During construction, people face a lot of different problems. One of them is arranging the roof and calculating the amount of material required for its construction. You can find out only if you correctly calculate the area that needs to be covered.
Peculiarities
It will not be possible to calculate the roof area using some universal formulas. For a simple pitched roof, such calculations are the simplest, but there are always nuances, ignoring which leads to dire consequences.
Calculating area always involves:
- accurate height measurement;
- determining the degree of inclination;
- determining the volume of required building materials and fastenings to them (as the final stage).
Design forms
The area of a pitched roof is calculated depending on what 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 lean-to option is calculated using the formula for a rectangle.
If there are two slopes, you just 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, you will need to spend more time, but the basic principles remain roughly the same. The first step is to break it down into simple geometric shapes. Then the same formulas are used 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 eaves to the ridge elements.
When the area is of irregular shape, it is advisable to divide it into even smaller fragments in order to radically simplify the calculations.
Chimneys and ventilation ducts should not be subtracted from the results., windows built into the roof and other similar elements. When calculating the area 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 the very in simple form square flat roof can be taken equal to the total area of the building, with the addition of overhangs and other elements extending beyond the contour. But such a calculation scheme is acceptable only if there are actually no angles.
With due diligence, it will not be difficult to calculate the area of the pediment yourself. To do this, there will be no need to even turn to online calculators. The configuration of the pediments is closely related to the geometry of the slopes: thus, triangular options most often accompany the formation of roofs with two slopes. When installing the structure, before preparing the rafter frames, the area and height of the gables must be calculated with special care.
Produce necessary calculations, as always, using “school” formulas helps. It is advisable to use electronic calculators only for self-testing.
The lengths of the end walls, divided in half, are multiplied with the tangent of the angle, which creates the slope and base of the roof. For a non-residential space under the roof, the height will be much lower than for one actively used by people. A 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 and multiply it by the height. The pentagonal pediment is conventionally divided into an upper triangle and a lower trapezoid - this simplifies the calculation.
Calculating the area of an L-shaped roof with different slopes is also not particularly difficult. By its nature, it is formed from a pair of standard gable structures joined at right angles. To simplify calculations, the general configuration is divided into four similar rectangular trapezoids. The calculated areas are summed up and the final result is obtained.
You can simplify your work (eliminate measuring individual slopes and planes) if you have a carefully prepared plan in hand.
Calculation method
It will not be possible to calculate the square footage of the roof of a house correctly unless you figure out exactly what its shape is. In the absence of clear and unambiguous plans, you will have to prepare them yourself, drawing all the necessary drawings by hand. An equilateral 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 must reflect all lengths, widths and heights with an error of no more than 1 cm. If it is possible to 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 step of the calculation. A mistake can be very expensive, in the literal sense of the word. You can determine the number of square meters from the ground, from the roof itself, and from the attic.
To increase 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 roof sloped at an angle of 9 degrees is 10% larger in size than an identical flat one.
If the slope increases to 56 degrees, the conversion factor already reaches 1.8, and its approximate change 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 separately is determined as the length of the house with the addition of the front and eaves overhangs, multiplied by the length of the rafters + the length of the overhang. If the roof is pitched, there is no need to double the resulting number.
For the most accurate calculation of the footage of a triangle or any other geometric figure The results obtained from the formulas should be increased by 10-15%. This will allow you to 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 you will also need to take into account the coefficients recommended by the fire inspection. They will allow you to compensate for both calculation errors and overconsumption of impregnating mixtures.
The problem is that the special impregnation is not applied to the roof, and on the sheathing and 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 treatment with fire retardants, you will have to enter a coefficient of 1.2. It will successfully “absorb” all the irregularities.
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 tiles, slate or corrugated sheets will have to occupy, we must not forget that one of the waves is spent on connections with adjacent sheets. Therefore, you will have to add another 10% to the resulting area after all the calculations and adjustments. It is also taken into account that sheet materials are measured in linear meters, which must first be converted into square meters, and only then compared with the dimensions of the roof. Additionally, you can check yourself by using specialized online calculators directly from major suppliers of selected coverage.
If the roof does not have a wall gutter, add 7 cm to the slopes above the eaves. And in the case where there is a gutter, a cornice, and an overhang, the length can be reduced by 70 cm. It is additionally necessary to calculate the areas of parapets, firewall walls and other structures that are not physically connected to the main covering. There is no need to take into account standing seams if individual parts are covered with roofing steel.
