the figures. Now let's move directly to the topic - how to calculate the roof area.

Shed roof

In fact, the shape of this roof is a rectangle. Its area is the product of two sides. Therefore, it is necessary to measure the length of the slope, the width from the facade to the rear wall, and multiply the resulting indicators among themselves. If a roofing project has been prepared for the house, then these parameters can be taken from it. Or use the suggested online calculator form below.

Gable

This type of roofing structure consists of two rectangles located at a certain angle to each other.

1. If the roof is symmetrical, then the calculation of its area is carried out in exactly the same way as in the previous case. Only the end result is doubled.
2. If asymmetric, then the indicator of each slope is calculated separately, and then the two parameters are summed up.

To calculate the area, simply fill out the fields of the online calculator and the program itself will automatically calculate the area of ​​the gable roof.

hip

This type of roofing structure consists of four slopes, two of which are trapezoids (identical), two of which are triangles (identical). Moreover, the triangles are isosceles, which simplifies the calculation.

Everyone knows from school geometry courses that the area of ​​a trapezoid is calculated using this formula:

S=(a+b)h/2, where “a” and “b” are the bases of the figure, “h” is the height. The base is the length of the ridge and cornice, the height is the distance from the cornice to the ridge.

Formula for an isosceles triangle:

S=ah/2, where “a” is the base of the triangle, “h” is its height. The base is the length of the cornice, the height is the distance from the cornice to the ridge.

Now, in order to find out the area of ​​​​the roof of the house (hip), you need to add the results obtained and double them. According to the formula it will look like this:

So=(Str+St)2, where So is the total area of ​​the roof, Str is the area of ​​the trapezoidal slope, St is the area of ​​the hip. And since the slopes on the roof structure are arranged in pairs, their sum increases by “2”.

Or simply use the form below to automatically calculate the hip roof area using an online calculator.

Half-hip

Before calculating the area of ​​a half-hip roof, you need to understand why it is called that. In it, the hip, which is a triangle, is presented in the form of a shortened triangular figure, so the main slope is not trapezoidal in shape. It is complex, so it is recommended to break it down into simpler forms.

Most often, the breakdown is made into a trapezoid and a rectangle. Therefore, for the calculation you will have to use three formulas at once: for a triangle, a trapezoid and a rectangle. The main task of the calculation manufacturer is to accurately carry out the breakdown and correctly measure the parameters of the roofing structure.

There is a variation in half-hip roofs in which the hip is present in the form of a trapezoid. That is, above it there is a triangular pediment, which creates this figure. It turns out that you will have to count area of ​​three figures: two trapezoids with different sizes and a rectangle.

Tent

One of the simple roofing structures, which are four isosceles triangles connected by the upper corners at one point. Therefore, you will have to calculate only one figure, and then multiply the resulting value by “4”.

Or you can use this formula:

To simplify the process of calculating the area of ​​a hip roof, we went further and created an online calculator. So you can simply enter your data into the form below and the system will do the calculation itself.

Attic

This variety belongs to the category of broken models. That is, each slope at the place where the racks are installed for the construction of walls has a break line. And more often the angle of the lower part is steeper than the upper. It is along the fracture line that the slope must be divided into two parts, and each one must be counted separately.

In this case, the figures of the lower and upper slopes are rectangles. Their touching sides will be the same, the only differences are in height. Therefore, you can use the generalized formula:

S=(h1+h1)b, where “h1” and “h2” are the heights of the rectangular slopes of the sloping roof, “b” is the length of the slope along the eaves. And since there are two stingrays, a two is added to the formula. Final formula:

Complex roofs

There are not many problems with complex roofing structures. The main task of the calculation producer is to break them down into simple geometric shapes. And then calculate their areas and add them into one result. There are no other rules.

Automatic area calculation

If you don't want to waste time studying the textbook again high school in mathematics - just enter the parameters of a complex roof required by the online calculator and you will receive an automatic calculation of both the total area of ​​the entire complex roof and its individual parts. The calculator is structured for your convenience. Our online calculator can also calculate the area upon your request. dormer window and chimney, you only need to use the switch suggested in the calculator.

Roof area - depending on roofing material

The variety of roofing coverings does not seem to affect the question posed by the topic of the article, how to calculate the roof area. But it is necessary to understand that the calculation of the roof area is carried out precisely in order to purchase the required amount of coverage for it.

And since there are a huge number of roofing materials on the market, there are also a lot of technologies for their installation. For example, sheet materials, the sizes of which are divided into general and useful. It is the latter that is taken in order to calculate the required quantity.

Thus, a profiled sheet of grade H20 has a total width of 1150 mm, a useful width of 1100. To calculate the quantity, the second indicator is taken, because the profiled sheets are laid overlapping. This applies to both slate and metal tiles.

In terms of the length of materials used. Corrugated sheeting is sold in lengths up to 12 m. It can be cut so that it covers the slope completely without joints. As for slate and metal tiles, here, as with the width, you will have to take into account the overlap. Therefore, 13–15% is added to the quantity.

