The importance of the roof for a house is in some ways similar to the importance of the foundation - it is quite difficult to overestimate it. The functions of the roof include protection from precipitation, thermal insulation of premises and the formation of an individual style of the building.
Building designs vary, and local climate conditions always impose a number of specific requirements. Therefore, it is extremely important to know how to correctly calculate the area of two pitched roof so that it can provide the owners with protection from cold, rain and snow at the proper level.
In this article
Base design
All features and design parameters directly depend on the rafter frame. In most cases, it is built according to one of two traditional systems:
- Layered. The rafters have two points of support: the mauerlat/floor beams at the bottom and the purlin (ridge) at the top. The last element is in turn supported by the internal load-bearing wall or a special support system (for example, a series of columns), which is constructed even before the construction of the roof begins. Most often, the layered system is used for large houses.
- Hanging. The lower part of the frame is still supported on the Mauerlat or on the floor beams. However, at the top the rafters do not rest against the ridge, but solely against each other. As a result, the bursting load is not transferred to the walls of the house (unlike the first case). However, the absence of a skate also predetermines important nuance: this type is suitable only for small buildings with small spans.
Calculate the width
Having decided on the type of rafter frame, it is time to calculate the width of the future roof:
- If the rafters are installed on floor beams, then they determine the dimensions of the entire structure.
- When installing the frame on the Mauerlat, the width of the roof will be the sum of three parameters: the width of the house box itself and two projections of the width of the eaves.
The width of the overhangs mainly depends on the roof covering material:
- For slate roofing the recommended width of the cornice is no more than 10 cm;
- For bitumen shingles, an interval of 30-40 cm should be maintained;
- Suitable cornice width for metal roofing is 40-50 cm;
- If corrugated sheets are used, the maximum width of the overhang should be no more than 50 cm;
- Ceramic tiles allow you to install cornices up to 60 cm wide.
There is a special nuance for houses whose walls are built from logs and beams. Such materials require enhanced protection from slanting rain. To do this, the cornice must be additionally increased by 10-15 cm.
Steepness of slopes
The angle of inclination of the roof determines its resistance to rain, snow and gusty winds. The steepness can vary from 10 to 60 degrees. However, for each house this value is calculated individually:
- Type roofing. Determines the specifics of installation and the structure of the sheathing. The denser the roof, the smaller the angle needed for the roof. The fewer joints and layers between roofing elements, the lower the minimum limit for roof height. Both of these nuances also work the other way around.
- Weight of the roofing pie. It puts a constant load on the rafters. However, not entirely, but only with its projection. Therefore, increasing the roof slope will reduce the mass transferred to the rafter frame. The heavier the roof, the steeper the angle between its slopes should be.
- Features of the local climate. Living in regions with high level annual precipitation, it is recommended to build a steeper roof - this will facilitate faster removal of snow and water. However, high slopes will be much more susceptible to winds than flat slopes. Therefore, in areas with strong winds, it is recommended to build a roof with a smaller angle of inclination.
The steepness of the slopes also directly affects the height of the ridge. Of course, with a few important caveats.
Apex point
Quite rarely, owners equip attic space gable roof for living space. The small space under such a structure does not help this at all. However, regardless of the intentions and desires of the owners, some restrictions will still have to be observed.:
- In order to fire safety the distance from the ceiling to the ridge must be at least 1.6 meters.
- There are no clear regulations regarding maximum limits. It is perhaps not recommended to erect a roof whose height is greater than the frame of the house itself - this may affect the latter with increased loads and, as a result, deformation.
For a more detailed calculation, two parameters will be required: the width of the house and the angle of the roof. Introducing gable roof in the form of a triangle, we will conditionally designate the desired height of the ridge as leg “a”, which is located perpendicular to the ceiling. It divides the attic space into two right-angled triangles, each of which has a leg “b” - half the width of the house.
Knowing the degree of steepness of the slopes, you can find the value of leg “a” using a geometric formula known from school:
a=b*tgα,
where “α” is the angle of inclination of the roof.
For example, if the width of the house is 8 meters, and the steepness of the slopes is 40 degrees, then optimal height skate will be:
4*tg35°=4*0.7=2.8 meters.
Preparing the roof covering
Before calculating the area of a gable roof and determining the required amount roofing material, you need to imagine both slopes in the form of two parallelograms. The area of each of them is the product of its height (“a”) and its width (“b”). The area of the entire roof is the sum of the areas of its slopes.
S roof = ab + ab = 2ab.
The formula is true even for asymmetrical slopes with unequal height and width.
One more important nuance must certainly be taken into account: if the roofing elements are installed overlapping each other, then, accordingly, a much larger volume of material will be required.
Difficult calculations of an elementary roof
For all its external simplicity and uncomplicated shape, a gable roof must be designed taking into account all technical nuances described above. A thoughtful approach to calculating the rafter base, the width of the structure, the steepness of its slopes and the height of the ridge is the basis for the correct construction of a roof that will reliably protect the house at any time of the year.