You can also ignore the bypass of the base beam with rolled coverings. Essentially, it does not play a role, just like the arrangement of aprons.
And one more thing about ignored details: there is no need to calculate the roof connections to:
- parapet;
- skylight;
- thermal seam;
- pipe;
- ventilation shaft;
- wall.
Coverings of parts of the same roof located in different planes and separated by other materials are calculated separately. If there is no building design or it raises certain doubts, it is better to measure all values in fact. The effort spent will pay off handsomely; repairing or building from scratch will be much easier. Moreover, the centimeters not taken into account on large-scale plans and diagrams in reality turn into whole meters of error.
Construction of any kind is impossible without preliminary calculations, so this preparatory stage should never be neglected. 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 there should not be any special problems 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.
Designation of fields in the calculator
Specify roofing material:
Select a material from the list -- Slate (corrugated asbestos cement sheets): Medium profile (11 kg/m2) Slate (corrugated asbestos cement sheets): Reinforced profile (13 kg/m2) Corrugated cellulose-bitumen sheets (6 kg/m2) Bitumen (soft , flexible) tiles (15 kg/m2) Galvanized sheet metal (6.5 kg/m2) Sheet steel (8 kg/m2) Ceramic tiles (50 kg/m2) Cement-sand tiles (70 kg/m2) Metal tiles, corrugated sheets (5 kg/m2) Keramoplast (5.5 kg/m2) Seam roofing (6 kg/m2) Polymer-sand tiles (25 kg/m2) Ondulin (Euro slate) (4 kg/m2) Composite tiles (7 kg/m2) ) Natural slate (40 kg/m2) Specify the weight of 1 square meter of coating (? kg/m2)
kg/m2
Enter the roof parameters (photo above):
Base width A (cm)
Base length D (cm)
Lifting height B (cm)
Length of side overhangs C (cm)
Front and rear overhang length E (cm)
Rafters:
Rafter pitch (cm)
Type of wood for rafters (cm)
Working area of the side rafter (optional) (cm)
Lathing calculation:
Sheathing board width (cm)
Sheathing board thickness (cm)
Distance between sheathing boards
F (cm)
Calculation of snow load (pictured below):
Select your region
1 (80/56 kg/m2) 2 (120/84 kg/m2) 3 (180/126 kg/m2) 4 (240/168 kg/m2) 5 (320/224 kg/m2) 6 (400/280 kg/m2) 7 (480/336 kg/m2) 8 (560/392 kg/m2)
Wind load calculation:
Ia I II III IV V VI VII
Height to the ridge of the building
5 m from 5 m to 10 m from 10 m
Terrain type
Open area Closed area Urban areas
Calculation results
Roof angle: 0 degrees.
The angle of inclination is suitable for this material.
It is advisable to increase the angle of inclination for this material!
It is advisable to reduce the angle of inclination for this material!
Roof surface area: 0 m2.
Approximate weight of roofing material: 0 kg.
Number of rolls of insulating material with 10% overlap (1x15 m): 0 rolls.
Rafters:
Load on the rafter system: 0 kg/m2.
Rafter length: 0 cm
Number of rafters: 0 pcs.
Lathing:
Number of rows of sheathing (for the entire roof): 0 rows.
Uniform distance between sheathing boards: 0 cm
Number of sheathing boards with a standard length of 6 meters: 0 pcs.
Volume of sheathing boards: 0 m3.
Approximate weight of sheathing boards: 0 kg.
Field decoding
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. You also need to decide on the type of roof. So, Builders distinguish several types of roofing:
- (hip);
- multi-slope;
If the roof is of a fairly simple shape, without unnecessary kinks, then calculating its area will not be difficult. If the roof has a more complex configuration, with many slopes, then you will have to arm yourself with all your knowledge of 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.
Types of roofs
In most cases, the roofs of private buildings come in the following geometric shapes. The area of pitched roofs is calculated using these formulas:
- Trapezoid. Calculation formula (A+B)*H/2.
- Rectangle - A*B.
- Parallelogram - A*H.
- A triangle with equal sides is (A*H)/2.
PLEASE NOTE!
