The initial stage of the construction of the roof: Roof calculation

Welcome to "All about the Roof," where we explore the fundamentals of building a roof. Roof calculation is an essential first step in any roofing project. This procedure ensures that materials, measurements, and structural requirements are carefully planned, setting the foundation for the entire construction phase.

The first step in roof calculation is to precisely measure the roof surface’s dimensions. This entails determining the horizontal area that needs to be covered as well as the pitches or slopes that control the direction of water flow off the roof. These measurements are essential because they show how much roofing material—like metal sheets, tiles, or shingles—is required.

Finding the roof’s square footage is the next step in the roof calculation process after obtaining measurements. This computation takes into account the entire area of the roof surface, taking into account any angles, protrusions, or complex architectural elements that could have an impact on the amount of materials needed and how they are installed.

Roofing experts determine the kind of materials best suited for the project after calculating the square footage. This choice is influenced by various factors, including the local climate, building codes, and aesthetic preferences. The choice of roofing material is essential for longevity and performance, regardless of whether you choose to install contemporary metal roofing, traditional clay tiles, or robust asphalt shingles.

Moreover, roof calculation includes estimating other parts that are required for installation, like fasteners, flashing, and underlayment. These components are essential to maintaining the integrity of the roof and its resistance to weather over time. Accurate estimating helps to keep projects on schedule by preventing shortages during construction.

To sum up, roof calculation involves careful planning and preparation in addition to math calculations. Experts make sure that every roofing project gets off to a strong start by taking precise measurements, figuring out square footage, choosing suitable materials, and estimating extra parts. Tune in to "All about the Roof" for additional perspectives on becoming an expert in the field of roofing construction.

Common types of roofs

The following roof types are the most well-known:

• single -to -shut -off – is based on two walls located at different levels of heights, and is built specifically for household objects and small buildings;
• gable – consists of two connected at an angle of slopes, the area of ​​which may be unequal;
• a tent – assembled from four slopes in the form of an isosceles triangle, as a result of which it has a similarity with a pyramid and is ideal for square houses;
• Helmes – created from two trapezoidal and two triangular slopes;
• attic – used to create a room in the attic and is formed due to a change in the shape of the roof, for example, using broken lines;
• Multiciper – built on buildings built in the form of a polygon.

Roof calculation in the online calculator

To compute the roof using the online calculator, one must select the finish coating type, enter the following sizes into designated cells, and determine the area and angle of inclination of the roof in addition to the quantity of lumber and other building materials.

• the width of the base of the roof from the end of the house (without adding the width of the overhangs);
• the length of the base of the roof on the side of the building (not taking into account the length of the overhangs);
• skate height (the distance from the future base to the skating beam);
• overhang length (at least half a meter).

For a roof with multiple slopes and varying inclination angles, individual computations are performed. The collected data was then summarized.

Roofing loads

The amount and cross-section of rafters required to create a sustainable frame are determined by calculating the loads acting on the roof, i.e., the pressure from wind and snow.

Snow load

Use the formula S = µ · SG to calculate snow pressure, where s is the desired snow load (in kg/m2), µ is the coefficient (determined by the ramp’s slope), and sG is the normative snow load (in kg/m2). The area determines the value of sG, which is displayed on a unique map.

The following procedure is used to calculate the snow load:

1. Using the geometric formula tg a = a/b (the angle of the angle in a rectangular triangle is equal to the ratio of the opposite leg to the adjacent), the roof height is divided into half the width of the outer wall of the house. The value of the angle in degrees is taken from a special table given at the end of this section.
2. Calculate the coefficient µ:
3. If the angle of inclination of the roof α does not exceed 30 O, it is taken equal to 1;
4. On steep roofs with a slope of more than 60 o, snow load is not taken into account at all, t. e. µ = 0;
5. At 30 o ≤ α ≤ 60 o, the formula µ = 0.033 · (α–36 o) is used.
6. Normative snow load is found on the map application No. 5 SNiP2.01.07–85 "loads and exposure" or in the table (see. below). For each snow area, and there are 8 of them, it is characterized by its own indicator, expressed in KPA or kg/m². For example, in Moscow, located in the third zone, it is 180 kg/m².