Building a house is a very responsible and expensive project, and one of the most difficult and costly stages is building the roof. Correct calculation of its area can significantly reduce the costs of its construction. In this regard, it is necessary to clearly understand the procedure and methodology for calculating the roof area. The first step is to determine the type of roof for which the calculation will be performed. Anyone who is looking for an answer to the question of how to calculate a hipped roof will find our article useful.
Today there are the following types of roofing, which differ in their design::
- single slope;
- gable;
- hipped;
- half-hip;
- mansard type;
- hip roof;
- 4-slope spire-shaped.
Regardless of the type of roof, when purchasing building materials, the correctness of the calculations made is crucial. Considering the trend towards a constant increase in prices for all building materials, precise definition roof area will be an effective way to save Money. But the calculation method itself is not so complicated; it requires attentiveness, knowledge of a school geometry course, knowledge of the geometric parameters of the building and the ridge, as well as the correct names of the roof structural elements.
Hip roof area
The most popular roofing option today is the hipped roof, which involves the presence of 4 slopes located at an angle to the base. To calculate the area of a hipped roof we need:
- calculate this value for each slope;
- add the resulting values together.
It is very important to check the results of your calculations several times, otherwise you may end up with a surplus or deficit building material.
In most cases, all construction and design companies have as initial data the projection of the roof, that is, the area of the base under it. Before starting the calculation work, we will divide the projection zone into simple component figures: trapezoids, triangles, rectangles and squares. The formula for calculating the area of each of these figures is well known to every schoolchild, so it will take a little time to get the result using a calculator. Taking into account that each element of the projection is at an angle, its area should be multiplied by the accepted cosine of the angle of inclination of the slopes. After adding up all the results obtained, we obtain the area of the hipped roof. As can be seen from the description, calculating this value will not cause any particular difficulties for people with an average level of knowledge of a school geometry course. For this reason, many builders entrust the functions of performing such important tasks to their production workers: foremen, technical supervision workers and other engineering and technical workers.
One of important conditions It is important to carry out calculations based on the eaves overhang, and not the edge of the building, otherwise the result will be incorrect.
The area of a hipped roof is calculated in compliance with the following rules:
- It is necessary to take into account the area of the following elements: ventilation ducts, chimneys, attic and its windows;
- the length of the slope is measured from the bottom of the ridge to the top of the cornice;
- for parapets, overhangs and firewalls, add 5% of the length;
- in order to calculate the required consumption of building material, you need to know the type of roofing, since each of them has its own consumption rates;
- when covering bitumen shingles or rolled materials, the length of the slopes will decrease by at least seventy centimeters.
You should know that roll materials most economical option roof coverings with complex shapes. They fit perfectly on almost any surface, their installation is not difficult and takes place in the shortest possible time.
Calculation of roofing materials
The purchase of roofing materials is accompanied by significant financial expenses, the optimization of which can save huge amounts of money. For this reason, when calculating the area of a 4-pitch roof for the purchase of roofing material, the following features must be taken into account:
Using a simple calculation method using the above formulas, you can obtain a reliable result, which, with the right approach, is converted into money saved on the purchase of building and roofing materials.
How to calculate the area of a hipped roof. Calculation of the amount of material for a hipped roof. Necessary formulas for calculating area
How to calculate roof area? Calculation of the roof area of a hipped roof
Before you start building a roof, you should definitely draw up an appropriate project. This will save money and avoid unnecessary rework. For calculation required quantity material, the roof should be roughly divided into simple geometric shapes. Next is the area of each element. The results obtained are added up. Let's look at how to calculate the area of a roof of one type or another in more detail.
Rules for measuring roofs
First of all, you need to decide on the angle of inclination of the slope. It is its size, as well as the width of the pediment and the length of the slope, that in most cases are the main values used in the formulas for calculating the required amount of roofing material and elements rafter system. If the latter has already been erected, additional measurements should be made. This will allow you to more accurately determine the amount of roofing material, vapor and waterproofing films, as well as insulation required.
First, let's figure out how to take roof measurements. The rules for carrying out work in this case are as follows:
- The length of the slope is measured from the very high point on the ridge to the lowest eaves overhang.
- Horizontal measurements are taken not along the facade, but along the eaves of the roof itself.
- The correctness of the slope measurements is checked by taking a diagonal measurement.
- Write down the results on paper with a roof diagram drawn on it in advance.
How to find out the area of a pitched roof
- K = √A 2 + B 2, where A is the width of the span, B is the height of the rafter stand. To the obtained result K, add the length of the overhang and get the length of the rafters T.
- C = T x M, where C is the roof area, M is the length of the slope eaves.
If the height of the rack is not known, the length of the rafters is often found a little differently: the width of the span is multiplied by the cosine of the angle and the length of the overhang is added.
Gable roof area
The question of how to calculate the area of a gable roof is also not particularly difficult. The area of a gable roof is exactly the same as that of a single-pitch roof. The same formulas are used. The only difference is that the area of the slope must be multiplied by 2. Sometimes the gables of such a roof are sheathed with roofing material. In this case, the calculation is carried out using the formula for finding the area of a triangle:
- C = 1/2 N x A, where H is the height of the roof, A is the width of the span.