It is worth understanding that the more complex the roof, i.e. if it consists of several slopes, the more difficult it is to build, as well as in other aspects - insulation, maintenance, etc. The financial issue has also not been canceled, because such a roof will require more building materials.
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=A*B, Where
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.
Designations have been changed
How to calculate the area of a gable roof?
This type of roof consists of two pitched roofs on different sides, so the calculation will take place 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.
Designations have been changed
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.
Designations have been changed
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 familiar from school, 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.
CAREFULLY!
No way do not subtract such roof elements from the resulting area value, like a chimney, ventilation ducts, attic windows, etc. This may result in you simply purchasing less roofing material than required. Be extremely vigilant!
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 a role important role, because the technology of its flooring may 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 the “usable area” of a material, so you need to take it into account, and not the actual indicators. If the manufacturing company is of a high level, then it will necessarily 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 in the width of the roof and the total number of 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, calculating all parameters is not such a difficult 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 do not have a detailed house plan, then you will have to carry out all measurements yourself, 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.
Currently, all over the world, including in Russia, such a branch of the national economy as construction is developing at a rapid pace. Since ancient times, this type of activity has been highly valued and in demand. And to this day nothing has changed. Every year thousands of new houses are built, new ones are furnished and renovated. Owners of private houses who decorate their properties are of particular interest in construction. These can be small dachas, houses or large cottages. One of the important stages of construction is roofing.
Construction of a house is never complete without a roof, so you should carefully approach the design of this part of the house, because... It is this that protects the house from precipitation and other natural influences.
Home, that is, his appearance, is largely determined by it. The roof can be covered with various materials: slate, metal tiles, metal sheets and so on. Work requires accurate calculations material and necessary tools. Both specialists and the owner of the house can cover it, it all depends on desire and skills. Plus, you can save a lot of money. Let's take a closer look at how to calculate the area of this part of the house, because this is one of the main and most important preparatory stages in the course of work.
Main types of roofs and their advantages
Before making a roof, you need to decide what materials will be used for roofing, thermal insulation, waterproofing, and so on. It is necessary to draw up an accurate plan on which all dimensions will be plotted, preferably everything should be in digital values. It is not necessary to know the area; this is necessary in order to accurately calculate the amount of material for construction and not overpay. Once all the information has been collected, the developer can begin installing the roof for the house.
Any specialist in this field should know what types there are. They come in single-slope, double-slope, tri-slope, hip, half-hip, gable and multi-slope types. The easiest way to count those that do not have kinks. But increasingly, builders are making multi-slope and hip roofs, so the material has to be carefully calculated. If in simple roofs all surfaces are presented in the form of regular triangles or trapezoids, then in the latter case they can have a variety of geometric shapes.
How to make a roof plan
Scheme of a pitched roof.
If there is no plan for the house itself yet, but rafter system is already ready, then you need to start taking measurements. In this case, it is necessary to measure all of it. First, its height is measured from the ridge to the ceiling. If the roof consists of several levels, then they are all calculated. It is recommended to make a drawing for greater clarity, preferably in profile. Having all this, the future roofing process will be much easier and faster. It must be remembered that even if all the components into which it is decomposed are simple, you do not need to limit yourself to measuring only the perimeter of the roof; in addition, the dimensions of the overhangs of the future roof are also taken into account.
Let's take a closer look at how a pitched roof is calculated, how it is broken down into components, what formulas are used for this purpose, and the like.
Example of roof area calculation
The roof slope has the shape of a rectangle (ABDC). The area of such a rectangle is equal to the product of the lengths of its two adjacent sides.
The roof area to be covered with slate is calculated using a simple formula. If the roof is gable, then the area of the slope is first calculated, and the resulting figure is multiplied by half. Most often, the roof slope has the shape of a rectangle. The area of a rectangle is equal to the product of one side, that is, the length, and the other side (the width of the house).
For example, if the size of the house is 8x6 m, the length of the rafter leg is 3.38 m, the length of the eaves overhang is 0.5 m, the size of the front overhang is also 0.5 m, then the area of one slope is 37.62 meters.
The calculation was carried out as follows: (8 + 0.5 + 0.5) x (3.68 + 0.5) = 9 x 4.18 = 37.62 m. Then the entire area will be equal to 37.62 x 2 = 75, 24 m. Thus, the lengths of the overhangs and rafters must be taken into account.
