Once before the developer, the question arises how to calculate the roof plane for pre-ordering roofing material, insulation or waterproofing. You can contact the experts, but some prefer to participate closely in the process. Depending on the complexity of the design of the roof, it is divided into different types.

Four main types of roofing

• Flat roof.
• Simple pitched roof:
  • single slope;
  • gable;
  • broken line;
• Quadrant roof:
  • hip;
  • half-hardened;
  • hip;
  • dome (in the form of a cone);
• Combined roof, which includes in its configuration any elements from all types of roofing.

To calculate the area of ​​the roof needed roulette, calculator and knowledge of simple laws  geometry at level 5-6 class. There are some features specific to the calculation of the roof area.

How to calculate the size of the roof shed roof

The roof with one slope is the simplest of the species. It is used infrequently, because with modern high aesthetic requirements for the external appearance of the house of beauty, such a design will not add to it. Most often, a shed option suit on barns, mobile cellars and other outbuildings.

Sometimes the designer does not use one in the exterior of the house, but several such scattered roofs in different levels, which looks very original in itself.

Such a roof at the top has the shape of a rectangle and is calculated by multiplying the length by the width. With a length of clear, its size is taken along the length of the eaves overhang. The width (length of the inclined plane) is measured by fact or is calculated by the formula.

The pediment is a right triangle, and the length we need is the hypotenuse in it. The height of the gable and its length are separately squared and folded. From the obtained value take the square root  using a calculator. It turns out the value of the second side of the rectangle.

How to calculate the area of ​​a gable roof

A simple gable roof consists of two single-sided surfaces on both sides of the ridge and connected under its upper horizontal side. This type of roofing is often used, as the simplicity of implementation does not require the expenditure of material and human resources. Warming, waterproofing are made quickly.

It happens that developers use the inner loft space  for the attic equipment. For this option, more suitable broken gable roof with different slopes of the side slopes.

How to calculate the roof area? Counting a simple and broken gable construction is reduced to calculating the areas of rectangles and adding their values ​​to each other. The calculation of the long inclined side is made similarly to the previous single-pitch roof. The Pythagorean Theorem is used that the square of the hypotenuse is equal to the sum of the squares of the legs. Often there are options for the calculation using sines and cosines. They have the right to exist, but on the construction site there is simply no place to take the tables with their values.

How to calculate the area of ​​the hip roof

Hip construction

This roof was popularly the name of the "envelope". If you look at the top, then it is exactly the form that reminds him. It differs from the gable structures in that instead of two side gables there are two more full-length slopes, often inclined towards the central part of the roof. This upper part of the house they prefer to arrange in areas where large wind loads continue most of the year.

To calculate the area of ​​the four-slope roof, use the areas of two figures: a trapezoid and an isosceles triangle. To calculate the area of ​​a trapezoid, you need to multiply the length of the base (measured by the length of the eaves) by the height. The height is called a straight line lowered from the upper base of the trapezoid at an angle of 90º to the lower base. It is measured in place.

Area of ​​an isosceles triangle calculated by the formula of Gerona:

S = √ (p * (p - a) * (p - b) * (p - c)), where a, b, c are the lengths of the sides of the triangle. They will have to measure at the height of the rafters, not forgetting to add the thickness of the batten. You can calculate the drawing of the roof, but the calculation is complex and not always accurate. The letter p denotes half the perimeter of a triangle (the sum of the lengths is added and divided by two). The formula, despite the complexity is very accurate. Calculation chetyrehskatnoy roof can be considered complete.

Half-gummed roof

This chetyrehskatnaya design differs from the hip roof that are arranged on the sides small vertical gables  at the top of the ramp. In their plane equip light windows for the interior of the attic. Differs in labor-intensive design and high consumption of roofing material.

The calculation of the area is obtained by two isosceles triangles and two side slopes, which have a complex, different from the shape of a trapezoid. On closer examination, it is possible to divide such a shape into a trapezoid and a right triangle. How to calculate the area of ​​these figures was described above.

Hip construction

Such a four-slope roof consists of isosceles identical triangles, connecting with their vertices at one point. It seems possible to build such a system if the square is at the base of the house. It is a type of hip hip roof. Sometimes combined with the main roof.

When calculating the area of ​​one isosceles triangle is multiplied by four.