There is another answer to the question of how to calculate the area of a gable roof. If the height of the roof is not initially known, calculations can be made based on the angle of inclination of the slope. In this case, the formula for the area of a triangle will look like this:
- C = 1/2 A x B x sine a, where A is the width of the span, B is the length of the rafter, and is the angle of inclination of the slope.
Area of a broken gable roof
A gable sloping roof consists of four planes. First you need to calculate their areas. To do this, first find the length of the layered or hanging rafter(K = √A 2 + B 2). Next, the formula for the area of a rectangle is used, that is, the result obtained is multiplied by the length of the cornice or purlin, respectively. At the final stage, we add up all the resulting numbers.
How to find the area of a hip roof
The most difficult thing to do is calculate the roof area of a hipped roof. The calculation method primarily depends on the design features of the rafter system. First, let's look at the calculations hip roof. It consists of four triangles of the same area. This is the design that is used most often. Therefore, in this case we apply the same formulas that we used to calculate the area of the gable roof.
The calculation of the roof area of a hipped hip roof is carried out taking into account the fact that it consists of two triangles and two trapezoids. We find the area of triangles using the formula:
- C = 1/2 N x A, where H is the height of the triangle, A is the length of the crossbar. We multiply the result by 2.
- C = (A + B) x H: 2, where A is the length of the upper purlin, B is the length of the lower, H is the height of the roof.
Thus, we multiply the resulting result by 2 and add to it the area of two triangles.
Nuances of calculating sheet roofing material
We found out how to calculate the roof area. Next, we’ll figure out how to find out the amount of roofing material needed. Of course, in order to find out the number of sheets needed to cover the roof, you need to know their length and width. In addition, when calculating, you should take into account the length of the overhangs of the cornices, as well as the width of the horizontal and vertical overlaps. Usually they are 15-25 cm. The area of the pipe and ventilation outlets in case of use sheet materials is not deducted from the total area. In addition to the roof area, in this case you will definitely need to find out the required number of ridge elements and valleys. Calculation of rolled soft material is carried out according to the same rules. The only thing in this case is to take into account the width of the overlap at the ridge and in the valleys.
How to correctly calculate the required amount of piece roofing material
When calculating the amount required to cover the roof ceramic tiles its length and width should be taken into account. The usable width is indicated by the manufacturer. The useful length is calculated taking into account the overlap, which can be different at different angles of inclination of the roof. You will first need to calculate how many tiles will be needed to cover 1 m2 of roof. The result is multiplied by the roof area.
Sometimes roofs are covered with such interesting material as wood shingles. The calculation in this case is performed in the same way as for the usual one. However, the elements of this roofing material are most often laid in three layers. Thus, the resulting result should be further multiplied by 3.
Calculation of waterproofing material
The waterproofing film is mounted on the roof in strips with an overlap of 10 cm. This must be taken into account when calculating. The overlaps on the eaves and gable overhangs will need to be 15 cm. It should also be borne in mind that the film is almost always laid at a distance of 30 cm from the ridge. This place is covered with a special insulating tape. Among other things, the waterproofing film must be overlapped in the area of the valleys and pipes.
Finally, let's give a couple useful tips regarding how to calculate the roof area and the amount of material. After completing all the necessary calculations, be sure to add 10% to the result. The fact is that losses during roof cladding work are inevitable. Almost all roofing materials are sold in batches. This means that it will be impossible to select additional sheets of exactly the same shade as those already used for the coating. If the roof has a complex configuration, the margin should be increased to at least 13%, since the number of trimmings in in this case increases. Especially a lot of waste remains when cladding gables and triangular slopes. If the roof structure contains many such elements, more than 13% of the material should be additionally purchased.
Thus, you now know how to calculate the roof area correctly. The work is quite complex and requires precision. However, it is quite possible to do it yourself. Especially if the roof is not very complex design. The same applies to the calculation of roofing material.
In order to determine the amount of roofing material needed, you should know how to calculate the roof area. This procedure is quite complex and requires precision. The calculations use formulas for finding the area of simple geometric shapes.
How to calculate the area of a hipped roof - rules and sequence
Hip roof of a house
Hip roofs are the most popular option in modern private construction. Developers often have a question: how to calculate the area of a hipped roof. This is necessary to determine the amount of roofing material, waterproofing and insulation.
Today you can do the calculation using computer programs, designed for all types of roofs. This has its advantages: high accuracy, choice various options designs, convenience. However, some builders prefer to rely on their wits and not spend money on something they can do themselves.
Before you start calculating the roof area, you should draw up detailed plan, where all dimensions will be plotted. Not a single element of the roof should be overlooked. In addition, already at the stage of designing a house, you should decide on the choice of roofing material, since the slope of the roof depends on this. The sharper the angle of inclination, the longer the roof slope. This means more material consumption. In addition, each roofing material is individual. For example, profiled metal sheets require much more overlap during installation than, say, natural tiles.
Having an accurate calculation of the roof area of the house, you can choose the most profitable roofing material, as well as insulation, steam and waterproofing.
Hip roofs can differ in shape:
- directly hipped;
- half-hip;
- hip;
- hipped gable.
The easiest way to calculate roof areas is those whose slopes are regular trapezoids and triangles and do not have any kinks on the slopes.