If the roof is single-pitched, the dimensions of the house are 8x6 m, the length of the rafter leg is 7.35 m, the length of the overhangs is 0.5 m, then the area of the roof slope will be 66.15 m: (8 + 0.5 + 0.5) x 7, 35 = 66.15. For a hipped roof, everything is a little more complicated. In this case, you need to calculate the area of an isosceles triangle, and then multiply the result by the number of triangles, that is, 4. Its area is equal to the product of its height and half the length of the base. Here, the length of the rafter leg, the base of the roof and the dimensions of the ridge are also taken into account. The length of the altitude of a triangle is calculated using the Pythagorean theorem. It is equal to the square root of the difference between the square of the length of the rafter leg and the square of the length of one side of the roof base.
How to calculate roof area for slate roofing
Depending on the roof configuration, there are various ways laying slate.
When building a roof, it is important not only to calculate the area of the roof itself, but also the area of the required roof, that is, the material. The thing is that some roofing materials require a large overlap, so they may not coincide with the data obtained by calculating the roof surface area. Thus, material consumption increases. When calculating roofing coverage, the easiest way is to use a roof area calculator.
There is a formula to determine the coverage area. It is suitable if you plan to cover the roof with slate. It looks like this: S = (2 x A + B) x (2 x A + C) x cos 30, where S is the total roof area, A is the width of the overhang, B is the length of the building, and C is its width, 30 - roof inclination angle. Here it is important not to make mistakes in the calculations and sequence of actions. Even a schoolchild can carry out similar calculations. An interesting fact is that for everyone building material There are formulas and methods for obtaining reliable data. Therefore, before doing anything, it is important to decide on the choice of building material.
How to calculate the material and area to cover with tiles
When calculating the required amount of metal tiles, it is necessary to take into account the type and technology of installation, as well as the angle of the roof.
Along with slate, metal tiles are a very popular material in the construction industry. When calculating areas, you need to take into account some subtleties. If in the previous case there was no need to take waste into account, then here it is very important. If during normal work with a simple roof the percentage of production waste is approximately 7-10%, then for complex and fancy structures this figure increases to 20%. Calculation of a soft roof is done according to the scheme described above. The type and technology of installation are taken into account. The areas of the skates are measured separately and not in square meters, but in uniform.
You always need to remember how the roofing material is supposed to be connected; the size of the overlap and, accordingly, the volume of the roof depend on this. Much depends on the angle of the roof. The higher it is, the less overlap is planned. There are so-called correction factors for complex roof configurations. It is not recommended to start work without having a roof diagram and drawings with calculations on paper, otherwise you may not get what you want.
We can conclude that covering a roof with one material or another is a fairly simple matter. Be sure to select required material, take measurements, following all instructions, calculate the required amount of roofing and compare it with previous measurements. The basic principle underlying calculations is the breakdown of large and complex surfaces into smaller geometric structures, for example, regular triangles, squares, trapezoids. This is not necessary, but it will make things easier and will save you a lot of time. If your abilities in mathematics are weak, then it is best to seek help from specialists who know a lot about this matter. They will do everything quickly and efficiently.
There is a formula by which calculations are carried out. It contains data such as the length and width of the house, the length of the rafter leg and the dimensions of the slopes. For this part of the house, it is important to measure the size of the overhangs and take into account the percentage of expected waste, most often it is 10-15%, which is a lot. The amount of work is largely determined by the type of house. Houses can be simple with a pitched roof or with intricate outlines, respectively, and the surface of the roof will be uneven. Great value also has a styling technique. It’s one thing if the work is done by professionals, and another thing with inexperienced owners who don’t know all the intricacies. Therefore, if you plan to cover the roof of your house with your own hands, then this material will help you do everything correctly and consistently. If difficulties arise, it is better to call a team of specialists.
Online calculators for calculating roofing and roofing are mandatory tools present in the arsenal of architects and professional construction firms. Although, in principle, such calculators are also useful for simple owners of suburban areas who have started building a house with their own hands (here you will also need to calculate the roof). And it’s not surprising, because the quality and accuracy of such calculations directly affect not only the durability of the entire roofing structure, but also general view Houses. This section of the site contains the best calculators for calculating the roof, which will help you in the most common cases when building a house yourself! Here you will find useful tools for calculating the area of a three-gable roof, the amount of slate, the area of a hip roof, the length of the rafters, the height of the ridge and much more! All online calculators were created by experienced professionals, each tool is accompanied by detailed explanations and calculation instructions.