The most difficult thing with complex roofs, where the roofing material has to be cut to the required shape. This not only increases waste, but also the complexity of assembly. This especially applies to matching the flooring to the drains.

Conclusion on the topic

In conclusion, it should be noted that the question of how to calculate the roof area does not require the most in-depth knowledge. A school geometry course is enough. The main task is to accurately make measurements that are required to carry out mathematical calculations. You will encounter difficulties when you have to calculate complex roofing structures. Here you need to correctly break down complex figures and shapes into simpler ones. The main thing is not to lose even the smallest element of the breakdown.

At the same time, we should not forget that the purchased roofing material is a variety of laying technologies, which mainly take into account not the general dimensions, but the useful ones.

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The construction of every house does not begin with digging pits or pouring foundations.

Construction begins with project development and calculations.

With a roof, everything happens in a similar way: before starting to install it, a careful calculation of the height, the size of its surface is carried out, the number of structural elements and the amount of material for the roofing cake are determined.

The strength and reliability of the roof, as well as the quantity financial resources, which will be spent on its device.

Surface calculations always start with:

• measurements of the main parameters of the roof: angle of inclination, ridge length, length, width and height;
• determining the type of roofing material that is planned to be used in the future when constructing the roof.

One of the most important characteristics is a calculated coefficient used in almost all formulas in calculations.

The value of this coefficient depends on 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 shapes, the area for which is calculated in an elementary way.

And at the end, the results obtained are summarized.

Calculation procedure for a pitched roof

This is geometry from a school course.

Houses with a pitched roof 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.

You should also not forget the coefficient mentioned above.

Calculating a gable roof

Calculations for the surface of a gable roof are more complicated.

And many more factors should be taken into account in such calculations.

To begin with, we decompose all complex elements, as mentioned, into separate simple shapes: rectangles, squares, triangles.

After all, on the roof, each corner is formed only by the ceiling and the slope.

Therefore, in order to calculate the roof surface, it is necessary to multiply the area of ​​each 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 eaves line.

Any roof with any number of slopes is calculated in exactly the same way.

You just need to sum up the resulting surfaces of all 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 figures and the area of ​​each of them is calculated.

Then all surfaces are summed up.

Let's look at how this is done using the following example: a house has dimensions of 10 x 8 meters.

The rafters are 4.5 meters long.

Naturally, there is an overhang.

The overhang length is standard - 50 cm.

First, let’s 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, dormer and attic windows, parapets, they are not subtracted from the resulting area value.

We consider the hipped roof

Then you should determine how difficult each of them is.

The simplest one has a pyramidal shape.

Therefore, when calculating its surface, the formula for a pyramid is used.

If all the slopes have the same dimensions, then it is enough to calculate the area of ​​one of them and then multiply by four.

In the case when it has complex shape, then it is divided into simple figures and the surface of each of them is calculated separately.

Then the results are summed up.

But there is one subtlety: when calculating the area of ​​each slope, it is necessary to take into account the angle of its inclination.

After all, for such a roof, the angles of inclination can differ significantly for different slopes.

It should also be remembered that dimensions are taken not along the perimeter of the building, but along the overhangs of the eaves.

Calculating a hip roof

In order for the calculation to be performed correctly, the following must be taken into account:

• window size and chimney size;
• the length of the slope (between the ridge and the cornice);
• parts that are not included in the roofing covering (overhangs, parapets, etc.);
• When performing calculations, the junctions of roofing slabs, paving ledges, and standing seams are not taken into account.

Calculating the surface of a hip roof consists of 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 shapes and calculations are made separately for each of them.

And then the calculation results for each figure are summed up.

You should know that even though hip roof- this is the best roofing solution, its installation is not cheap.

Calculation for a hip roof

A hip roof is one of the varieties of a hipped roof.

So let's say this classic roof with four slopes.

The basis of this design is a quadrangle.

And the slopes are isosceles triangles converging at the central upper point.

This type of roof is the most economical, since it has no gables at all.

Since the slope is equal to isosceles triangle, That:

b is the length of the base of the triangle;

h - height;

S is the area of ​​the triangular slope.

Calculation of a broken attic roof

Area, despite its apparent complexity, is quite simple to calculate.

To do this, you should, 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.

For a rectangle:

In this formula:

a - length,

b is the width of the figure.

For a triangle:

In this formula:

a - the base of the figure,

and h is its height.

For trapezoid:

h x (a + b) / 2.

h - height of the figure,

a and b are the dimensions of the upper and lower bases.

After the area of ​​each of the simple figures into which the broken line is divided is calculated mansard roof, the results obtained are summarized.

Video about construction calculator to calculate the roof.

Sergey Novozhilov - roofing materials expert with 9 years of experience practical work in the field of engineering solutions in construction.

At the design stage of a gable roof, it becomes necessary to calculate the amount of roofing material. To do this, find the area of ​​the gable roof, taking into account gable and eaves overhangs, superstructures, ventilation, etc. To calculate the area, it becomes necessary to calculate a number of roof parameters. The main parameters include:

• roof angle;
• length along the ridge girder or eaves overhang (which is the same thing);
• length of slopes;
• height from ceiling to ridge.