However, in modern construction Increasingly, hip roofs are being erected, with many slopes, the surface of which can consist not only of triangles and trapezoids, but also rhombuses, rectangles and other geometric shapes.
That is why, before you start calculating a hipped roof, it is advisable to brush up on your knowledge in a school geometry course.
Independent calculation of the area of a hipped roof
As mentioned earlier, first of all it is compiled full plan roofs. If there is no house design or the rafter system has already been installed, then the roof plan will have to be drawn up based on the existing frame. To do this, you only need a tape measure and an angle. Using this tool, all roof lines are measured, from the ridge to the ceilings. If the roof is multi-level and consists of different heights, then the drawing must reflect which height is which. It is also advisable to draw up a projection plan of the roof. This will help to present the picture more clearly. However, it is necessary to draw up a roof projection only if you have drawing skills.
Having compiled detailed drawing, it will not be difficult to decompose the roof into individual geometric components. This is necessary for more accurate calculations.
Remember that the size of the roof cannot be limited only by its perimeter. It is also necessary to add the length of the roof overhangs where it is expected.
Rules that must be followed when calculating a hipped roof:
- It is necessary to break the drawing into separate geometric shapes. Draw each of them into a separate drawing. Transfer all dimensions.
The simpler the figures are, and the more parameters you know, the easier it will be to make the calculation.
- The length of one slope is determined by measuring the distance from the extreme line of the eaves to the ridge.
- Each roof slope is calculated as follows: the area of the figure is multiplied by the cosine of the angle at which this roofing element is located.
- If any slope is an irregular rectangle, it must be divided into regular geometric shapes. And also carry out the calculation of each separately.
- After each element has been calculated separately, the resulting digital values are summed up.
Area calculation hip roof
As an example, we give the calculation of the roof of a hipped roof.
Let's assume that our hipped roof consists of the following elements: two regular trapezoids and two isosceles triangles. The roof slopes are located at an angle of 30°. The cosine of this angle is 0.87.
Trapezoidal slopes have the following parameters: one side is 10 m, the other is 7 m, height is 3 m.
Triangular slopes: two sides are 3.34 m, one side is 7 m. The height of the triangle is 4.8 m.
Let's start with the calculations.
The area of a trapezoid is found as follows: sum the length of the horizontal sides, divide by 2, multiply by the height. That is, in our case: S=(10 +7)/2 x 3 = 25.5.
Do not forget that the resulting number must be multiplied by the cosine of the angle, in our case by 0.87. As a result, the area of the trapezoidal slope is 22.185. We round up to 22.5 meters.
The final stage is the summation of all areas: S = 22.5 × 2 + 14.7 × 2 = 74.4. Round up to 75.
Thus, the area of the hipped roof, in our case, will be equal to 75 m².
During the calculation process, various small elements are not subtracted from the total area, such as: dormer windows, ventilation ducts, chimneys, parapets or skylights. Since their area is small, they do not entail any special financial costs. In addition, it is quite possible to make a mistake when calculating.
Calculation of roofing and other materials
After the calculation of the hipped roof has been carried out and the total area has been calculated, you can begin to calculate the required footage of roofing material. It is a mistaken opinion that the area of the roof drawing and the area required material match up. The bottom line is that all elements of the roofing material must be overlapped. In addition, each roofing material has its own technical indicators for the amount of overlap. Accordingly, material costs increase significantly.
When calculating the required amount of roofing material for a multi-level roof, it is advisable to seek help from a computer program. It will make calculations faster and more reliable.
But you can calculate the required material for a simple roof yourself. This does not entail any special difficulties.
Let's give an example of calculating the amount of slate for our hipped roof, the area of which we calculated earlier.
To do this we need to create a proportion:
X – 15%, where S is the roof area, X is a margin equal to 15%.
After X has been calculated, the resulting number must be added to the area S. The result will be the area of the required amount of material.
So, in our case the proportion will look like this:
X = 15 x 75 / 100 = 11.25. round to 11.5.
11.5 + 75 = 86.25 (m?) - the area of the required roofing material.
Calculation of roofing materials
In addition, when calculating the required material, you should remember that there will invariably be waste, which may require up to 20% of the material. That is, a proportion should again be drawn up, where X is now the expense. We add the resulting result to the area.
During construction complex roof You should take a material reserve of not 15%, but not less than 20%.
The calculation of soft roofs is carried out according to the same formulas as the calculation of slate. Consumption depends on the type of roofing material and the technology of its installation. The areas of valleys and ridges are calculated and ordered separately, since they are measured not in square meters, but in linear meters.
Length roofing sheets, determined by the height of the slope, is calculated by the size of the roof of the house. As a rule, metal tiles are produced up to 8 meters long. In this case, the thickness of the sheets ranges from 0.2 to 0.4 cm. As a result, long metal sheets bend very strongly. This may complicate the transportation process, as the sheets may break along the way. Therefore, when ordering metal tiles, take into account the area of the roof and roofing sheets, and select the most suitable sizes. You should also take into account the qualifications of the workers who will be laying the roof. Thus, with a roof area of up to 150 m? Is it recommended to purchase roofing sheets up to 2 m long for a roof area of up to 250 m? Are roofing sheets up to 4 m long preferred for roof areas over 250 m? purchase sheets longer than 6 m. Metal sheets, more than 6 meters long, are difficult to lay, as they bend very much. To install them, you must hire experienced roofers.