What are the advantages of our online calculators? They differ from their numerous (and often paid) analogues in that they do not need to be downloaded to a local computer. Complex, carefully tested algorithms are used to carry out calculations, and the calculation results are displayed in a simple and accessible form. Another advantage is that you can add a page with an online calculator of interest to your browser bookmarks and use it at any time!
Note! When carrying out online calculations, construction standards, GOSTs and SNiPs, which are accepted in the Russian Federation and the world, are used. In addition, the world practice of modern construction is taken into account.
When creating a roofing project, first of all they think about reliability, and not the whims of the building owners. In other words, when designing a structure on paper, the requirements regarding roof type, slope, height, loads and amount of material are taken into account.
Common types of roofing
The most famous types of roofs are:
- single-pitch - rests on two walls located at different height levels, and is constructed specifically for utility facilities and small buildings;
Shed roofing is laid on walls of different heights
- gable - consists of two slopes connected at an angle, the area of which may not be the same;
A gable roof usually has two equal slopes
- tent - assembled from four slopes in the shape of an isosceles triangle, as a result of which it resembles a pyramid and is ideal for square houses;
Hip roofing is constructed on square-shaped buildings
- hip - created from two trapezoidal and two triangular slopes;
The hip roof consists of four unequal slopes
- attic - used to create a room in the attic and is formed by changing the shape of the roof, for example, using broken lines;
The attic roof looks like a complex structure, because underneath it an additional floor of the house is created
- multi-gable - constructed on buildings built in the form of a polygon.
Multi-gable roofing is an interesting combination of roofs of different shapes
Roof calculation in an online calculator
To calculate the roof in an online calculator, that is, find out what the angle of inclination and area of the roof should be, as well as the amount of lumber and other building raw materials, you need to select the type of finishing coating and enter the following dimensions in special cells:
- the width of the roof base from the end of the house (without adding the width of the overhangs);
- the length of the roof base on the side of the building (not taking into account the length of the overhangs);
- ridge height (distance from the future base to the ridge beam);
- overhang length (at least half a meter).
For a roof with several slopes and different angles of inclination, calculations are carried out separately. Then the obtained data is summarized.
Roofing loads
The loads acting on the roof, that is, snow and wind pressure, are calculated in order to determine how many and what cross-section rafters will be needed to create a stable frame.
Snow load
To determine snow pressure, use the formula S=µ·S g, where S is the desired value of the snow load (in kg/m²), µ is the coefficient that is determined by the degree of slope of the slope, and S g is the standard snow load (in kg/m²) . The value of S g is indicated on a special map and depends on the area.
The entire territory of Russia is divided into 8 snow regions, each of which has its own level of snow.
The snow load is calculated as follows:
Table: snowy regions of Russia
| Snowy regions of the Russian Federation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| S, kPa (kg/m2) | 0,8 (80) | 1,2 (120) | 1,8 (180) | 2,4 (240) | 3,2 (320) | 4,0 (400) | 4,8 (480) | 5,6 (560) |
- Find on the map the standard snow load for Kaliningrad (second zone, 120 kg/m²).
- Divide half the width of the wall by the height of the ridge: 2.5/3.5 = 0.714.
- From the table, find the angle of inclination using its tangent. In our case it is 36°.
- Determine the coefficient µ: 0.033 · (60–36) = 0.79.
- Find the required value of the snow load S = 120 · 0.79 = 94.8 kg/m².
Table: determining an angle by its tangent
Wind load
As indicated in SNiP 2.01.07–85 “Loads and impacts”, wind pressure on the roof is calculated using the formula W m = W o K C, where W o is normative meaning wind pressure indicated on a special map, K is a coefficient that is affected by changes in wind load along the height, and C is a special aerodynamic coefficient.
The aerodynamic coefficient is a constant value, depending on the roof configuration. If the roof has steep slopes, then this indicator is -1.8. For a flat roof, which the wind does not lift but compresses, the aerodynamic effect is +0.8. In most calculations, this coefficient is taken equal to the largest positive value (i.e. 0.8) to estimate the maximum possible wind load.