Calculation of roof slope angle

The slope of the slopes is determined at the design stage and depends on the choice of roofing, climatic conditions, type of attic (cold or attic), design of the roof itself.

If the house will be built in places with strong wind loads, then they try to make the slope small in order to reduce the load on the roof. When building a house in regions with heavy rainfall, the slope is made significant (up to 60°) in order to reduce the load from snow, melt and rain water.

However, there is a need to find out the slope angle of the constructed roof. In this case, an inclinometer or simple trigonometric formulas are used.

But, more often than not, a novice builder does not have an inclinometer at hand, and geometry comes to the rescue. Let's take gable roof and consider its section along the ridge. The resulting cross-section is pitched roof, the shape of which is a right triangle.

The first leg acts as half the width of the house. The second leg is the height from the ridge to the ceiling. Hypotenuse is the length of the slope. Knowing any two parameters, you can easily calculate the slope. Let us give an example for greater clarity and understanding.

The width of the house is 8 meters, the length of the rafter leg is 10 meters. The slope of a gable roof is found from the following expression:

where A is the roof slope angle;

c – half the width of the house;

b – length of the rafter leg.

IN in this example half the width of the house will be c=8÷2=4 meters. Let's calculate the slope:

cos A=4÷10=0.4.

The resulting value is the radian measure of the angle. To convert radians to degrees, we use the Bradis table, which is widely available on the Internet. The desired slope will be 66°.

Determining the height of a gable roof

After determining the slope of the gable roof, it is necessary to calculate the height of the ridge. Knowing the height of the ridge, you can use trigonometric expressions to calculate the length of the slope, which is the length of the rafter leg.

Height can be calculated in two ways:

• using a right triangle;
• using a table of ratios of the angle of inclination to percentages.

The first method of calculating the height is using the values ​​of the angle of inclination and half the width of the house. Let's look at an example for clarity. The width of the house is 12 meters, the slope is 40°.

Half the width of the house will be:

The height of the ridge is determined by the trigonometric formula for a right triangle:

a=c×tg A=6×tg 40°=6×0.84=5.05 m.

To find the tangent of 40°, the Bradis table was used, as in the example above.

In order not to look for a value in the Bradis table, you can use an engineering calculator that is installed on any operating system!

The second option for determining the height of the ridge is to use the table of ratios given below.

Here, each angle of inclination corresponds to a certain relative value, expressed as a percentage. The height is found by multiplying half the span width of the house by the relative value. Let's look at an example for clarification. Let's take a house with a span width of 7 meters and a slope angle of 27°. The height of the ridge will be:

(7÷2)×0.509=3.5×0.509=1.78 m.

Determining the area of ​​a gable roof

When finding the area of ​​a gable roof, the following points must be taken into account::

• The total area will be the sum of the areas of each of the slopes. Therefore, first find the area of ​​one slope and multiply by two;
• Rarely, there are cases when the slopes in a gable roof may differ in one or more parameters (sizes). In this case, the area of ​​each slope is calculated separately. The total area is found by summing the areas of individual slopes;
• It is necessary to take into account that if the roof slope is an irregular rectangle (i.e. at least one of the angles of the quadrilateral is not equal to 90°), then the slope should be “broken” into simpler figures and the areas for them should be found. When such a situation arises, the slope is divided into a rectangle and a right triangle;
• When finding the area, chimney pipes, auditory and skylights, holes for ventilation;
• Pediment and cornice overhangs, parapets, and firewalls are taken into account.

Consider finding the area on simple example. The box of the house has dimensions of 7x9 m, the length of the rafter leg is 4 meters, the eaves overhang is 0.4 meters, and the gable overhang is 0.6 meters. The area of ​​one slope will be:

S=(L dd +2×L fs)×(L c +L x);

where Ldd is the length of the house (9 meters);

L fs – value of the length of the gable overhang (0.6 meters);

L c – length of the rafter leg, i.e. slope length (4 meters);

L ks – length of the eaves overhang (0.4 meters).

Let's find the required area of ​​the slope:

S=(9+2×0.6)×(4+0.4)=10.2×4.4=44.9 m2.

The area of ​​the gable roof will be:

S=2×44.9=89.8 m2.

In the case of using roofing tiles or roll material the length of the slopes will decrease by 0.6-0.8 meters.

Roofing area

Square gable roof is calculated in order to find out the required amount of material that will be placed on the roof. The steeper the roof slope, the more material will be required to cover it. It is recommended to purchase material with a reserve of 8-15%. This overspending is caused by the overlap with which the material is laid. To determine the missing material, you should use a table that takes into account the slope and determines the material reserve factor.

When calculating the area of ​​a gable roof, it is necessary to take all measurements correctly and use a roofing calculator on the Internet to check your own calculation. In addition, if the calculation is done correctly, you will not have to buy additional material.