Table: Snow areas of Russia

Snow regions of the Russian Federation	1	2	3	4	5	6	7	8
S, kPa (kg/m 2)	0.8 (80)	1.2 (120)	1.8 (180)	2.4 (240)	3.2 (320)	4.0 (400)	4.8 (480)	5.6 (560)

We offer to compute the actual snow load. Assume that a 7 x 10 m house with a 2.5 m skate height is being constructed in Kaliningrad. After that, you must compute the following:

1. Find on the map a normative snow load for Kaliningrad (second zone, 120 kg/m²).
2. Divide half the width of the wall into the height of the skate: 2.5/3.5 = 0.714.
3. From the table, find the angle of inclination by his tangent. In our case, it is 36 °.
4. Determine the coefficient µ: 0.033 · (60–36) = 0.79.
5. Find the desired snow load s = 120 · 0.79 = 94.8 kg/m².

Table: Definition of the angle by his tangent

TG α	α
0.27	15 °
0.36	20 °
0.47	25 °
0.58	30 °
0.7	35 °
0.84	40 °
1	45 °
1.2	50 °
1.4	55 °
1.73	60 °
2.14	65 °

Wind load

Wind pressure on the roof is calculated using the formula Wm = WO K · C, as shown in SNiP 2.01.07–85 “loads and exposure.” Here, WO stands for the normative value of wind pressure as shown on a special map, k is the coefficient that changes as the wind load increases in height, and C is a unique aerodynamic coefficient.

Aerodynamic coefficient: constant value that varies with roof configuration. Indicator value for a steeply sloping roof is -1.8. The aerodynamic effect on a gently sloping roof, where the wind squeezes rather than rises, is +0.8. To determine the maximum possible wind load, this coefficient is typically taken to be equal to the largest positive value (t, i.e., 0.8).

Table: wind loads in Russia by regions

Wind areas 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)

To be clear, we will attempt to calculate the wind load on the Russian village of Babenki’s roof in the Ivanovo Region. Assuming that the skate is six meters above the ground and that the roof has a 36° inclination, the following computations will be made:

1. W_O = 30 kg/m², since the terrain belongs to the second wind area, which is indicated on the SNiP application map and in the above table.
2. K = 1, since all buildings in this area are below 10 m (cm. The table of values ​​of the coefficient K).
3. W_m = 30 · 0.8 = 24 kg/m².

Table: The value of the coefficient K for calculating the wind load

The height of the house	Open area	Closed area with obstacles above 10 m	Urban areas where houses have a height of more than 20 m
up to 5m	0.75	0.5	0.4
5–10m	1.0	0.65	0.4
10–20m	1.25	0.85	0.53

Roof calculations are an essential starting point for roof construction. To ascertain the components, measurements, and structural specifications required to build a strong and useful roof, it entails exact measurements and evaluations. This step is crucial because it guarantees that the roof will fit precisely, endure the weather, and offer long-term protection. In order to guarantee that the roof is both safe and effective for the building it covers, proper calculation takes into account variables like roof pitch, area dimensions, material durability, and local weather conditions. A successful and long-lasting roof construction process is predicated on comprehending and carrying out precise roof calculations.

Calculation of the angle of inclination, height and weight of the roof

You must choose the slope angles of the slopes before figuring out the roof’s height. This will support the regulatory documents, namely the Code of Rules SP20.13330.2011, which establish the requirements for roofing work based on SNiP 2.01.07–85 "loads and exposure" instructions.

Tilt angle

The finish material that is used determines the roof’s angle, as per the regulations.