Depending on the wind load, the territory of Russia is conditionally divided into 8 regions
Table: wind loads in Russia by region
| Wind regions of the Russian Federation | 1a | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Wo, kPa (kgf/m2) | 0,17 (17) | 0,23(23) | 0,30 (30) | 0,38 (38) | 0,48 (48) | 0,60 (60) | 0,73 (73) | 0,85 (85) |
For clarity, let’s try to determine the wind load on the roof of a house in the village of Babenki Ivanovo region Russia. Provided that the height of the ridge from the ground is 6 m, the angle of inclination of the roof is 36°, the calculations will be as follows:
- W o = 30 kg/m², since the area belongs to the second wind region, as indicated on the map of the SNiP application and in the table above.
- K = 1, since all buildings in this area are below 10 m (see table of K coefficient values).
- W m = 30 · 0.8 = 24 kg/m².
Table: K coefficient value for calculating wind load
Calculation of the angle of inclination, height and weight of the roof
Before calculating the height of the roof, you need to determine the angles of inclination of the slopes. Regulatory documents that set requirements for roofing work, that is, a set of rules SP20.13330.2011, based on the instructions of SNiP 2.01.07–85 “Loads and impacts”.
Tilt angle
According to the rules, the choice of roof slope depends on the finishing material used.
At what angle to build the roof, they decide, focusing on the finishing material
Table: angle of inclination for roofs with different coatings
| Recommended roof angle | Finish coating |
| 1–2° | Rolled materials on a bitumen basis - at least four layers, with an external gravel topping, recessed into a layer of molten mastic |
| 2–3° | As in the previous line, but for the reliability of the roof, three layers of rolled material are enough |
| 3–10° | Rolled materials similar to those described above (at least three layers), but without external protective gravel topping. |
| 10–15° | Rolled roofing materials glued to hot mastic in at least two layers |
| 13–15° | Tiled clay covering |
| 15–17° | Reinforced asbestos cement sheets |
| 17–20° | Roofing sheet steel with flared joints |
| 18–35° | Corrugated sheeting, metal tiles |
| 27–44° | Natural piece tile covering, bitumen-polymer or slate tiles |
| 38–45° | Shingles, wood chips, natural shingles |
| 40–60° | Dutch tiles |
| 5–90° | Asbestos cement slate |
| 20–90° | Artificial slate |
Ridge height
Having chosen the roofing material and decided what the slope of the roof will be, we begin to determine the height of the ridge beam. To do this, they turn to geometry, because the roof in section looks like two triangles connected to each other.
When calculating the height of the roof, use the formula a=b · tg α, where a is the height of the ridge, b is half the width of the building, α is the angle of inclination of the roof.
The tangent of the roof inclination angle is determined using the trigonometric table given above.
To find the height of the roof, you need to multiply half the width of the wall by the tangent of the angle between the wall and the slope
For example, let’s calculate the height of the roof at a slope of 40°, which is planned to be built on a house measuring 6x9 m. For this purpose, let’s perform the following calculations:
- Divide the width of the house by 2 and determine the length of the lower leg of the right triangle of the roof: b = 6 / 2 = 3 m.
- From the table we find that the tangent of an angle of 40° is 0.84.
- Let's calculate the roof height a = 3 · 0.84 = 2.52 m.
Video: calculating the height and angle of the roof
Weight
The weight of the roof includes the weight of all layers of the roofing pie: topcoat, counter-battens, sheathing and insulating materials.
You can find out how much 1 m² of any material weighs from a seller in a hardware store or calculate it yourself by looking at the label for the density of the material in m³, as well as the thickness, width and length of its roll. Using these indicators, you can calculate the weight of 1 m² of any building material.
The weight of the roof includes all materials up to thermal insulation boards
Let's say we need to determine the weight of a roof covered with bitumen shingles and insulated with a material with a density of 35 kg/m³, rolled into a roll 0.1 m thick, 10 m long and 1.2 m wide. In this case, we need to do the following:
- Calculate the weight of 1 m² thermal insulation material according to the formula 0.1 · 1.2 · 10 · 35 / (10 · 1.2) = 3.5 kg/m².
- Find all other data, that is, the weight of 1 m² of the finishing coating, vapor and waterproofing and the wooden frame of rafters and sheathing, in the table (see below) or on the product label in the store.