Dome version

The roof of this type is a cone. It is rarely used, sometimes for the construction of roofs of decorative gazebos or for individual small protruding elements of the height of the roof. It has a large amount of roofing waste due to the difficulty of cutting to size. The area is calculated using the cone formula.

Combined roof

Every owner who builds a house wants to have a unique, individual structure. Designers respond to such wishes with more and more varied roof designs. As a result, very complex forms appear, having up to a dozen surface configurationscombined with skates, valleys, cornices and parapets.

Often, when purchasing a material for coating, it is necessary to take into account a large waste of material for a not entirely economical cut. It is not recommended to calculate such a roof area on your own, it is better to contact specialists.

Calculation of the area under slate

When calculating the required number of asbestos cement sheets take into account that the installation of slate is with the entry of one wave to another. The transverse joints also suggest an overlap of at least 15 cm.

The area of ​​the roof is calculated as usual. Further, its value is divided by the area of ​​a slate sheet. Here you need to be careful. They divide not by the total, but by the useful area of ​​the sheet, the one that represents the quadrature of the surface to be covered. This area can be calculated independently or in the tables.

For the most common in the work of 7 wave sheets of slate, the entire area of ​​the roof is divided into useful leaf area equal to 1,335 m2. At 8 wave standard sheets, this figure will be 1.56 m2.

Such calculations are relevant for simple single-pitch and gable roofs, more complex ones should be considered taking into account the layouts and the cut-map.

Calculation of the surface under the metal tile

When calculating this option, you must take into account the width of the strip of material along the entire length. This indicator depends on the name of the variety and in each case is different.

When counting pay attention to the angle of inclination. The smaller it is, the wider the transverse joints are planned. Simple roofs require a correction factor of 1.1 to be applied to the total area, and in complex and combined structures, the overrun can be up to 40–60%.

Counting the roof is difficult, but necessary occupation. Sometimes this needs to be done in order to approximately check the craftsmen working on your roof.

To ensure the comfort of the house and keep the precious warmth, mankind has invented a roof for its quiet corner. In proportion to the development of human needs, the surface of the house began to take on different forms over time, expanding the useful space in the house. Cover is the most important element of the roof, because the question of calculating the area of ​​the roof remains always relevant, because not everyone is given the opportunity to understand this geometry the first time.

The hip roof has four slopes interconnected, two of which are in the shape of a trapezoid, and the other two end (“hips”) in the shape of a triangle.

The calculation of the classic gabled coverage does not entail any complex mathematical operations.

Therefore, we will not dwell on viewing the calculation of this type of roof and immediately proceed to the consideration of a more complex type - hipped (hipped) roof.

What is a hip roof and what are its varieties?

In the picture: A-hip roof, B-hip roof, C-semi-hinged roof with gable, D-half-hinged Danish roof.

Chetyrekhskatnaya has in its title a direct explanation of its non-standard design. Planes on the roof, which drains rainwater, are called slopes. It should be understood that these four planes have four planes. As for the varieties of this type, there are several of them, consider the main ones:

1. Classic with four ramps.
2. The four-pitched shelter of the L-shaped house.
3. Danish hip.
4. Tent.

So, we dealt with the main types. So how can you now calculate the S roofing of such roofs using a simple calculator, without resorting to complex mathematical calculations, whose integral elements are often incomprehensible sines and cosines, and get an easy calculation?

Make it easier than you thought!

Calculate S roofing

If you look at the elements (slopes) of four-sided roofs, you can easily notice that each slope often represents a simple geometric figure. And recalling the school geometry, we recall the statement: the area of ​​a complex geometric figure, which can be divided into more simple ones, is equal to the sum of the areas of these simple geometric figures.

In this case, we begin to look for simpler geometric shapes in each hip roof.

Looking at the first picture, we will see a complex geometric shape, which consists of four simple ones, two of which are mirrored by the other: this is a triangle and a trapezium.

Very important information

If there are chimneys in your hip roof, do not forget to deduct from the total area the area occupied by the chimney, which is not planned to be covered. The chimney describes a rectangle on the projection. If there are dormer windows, you should also subtract the S window from the total area. If you built a four-sided roof with vertical windows, which also need to be covered with roofing material, then, having examined such windows, you will see the same geometric figures, S of which we have already calculated, but pay attention: in this case, this window also describes a rectangle on the slope plane , S of which you first need to subtract from the total, and then to the total area you need to add the S of the roof of the vertical window. Only taking into account all these subtleties, you can correctly calculate S roofing.