When transporting long roofing sheets, the process of loading, transporting and storing the material should be monitored.
Since on complex roofs the consumption of material is high. It is preferable to purchase piece material. Piece material is soft roofing coverings, for example, bitumen flexible tiles. Thus, waste can be minimized due to small sizes elements. But with proper calculation and a responsible approach, roof installation can be carried out in such a way that high costs can be avoided.
Please note that soft roofs require the organization of continuous sheathing, as well as additional installation costs. At the same time, prices for these types of coatings are significantly higher.
Thus, calculating a hipped roof allows you to timely calculate the upcoming costs for purchasing roofing material, insulation and waterproofing.
How to calculate the area of a hipped roof without involving third-party specialists? What main parameters do you need to know in order to calculate the roof of a hipped or gable roof? An example of calculation is in our article.
This question arises before laying the roofing of a house.
The answer depends on the form and its complexity.
Before you start calculating the square footage of the roof, you need to find out exactly what shape it has.
If it's difficult with jagged edges, it is always possible to divide it into several simple figures and calculate them (area).
What shape is the roof most often: rectangular, square, trapezoidal, triangular, parallelogram shaped.
Besides this, the more different shapes slopes on the roof, the more difficult it is to calculate its area. But this fact should not stop.
The main advantage of any roof is that its area can be calculated by breaking it down into simple shapes. Let's take a closer look.
What types of roofs are there?
- Flat or flat. They have minimum angle slope, no more than two to three percent of the horizon.
- Pitched. They have an angle of ten percent or more (relative to the horizontal plane or horizon level).
The latter, in turn, are divided into single-slope and multi-slope (one-, two-, and so on). A fairly common option for building a roof is the so-called gable roof, that is, a regular gable roof.
It has two completely identical sides, shaped like rectangles, in which one side is a long edge running parallel to a long wall, and the second is a segment located at an angle.
To calculate its area, you need to multiply the length by the width, and also by two, since there are two slopes. When carrying out calculations with more complex forms, you will have to break them down into simple ones, calculate each of them and add (sum up).
To make a correct and accurate one, you must first draw a diagram of the arrangement of the roofing elements, applying on this plan the dimensions expressed in one system of units. If the plan has been preserved after construction, you can consult it or use it for calculations.
To determine how much roofing material is needed for hydro-, noise- and vapor barrier of a house, it is necessary to calculate the roof area. For simple single-pitched or double-pitched roofs, it is enough to know only two dimensions, but for complex shapes you will have to divide the plane into several simple geometric shapes.
Important points to consider before making calculations
- It is necessary to divide a non-rectangular structure into parts of a complex configuration to simplify further calculations. These parts can be triangles, squares, rectangles and so on.
- To calculate the amount of building material that will cover the roof, it is important to take into account the quality of the coating.
- The area of a pitched roof for the purchase of soft, galvanized, slate material can be calculated using the formula. S = (Width of overhangs x 2 + Length of house) x (Width of overhangs x 2 + Width of house) / cos (Slope angle).
If the width of one slope (the segment from the corner of the roof to the ridge) and its length are known for a gable roof, apply simplest formula to determine the area of a rectangle. Namely: S = A x B. Here A is the length, B is the width. The resulting value is multiplied by two, since there are exactly two stingrays.
When dividing a roof of a complex shape into several simpler shapes and further carrying out calculations, the area of a right triangle can be useful: S = 1/2 x A x B. Here the letters A and B indicate the legs, that is, those sides of this geometric figure, which are adjacent to right angle triangle.
To calculate the area of an isosceles trapezoid (if one of the roof slopes has a regular trapezoidal shape with sides of equal length), in addition to the width of the slope, you need to know the length of the base of the trapezoid (usually the length of the house or a little more) and its height h (a perpendicular segment drawn connecting the top of the ridge and the base of the trapezoidal slope): S = (a + b) / 2 x h.
When dividing the entire roof into different geometric shapes, you need to arm yourself not only with a tape measure, but also with formulas for calculating the area of a triangle, rectangle, trapezoid and parallelogram.
The procedure and rules for performing calculations
The first step, which will allow you to calculate the roof area, will be the preparation of tools and materials. Among them are the following: a detailed plan of the roof of the house (if necessary, in different projections) indicating all lengths accurate to the centimeter (or as accurately as possible), a tape measure (if you need to double-check the measurements on the plan or add a few more), a calculator, paper, pen .
It is necessary to decide exactly how the measurement will be made. individual elements, lengths of the roof or other parts of the house and the distances between them. This point is not needed if there is confidence in the accuracy of the numbers indicated in the plan.
Otherwise, you need to take measurements using one of the following: while on the roof, standing on the ground, or from the attic. For a more accurate result, you need to take into account even such complex and irregular elements as a roof window, a ledge, a wide ridge, a change in the angle of inclination, an asymmetrical edge.