- Add up all the obtained values and multiply them by the roof area, thereby determining the weight of the entire roof.
Typically 1 m² of roofing cake weighs about 50 kg. Therefore, in calculations, this value is often used, multiplied by 1.1 in order to make a reserve of 10%, that is, 55 kg/m².
Table: weight of 1 m² of roofing materials
Calculation of roof area
The easiest way is to calculate the roof area in two or four identical slopes. As the roof configuration becomes more complex, determining this parameter always becomes more difficult, which is explained by the need to calculate the area of each slope separately.
The roof area is determined using the following formulas:
- for a rectangular slope S = a · b, where a and b are the lengths of the sides of the rectangle;
The area of a rectangular slope is found by multiplying the length of the slope by its width
- for a triangular slope with equal sides S = (a · b) / 2, where a is the length of the sides of the triangle, b is its height;
The area of a triangular slope is found using the formula for an equilateral triangle
- for a trapezoidal slope S = (a + b) h / 2, where a and b are the lengths of the sides, and h is the height of the trapezoid;
The area of the trapezoidal slope is found by adding the length of the ridge with the length of the roof at the eaves and multiplying the resulting number by half the height of the roof
- for a slope in the shape of a parallelogram S = a · h, where a is the length of the side of the geometric figure, and h is its height.
The area of a parallelogram-shaped slope is found by multiplying its base by its height.
Let's imagine that we need to calculate the area of a roof with two identical rectangular slopes 5 m wide and 2.2 m long. In this case, the computational steps will be as follows:
- S c = a · b = 5 · 2.2 = 11 m² (area of one slope).
- S = 2 · S c = 11 · 2 = 22 m² (area of two slopes).
Calculation of the amount of roofing materials
When planning to build a roof, you need to calculate in advance the required number of finishing sheets, lumber and soffits.
Finish coating
Before determining the required amount of finishing roofing material, you need to know its useful dimensions. They are smaller than real ones, since it is necessary to take into account overlaps in the width and length of the sheets.
When making calculations, only the useful size of the material should be taken into account.
Suppose you need to find out how much metal tiles you need to buy with a useful sheet width of 1.1 m and a total length of 2.25 m for the roof of a house measuring 4.2 x 6 m. To do this:
- Let's divide the length of the roof by the useful width of the tile sheet: N = 6 / 1.1 = 5.45. Let's round this value to 6. This is the required number of sheets in one row along the width of the roof.
- From the actual length of the sheet (2,250 mm), we subtract the amount of overlap (150 mm) and thereby establish the effective length of the sheet (2,100 mm or 2.1 m).
- We divide the total length of the roof slope by the effective length of the sheet: K = 4.2 / 2.1 = 2. Thus, we determine that along the length of the roof, that is, from the eaves to the ridge, two sheets will be required in each row.
- The number of sheets in one row along the width of the slope is multiplied by the number of sheets along the length of the roof (6 · 2 = 12). That is, it will take 12 sheets to cover the entire roof.
Lumber
Let's calculate the amount of lumber required to construct a wooden frame for one roofing slope 6 m wide and 4 m long:
- The distance between the frame elements depends on the weight of the finishing roofing material. To cover the roof, we will choose light ondulin, which can be placed on the rafters in increments of 60 cm, and we will set the slope angle to 15 o.
- Let's calculate the number of rafter legs, for which we divide the width of the roof by pitch and add 1 to take into account the additional rafter leg laid on the edge of the roof. We get: 6 / 0.6 + 1 = 11.
- We determine the thickness of the rafter legs by subtracting the sum of the distances between the rafters from the total width of the roof and dividing the resulting figure by the number of frame elements (6 - 5.4 / 11 = 0.055 m = 55 mm). And we choose the width so that it is 2–3 cm greater than the thickness of the insulation board. Judging by the special table (see below), rafters with a cross section of 50 x 150 mm or 55 x 150 mm are suitable for us.
- Let's make sure that we have chosen the right section of rafter legs. To do this, we first determine the load per linear meter of each rafter leg using the formula Q r = A ∙ Q, where A is the pitch of the rafters, and Q is the total load on the roof, which consists of the weight of the roof, snow pressure and wind. Then we will check whether the inequality / ≤ 1 is satisfied, where L max is the working length of the largest section of the rafter leg in meters, B is the thickness and H is the width of the board in centimeters. If the inequality is not observed, you need to increase the width of the board or reduce the pitch of the rafters.