The four-pitched roofs of metal tiles are the most popular option for those who build a country house, cottage or cottage with their own hands. However, not all developers know how to properly. But without this there can be no question of correctly determining the amount of material for the roof, insulation and waterproofing.

For profiled metal sheets you may need a much larger overlap than for natural tile.

To date, the calculation can be done with the help of special computer software that is intended for all types of roofs. Such programs have their advantages: the possibility of choosing various design options, high accuracy, convenience, and so on. However, many builders, especially older people, like to do everything without using computer programs. How to calculate the area of ​​the hipped roof independently?

An example of calculating the area of ​​the roof

Suppose the existing roof will consist of 2 regular trapezoids and 2 isosceles triangles. The slopes will be located at an angle of 30 degrees. In this case, the cosine of this angle is equal to 0.87.

Trapezoid slopes can have parameters: one side is 7 m, the other is 10 m, and the height is 3 m.

Triangular slopes: two sides of 3.34 m, one side - 7 m. The height of the triangle is 4.8 m.

We find the area of ​​the trapezoid: the summation of the length of the horizontal sides is made, it is all divided by 2 and multiplied by the height. Therefore, in this case it will be: S = (10 + 7) / 2 x 3 = 25.5.

Do not forget that the resulting number will need to be multiplied by the cosine of the angle. In this case, multiplied by 0.87. The area of ​​the trapezoidal slope will eventually be equal to 22.185. It is worth rounding up - up to 22.5 m.

In conclusion, it is worth summing all the obtained areas: S = 22.5 x 2 + 14.7 x 2 = 74/4. You should round the resulting number to 75.

Roof covering and necessary materials

You can begin to calculate the metric area of ​​the roof frame. The opinion that the area of ​​the required material and the area of ​​the drawing are the same is wrong. All elements will need to overlap. For each roofing material has its own technical indicators of the magnitude of overlap. The cost of roofing materials will be significantly increased.

When calculating the amount of roofing material for a multi-level roof, it is recommended to ask for help from computer software. It can do all the calculations much faster and more accurately.

You can calculate the amount of material you need for an ordinary metal roof, and you can do it yourself.

X - 15%, where X - stock, which is equal to 15%, and S - roof area.

After calculating X, you will need to add the resulting number to the area S. As a result, the area of ​​the amount of material can be obtained.

In this case, the proportion will be as follows:

X = 15 x 75/100 = 11.25, should be rounded to 11.5.

11.5 + 75 = 86.25 sq. M - the required area of ​​roofing material.

When calculating the amount of roofing materials you need to remember that the waste will need another 20% of the material. During the construction of a complex roof of metal tiles, the stock does not take into account not 15%, but 20%.

Dare! After all, the house, created by its own, will be a double pride for the owners and the subject of admiration for the guests. Let your calculation of materials be correct, the roof reliable, and the future home beautiful and comfortable.

Modern buildings have the most extraordinary structures, this also applies to the roof. Everyone wants to have a home that will stand out among the rest.

The roof with four slopes does not contain gables, thanks to which the installation of the four-slope roof is somewhat easier, moreover, it does not require extra expenses for additional building materials for the wall.

The most important issue of concern to any builder of a private house is the correct calculation and, accordingly, the consumption of materials for its construction.

Broken and complex elements in the construction of the roof complicate this calculation. Despite this, it is possible to calculate the area of ​​the four-slope roof independently, thereby saving money on the services of construction engineers.

First you need to deal with the design features of a modern roof, since the amount of material depends on it.

The main types of roofing

The hip roofs include hip, half-hip, tent and their varieties.

In modern construction of houses there are the following types of roof:

1. Shed, which is characterized by one bias - from wall to wall. This type of roof is popular for those buildings that are located on busy city streets, where there is no opportunity to equip drainage and dumping of snow. This type is suitable for simple buildings: sheds, garages, warehouses, workshops, etc.
2.   is the most common option. It can be used in the construction of buildings of any type.
3. The hip roof, as is already clear from the name itself, has four ramps.

Types of hipped roof

This type of roof, in turn, has subtypes: hip, half-hinged, stud, mansard.