For the part of the roof that has a nine-degree slope, the smallest multiplier is applied - 1.1. The coefficient for a “steep” slope of 560 will be 1.8. Accordingly, on average, an increase for every ten degrees leads to an increase in this coefficient by 0.15.
That is, there is an increase of fifteen percent for every increase in the angle by ten degrees.
This follows from the following considerations: the difference between the maximum and minimum of the slope is 56-9=470. This means that the value in tens of degrees will be 4.7. The difference between the changes in the coefficient will be: 1.8-1.1=0.7. Now, when dividing one value by another, we get the answer to the question posed above: 0.7/4.7 = 0.15.
In order to find out the length of one of the slopes of a symmetrical gable roof, it is not necessary to climb up or into the attic. You need to measure the width of the house, or more precisely the length of the lower base of the isosceles triangle that both slopes form, the so-called end, and find out the slope of the slope.
You can do this like this: Roof slope width = Roof width / 2 / cos (Inclination angle), that is, you need to divide one second of the width of the house by the cosine of the inclination angle.
For example, if we consider a roof with a slope rotation of thirty degrees, the formula will look like this: width of the roof slope from ridge to edge = 5 m / 2 / cos (300) = 5 / 2 / 0.866 = 2.89 m. Now, By multiplying this number by the length of the house (length of the roof), the calculator will get each of the two parts of the roof.
So for a roof eight and a half meters long, the area will be 8.5 x 2.89 x 2 = 24.6 x 2 = 29.2 square meters.
At the end of the calculations, it is necessary to take into account a certain supply of material, if we're talking about about calculating the amount of roofing material needed for the roof. They usually add about ten percent, multiplying by 1.1. So the final number will be 29.2 x 1.1 = 32.12 sq.m.
These manipulations are easy to do for an ordinary classic gable structure. Suppose each part of such a roof has the shape of a regular, even rectangle, and its area, as stated above, is equal to the product of the lengths of its two adjacent sides (adjacent sides are those that touch each other at their ends, forming a right angle, as is the case for a rectangle ).
This means you need to multiply the length by the length of the rafters. Let's say the dimensions of the building are as follows: eight and a half and six and a half meters (8.5 m and 6.5 m).
Rafter (length rafter leg) – four whole and two tenths m (4.2 m). You will also need the size of the eaves overhang and the front overhang (for this example, these values are six tenths of a meter (0.6 m) each.
The area of one (and each) slope will be equal to: the length of the house (DD = 8.5 m), plus the front overhang (FS = 0.6 m), plus the eaves overhang (KS = 0.6 m), multiplied by the sum of the rafter length (DS = 4.2 m) and cornice overhang (KS = 0.6 m).
It turns out: Area = (DD + FS + KS) x (DS + KS) = (8.5 m + 0.6 m + 0.6 m) x (4.2 m + 0.6 m) = 9.7 x 4.8 = 46.56 square meters. And for both roof slopes 46.56 x 2 = 93.12 square meters. m.
For a pitched roof with a rafter length equal to 7.66 m (DS = 7.66 m), a length of eight point two meters (DD = 8.2 m), overhang lengths of fifty-five hundredths of a meter (KS = 0 .55 m and FS = 0.55 m), the calculation will look like this.
Roof area = (DD + FS + KS) x (DS + KS) = (8.2 + 0.55 + 0.55) x (7.66 + 0.55) = 9.3 x 8.21 = 76 .35 square meters. Note that in this case this number, obtained by simple calculations, is not multiplied by two, since there is only one slope on the roof.
The next option turns out to be a little more complicated than the previous two. This is a hipped roof. It has in its design four isosceles triangles or two triangles and two trapezoids. In the first particular case, you need to calculate the area of one slope and multiply by four (square house).
To carry out such calculations, it is worth knowing the height of the triangular part of the roof. This is a line segment drawn directly perpendicular from top to bottom. In the case of a triangle with equal sides, as in this example, this will cut the base (bottom side) in half.
This means that if the length of the house (which is equal to its width, since it is a square) is equal to seven point two meters, and the canopy will occupy four tenths of a meter, then the base of the calculated triangle is 7.2 + 0.4 = 7.6 m.
If its height is unknown and difficult to measure, you can find it using the Pythagorean theorem on a right triangle.
The fact is that this imaginary line divides each of the four sides of the roof into two figures of equal shape and area. These are right triangles. One of the legs is the indicated height, and the second is half of the lower segment, that is, 7.6/2 = 3.8 m.
If the length of the rafter (the hypotenuse of a right triangle or the longest side) is 4.5 m, then the height is square root from the difference: (4.5 x 4.5) – (3.8 x 3.8) = 20.25 x 14.44 = 292.41 (the sum of the squares of the legs is equal to the square of the hypotenuse).
The strict geometry of roofing coverings determines the method of calculating the total roof area as an arithmetically simple task. But the mass of different types of roof construction and the personal preferences of the home owner leave many questions and doubts about making the right choice method for calculating area.
The desire to organically fit the house into the surrounding landscape is dictated by the most elaborate roof designs. Tent, attic, and multi-gable projects complicate the calculations. So how can you reliably calculate the area of your roof? We will cover this issue in detail from the point of view of the end user of roofing.