To calculate the strength of a truss truss, it is necessary to determine the length of its largest working section.
- Based on the angle of inclination of 15°, we decide to lay sheathing boards every 60 cm. Dividing the length of the roof by the distance between them and adding 1 to the resulting number (board for attaching the ridge), we find that 8 rows are required.
- We find the width of the sheathing boards by subtracting the sum of the steps between them from the length of the roof and dividing the result by the number of sheathings (400 - 360 / 8 = 5 cm). Using the table below, we select the optimal thickness of the elements.
- Since the length of the slope is 4 m and it is necessary to make an overlap of 7 cm at the bottom and top, we come to the conclusion that it is necessary to buy two wind boards 4.15 m long.
To properly assemble the roof frame, you should calculate the number of rafters and sheathing boards
Table: dependence of the cross-section of the rafters on their pitch and length
| Rafter installation pitch (cm) | Rafter length (m) | ||||||
| 3 | 3,5 | 4 | 4,5 | 5 | 5,5 | 6 | |
| 215 | 100x150 | 100x175 | 100x200 | 100x200 | 100x250 | 100x250 | - |
| 175 | 75x150 | 75x200 | 75x200 | 100x200 | 100x200 | 100x200 | 100x250 |
| 140 | 75x125 | 75x175 | 75x200 | 75x200 | 75x200 | 100x200 | 100x200 |
| 110 | 75x150 | 75x150 | 75x175 | 75x175 | 75x200 | 75x200 | 100x200 |
| 90 | 50x150 | 50x175 | 50x200 | 75x175 | 75x175 | 75x250 | 75x200 |
| 60 | 40x150 | 40x175 | 50x150 | 50x150 | 50x175 | 50x200 | 50x200 |
The thickness of the sheathing boards is determined from a special table depending on the pitch between the rafters. In our case, it should be at least 20 mm.
Table: how the pitch of the rafters affects the thickness of the sheathing
Video: do-it-yourself calculation of the sizes of rafters and beams
Soffits
Lastly, we gradually determine the need for additional elements:
- Using the formula L = B ∙ 2 + D ∙ 2, where B is the length of the pediment overhang, and D is the eaves overhang, we find the perimeter of the overhangs along the eaves and pediment: 4 ∙ 2 + 6 ∙ 2 = 20 linear meters. Then we measure the width of the overhangs A (let’s say 30 cm) and determine the area of the eaves and gable overhangs (S = L · A = 20 · 0.3 = 6 m²). Now we calculate how much metal soffit measuring 3 x 0.325 m and area of 0.98 m² will be needed. To do this, divide the total area of the overhangs by the area of the metal soffit (6 / 0.98 = 6.2). Let's round the resulting number to 7, i.e. 7 sheets of spotlights will be required.
- Let's determine the number of J-profiles 3 m long, which are inserted under the overhangs near the walls. Dividing the perimeter of 20 m by the length of one element, we determine that to install the roof you will have to purchase 7 J-profiles.
- Let's count the number of frontal (installed at the end of the overhangs) and finishing (mounted in conjunction with the frontal) strips. Since the length of both elements is 3 m, and the perimeter of the overhangs is 20 m, we come to the conclusion that it is necessary to buy 7 front and finishing strips.
Metal soffits are needed for roof overhangs
Calculation of vapor and waterproofing
The required amount of material to insulate the roof from steam and moisture is determined by knowing the area of the roof slope.
When calculating the amount of waterproofing film, one should not forget that 15% of the material is spent on creating overlaps
Let’s imagine that we are faced with the task of covering a roof with two identical slopes 5 m long and 4 m wide with vapor barrier and waterproof films. In this case, the computational steps will be as follows:
- S c = 5 · 4 · 2 = 40 m² (area of two roof slopes).
- S = S c · 1.15 = 40 · 1.15 = 46 m² (the required amount of each insulating material, taking into account the overlap, which should be 15% of the roof area).
Without calculating the area, height, loads and other parameters of the roof, no home owner will be confident in the reliability of the structure. All dimensions of the future roof must be known in advance in order to prevent any overlays.