The planar plan of the hip roof helps to conditionally divide the roof into regular geometric shapes, the total area of ​​which is equal to the roof area.

1. most often used in the construction of buildings with a rectangular or polygonal plan. The vertices converge at one point.
2.   most often used in the construction of the house summer type.
3. The four-slope steeple-shaped roof variant includes four steep slopes of a triangular shape that converge at one vertex. Structural elements of this type are bay windows, towers, round wall structures.
4. Mansard type of roof consists of broken elements. Most often, such a construction can be observed in country houses of the dacha variant above the residential area. Due to the economical consumption of materials for its construction, the mansard roof type gained particular popularity among developers.

It becomes clear from the descriptions that the four-sided type of roof has a more complex structure. To install such a roof yourself, you will need the help of several more people.

Useful formulas for calculating the area of ​​the correct elements of the roof: the triangle and the trapezium, which make up the geometry of the hip roof.

Consultation of a professional is desirable, his practical guidance and advice will be very helpful.

Before starting construction you need to create a project for your four-sided roof. Without it, you can not do. Ideally, for the proper execution of a design project, it is better to resort to the help of a design engineer.

But if you are confident in your abilities, you can easily do without a professional.

Calculation of the area of ​​a simple roof

The four-pitch roof is a structure that consists of a pair of inclined planes of a trapezoidal or quadrangular shape and a pair of inclined elements in the shape of triangles. Moreover, the quadrangular (trapezoidal) planes with their upper edges converge and form a ridge. Triangular slopes close the roof from the end of the building.

The calculation of the four-slope roof area primarily depends on how complex its structural elements and configuration are. The calculation will be made on the example of a simple construction in the form of a pyramid.

The scheme for calculating the amount of material for the device hip roof: shows the layout of the material directly on the roof.

1. Know the formula for finding the area of ​​the pyramid.
2. Calculate the area of ​​one slope.

It is known from the school geometry course to calculate the lateral surface area of ​​the pyramid, it is necessary to find out the area of ​​each lateral face and put them together. Then, knowing the required value by the formula of one slope, we multiply this result by 4.

If the four-slope roof includes two rectangular slopes and two triangular, the area of ​​the whole structure is calculated as follows: the area of ​​the triangular slope is found (as in the previous example), and the result is multiplied by 2 (two slopes), and the similar value of the quadrilateral side is found and multiplied by 2. Add these two values ​​and get the value of the area of ​​your roof.

It is very important to double-check your calculation several times, because the error in a big way will entail an unnecessary expenditure of funds for the purchase of material, and in case of an error in the downside, the material will not be purchased in sufficient quantity.

Consider the fact that more roofing materials overlap, so they need to be purchased with a margin. Keep in mind that about 10% of the material will go to trim.

It is necessary to calculate the area of ​​the slope, starting from the eaves of the eaves.

How to correctly calculate the area of ​​a complex four-slope roof

The formula for calculating the eaves overhang hip roof. The area of ​​the roof itself is calculated according to the rules for determining the area of ​​an equilateral tetrahedron.

If you build a building according to a standard and individual project, it will be a determining factor for the entire cost of the house. The full cost of construction you will know after you calculate the roof area of ​​the roof. Sometimes there is a need to change the project in order to reduce the cost of construction.

Before starting the calculations, break the design calculation into separate geometric shapes. Calculate this value for all geometric elements separately, using formulas to calculate their areas.

Take into account the fact that the roof has a certain slope angle, therefore, each geometric element of the structure is also at a certain inclination relative to the ground. As a result, the area of ​​each element must be multiplied by the cosine of the angle of inclination. All the results obtained are added up.

Calculate the area of ​​the four-slope structure not at the edges of the building, but along its curtain eaves. This condition is the technology of laying roofing.

Your actions when calculating the roof area:

1. Do not calculate from the calculation of chimney pipes, ventilation holes, roof and dormer windows.
2. Measure the length of the slope as accurately as possible. It is measured from the bottom of the ridge to the top of the eaves.
3. Do not forget that you need to add length for parapets, overhangs, firewall walls.
4. Decide on the roofing coating, because each material has its own nuances of consumption and calculation.

Knowing how to calculate the cosine of an angle, knowing the mathematical formulas for calculating the areas of figures, you can calculate the total.