In this article
Classification of roof types
The choice of roof type depends on how the roof space will be used. In the case of a utility or technical room, the choice is usually made at pitched roof. In case of residential attic space choose an attic-type structure or, taking into account the availability natural light, build a complex multi-gable roof.
Naturally, the roof area increases significantly, and it will be more difficult to calculate it. Before you start designing a roof, you need to know what they are.
Based on the shape and number of slopes, roofs are divided into the following main types:
- a pitched roof is used for bathhouses and utility rooms, less often for residential buildings, which thereby acquire an original and non-standard appearance;
- gable roof, one of the most popular solutions in dacha construction, characterized by practicality, ease of installation and maintenance;
- the attic type of roof has certain advantages due to the presence of an additional residential attic space;
- the hip roof is hipped roof, which consists of two trapezoidal and two triangular slopes and is characterized by increased resistance to wind loads;
- hipped roofing has four or more triangular slopes and is used in the construction of both residential premises and all kinds of gazebos;
- multi-gable roof - a complex broken structure that has an attractive appearance and allows the use of an under-roof space for housing;
- domed roof is used as architectural element or as the roof of religious buildings.
Such a variety of designs gives wide scope for the owner’s imagination and the ability to combine different types roofs in one building. Determine area sloping roof is a rather complex technical problem, but we will try to simplify it.
Calculation of the area of a simple roof
Before calculating the roof area, it is necessary to know in advance not only the dimensions of the roof covering, but also the dimensions of the overhangs on the gables and eaves. Otherwise, it will not be possible to optimally arrange the sheets and calculate the required supply of material.
By purchasing additional coverage if there is a shortage, you run the risk of purchasing it from a different batch, which can lead to discrepancies in colors.
When determining the roof area of a house, it is necessary to prepare a number of tools and devices in order to draw up a detailed drawing. Based on it, the true area is found, which may differ from simple rectangular shapes. For measurements you will need:
- construction tape;
- trusted level;
- a square to determine the rectangularity of the slope;
- pencil and notepad.
The area of the slope, provided it is rectangular, is calculated by simply multiplying the length by the width of the roof. The parameters are fixed taking into account the gable and eaves overhangs, then the amount of roofing material required is calculated, not losing sight of the correction for sheet overlap.
The length of the slope can also be calculated using the Pythagorean formula, measuring the height of the ridge and the width of the house, taking into account the eaves overhang. If the roof is not strictly rectangular, we calculate the area by summing the area of the rectangle and two triangles.
When a house has a gable roof, it is necessary to calculate the square footage of each slope separately and sum them up to calculate the overall result.
Calculating the area of a hip roof
Complex roofs include multi-gable, hip and dome-shaped types of structures, the quadrature of which is the sum of the area of various geometric shapes. As an illustration, you can consider calculating the square footage of a hip roof. It consists of two isosceles triangles and two trapezoids.
The area of the triangle is calculated using the following formula:
S 1 = (a x h): 2,
where S 1 is the area of the triangle, a is the length of the base and h is the height of the triangle.
The area of a trapezoid is calculated using the following formula:
S 2 = [(a + b) x h]:2,
where S 2 is the area of the trapezoid, a and b are the bases of the trapezoid, and h is its height.
Thus, the total quadrature hip roof will be equal to:
S total = (S 1 + S 2) x 2
Calculation of roof area of complex configuration
In the case of calculating the quadrature of more complex roofs, the method of breaking it down into simple geometric shapes also fully justifies itself. The drawing made after the measurements will allow you to accurately calculate the quadrature of the fragments and, by adding, obtain the overall result. If the slope or fragment of the roof has the shape of a parallelogram, you can calculate the overall result using the formula:
where S is the area of the fragment, a is the length of the side and h is the height of the parallelogram.
When calculating the total amount of coating, you need to keep in mind that on triangular and trapezoidal sections of the roof, material losses can reach 20% or more.
Hip roofs consist of four isosceles triangles, the quadrature of which is summed to obtain the overall result. Domed roofs can consist of individual sheets of complex shapes, but nevertheless they are calculated by reducing them to individual geometric components for a simple calculation of the amount of coverage. It is necessary to separately say that in the case of using flammable roofing materials, it is necessary to ensure workplace fire protection means.
When calculating the required amount of roofing material, there is no need to take into account ventilation outlets, chimneys and window openings, by this we reduce the risk of a lack of coverage, since on complex roofs waste can be from 8 to 30%.
On a detailed drawing of a multi-gable roof, individual geometric shapes must be carefully measured, which can be:
- parallelogram;
- trapezoid;
- triangle;
- rectangle.
The position of these figures on the roof must be clearly and unambiguously recorded in the drawing, which will make it possible to draw up a cutting plan for the covering in relation to its overall dimensions. This will allow you to avoid large financial losses and install the roof optimally.
Additional roofing elements are calculated separately; it is best to do this with the participation of a qualified seller who can check your roof square footage calculations and give additional recommendations. In addition, there are special calculators on the Internet for calculating the area of complex roofs.
Conclusion
Thus, we talked about the correct calculation of the area of roofs of various types. Attentiveness and thoroughness of measurements, as well as a drawn up installation diagram will allow you to avoid miscalculations and gross mistakes. And then the roofing work will take place without financial losses and will bring joy.
You need to know the exact areas of the roof slopes not only in order to correctly calculate the amount of material to purchase, but also the amount of work for which you will have to pay when hiring a team. The dimensions of the roof, as well as the volume of work performed on it, are always calculated in square meters. The only difference is that when purchasing material, some corrections and coefficients are taken into account.
Table 1. Nuances when calculating coverage.
| Nuances in the photo | What to take into account: instructions |
|---|---|
| Whatever material you buy, when calculating it, you should always take into account the full area of the roof according to the existing project (or your calculations). Important! At the same time, it is impossible to subtract from it the areas occupied by superstructures: a chimney, a dormer or dormer window, mezzanine. And even vice versa, if they need to be lined with the same material, you should calculate how much it will take and add it to the total amount. |
| When measuring the parameters of the slope, you must remember that this is the size not between the ridge and the support point on the wall, but between the ridge and the outermost line, taking into account the overhang. |
| When calculating the material, the location of the gutter also matters. If it is not on the wall, but on the cornice, then 7 cm is added to the area of the slope. |
| The area of the walls of existing parapets on the roof, which require covering with the same material, is calculated separately. |
| When covering roofs with galvanized steel sheets, bypasses chimneys usually performed by installing folds that extend onto vertical surfaces. They do not need to be taken into account when measuring slope areas. |
| Sections of the roof in those places where it adjoins vertical structures, does not need to be taken into account separately. |
note and on such a very important nuance. When the roof has an overly complex configuration, which complicates the measurement process, the area can be calculated not from the slopes themselves, but from their projection, using correction factors. But for this you need to know the exact parameters of the slope.
Table 2. Slope parameters.
| Slope degree | Correction factor |
|---|---|
| 7 | 1,014 |
| 8 | 1,02 |
| 10 | 1,031 |
| 13 | 1,054 |
| 15 | 1,077 |
| 18 | 1,118 |
| 22 | 1,202 |
| 30 | 1,41 |
On a note. If the roof has several sections lying at different horizons, but not connected to each other by the roofing material, the area of each of them is calculated separately.
Prices for metal tiles
Metal tiles
Calculation of areas in the traditional way
Now that the general requirements and amendments have been agreed upon, you can proceed directly to the calculations. Actually, they come down to determining the area of one or another geometric figure, which is what any slope represents. Many people can remember the principles of calculations from a school geometry course; you just need to use a tape measure and a calculator correctly.
Pyramid and arched elements roofs
Depending on the roof configuration, you will most often be dealing with a rectangle or parallelogram, triangles or trapezoid. Quadrangles of irregular shape can always be divided into a regular rectangle and one or two triangles, and calculated each separately. For those who are good at mathematics, it may be easier to use the formulas presented in the picture below.
Before you begin direct calculations, you should already have ready plan and sections of the roof indicating horizontal and vertical dimensions. Those who have construction documentation are lucky, but if they don’t have it, they will have to climb onto the roof with an assistant, armed with a notepad, pencil and tape measure.
Let's figure out in what case and what exactly needs to be measured, and how to make calculations.
Roof with one slope - or two identical ones
If you were able to measure the full length of the slope, which, as already mentioned, is the distance from the ridge to the edge of the overhang, then multiplying the result by the width, you will get the area. Alternatively, to determine the length of the slope, you can use the projection method, for which you need to know two of the three dimensions of the triangle formed by the slope. The formulas are presented below.
When calculating the length of the slope according to the projection, do not forget to add the length of the overhang to the total. Using the same principle, you can calculate a gable roof. If its slopes are the same, it is enough to calculate the area of one and double the result.
Hip and hip roofs
The peculiarity is that there are no rectangular slopes, but triangles and trapezoids. In hipped roofs there are only triangles, since there is no ridge in such roofs, and the slanted rafters are connected at one central point. Therefore, the principle of calculating areas is one and gable structures not applicable here.
Your task is to calculate the area of each slope, differing in configuration, separately, using the appropriate formulas. For triangles they are the same, but for trapezoids they are different - moreover, there can be several methods of calculation.
If the house is square in plan, then with a hip roof all four slopes will be equal. If such a roof is made over a rotunda (a building with spherical walls), there can be 6 slopes with the same proportions. Therefore, having calculated the area of one, multiply the total by 4 or 6.
You can determine the area of the trapezoidal slope in three ways as shown in the photo below.
Roofs, most often mansard, can also have a half-hip design. They differ from hip ones in that, due to very small side triangles, large slopes do not have a trapezoidal shape, but an irregular hexagon configuration. Its area is calculated by dividing it into two figures: a rectangle and a trapezoid. In the picture this division is shown with a red line.
Calculate the area of each figure separately and then add it up.
Roofs with spherical configurations
The most aesthetically pleasing from an architectural point of view are combined ones, in which there are elements of different shapes. As a result, they make up a coating of a rather complex configuration, each section of which must be calculated separately. Including, on the roof there can be not only planes, but also spherical surfaces: a cone or hemisphere, which are usually designed over rounded walls or extensions in the form of towers.
In any case, the calculation of their area is also determined using mathematical formulas.