Table: Tilt angle for roofs with different coating

Recommended Roof tilt angle	Finish coating
1-2 °	Bitumen -based roller materials – at least four layers, with external gravel sprinkling, drowned in a layer of molten mastic
2-3 °	As in the previous line, but for the reliability of the roof three layers of roller material are enough
3-10 °	Similar to the above rolled materials (at least three layers), but without external protective gravelic sprinkling.
10-15 °	Roll roofing materials glued to hot mastic at least two layers
13–15 °	Tiled clay coating
15–17 °	Assosive -cement sheets of enhanced profile
17–20 °	Roofing sheet steel with joints of compounds
18–35 °	Corrugated board, metal tile
27–44 °	Natural piece tile, bitumen-polymer or shale tiles
38–45 °	Dranka, chips, natural gont
40-60 °	Dutch tile
5–90 °	Asbestos -cement slate
20–90 °	Artificial slate

The height of the skate

They start by figuring out the height of the ridge timber after selecting the roofing material and determining the angle of the roof. They use geometry to accomplish this because the section’s roof resembles two triangles joined together.

The formula A = b · tg α is used to calculate the height of the roof, where a is the skate height, b is the building’s half width, and α is the roof’s angle of inclination.

The trigonometric table above can be used to find the tangent of the roof’s angle of inclination.

For instance, figure out how high the roof will be at a 40° angle when it is intended to be built on a 6 by 9 m house. We will complete the following computations in order to achieve this:

1. We divide the width of the house by 2 and determine the length of the lower cabin of the rectangular triangle of the roof: b = 6 /2 = 3 m.
2. By the table, we find that the angle of the angle of 40 ° is 0.84.
3. Calculate the height of the roof A = 3 · 0.84 = 2.52 m.

Video: calculating the height and angle of the roof

Weight

The total weight of the roofing cake, including the insulating materials, counterparts, crate, and finish coating, is the weight of the roof.

The seller at a building supply store can tell you how much one m² of any material weighs, or you can figure it out for yourself by referring to the material’s label, which includes the density of the material in m³ as well as the roll’s thickness, width, and length. You can determine the weight of one square meter of any building material by using these indicators.

Let’s say we need to calculate the weight of a roll of insulated material with a density of 35 kg/m³ and bitumen tiles that is 10 m long and 1.2 m wide. The roll should be rolled into a 0.1 m thick roll. In this instance, the following must be made:

1. Calculate the weight of 1 m² of thermal insulation material according to the formula 0.1 · 1.2 · 10 · 35 / (10 · 1.2) = 3.5 kg / m².
2. Find all the other data, that is, the weight of 1 m² of finishing, steam and waterproofing and a wooden frame of rafters and crate, in the table (see. below) or on the label of goods in the store.
3. Fold all the values ​​obtained and multiply them by the roof area, thereby determining the weight of the entire roof.

1 m² of roofing pie typically weighs 50 kg. Therefore, in order to calculate a 10% supply, or 55 kg/m², this value must be precisely multiplied by 1.1.

Table: Weight 1 m² of materials for roofing

Material	Weight 1 m²
Slate	10-15 kg
Ondulin	4-6 kg
Ceramic tiles	35-50 kg
Cement-sand tiles	40-50 kg
Bitumen tile	8–12 kg
Metal tile	4-5 kg
Corrugated board	4-5 kg
Contact	18–20 kg
Chat	8–12 kg
Rafter system	15–20 kg

Calculation of the area of the roof

The simplest method for figuring out the area of a roof with two or four slopes that are identical. The definition of this parameter always gets harder the more complicated the roof configuration gets, which makes sense given that each slope’s area needs to be taken into account independently.

The following formulas determine the roof’s area:

• for a rectangular slope s = a · b, where a and b are the lengths of the sides of the rectangle;
• 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;
• for the 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;
• for a slope in the form of a parallelogram s = a · h, where a is the length of the side of the geometric figure, and h is its height.

Assume that two identical rectangular slopes, each measuring 2.2 meters in length and 5 meters in width, need to be used to determine the area of the roof. The computation actions in this instance will be as follows:

1. S_C = a · b = 5 · 2.2 = 11 m² (the area of ​​one slope).
2. S = 2 · S_C = 11 · 2 = 22 m² (area of ​​two slopes).

Calculation of the number of roofing materials

You must determine in advance how many sheets of finish coating, lumber, and sofits I will need when building a roof.

Finish coating

You must ascertain the useful sizes of the roof before calculating the necessary amount of finish. Since it is necessary to account for the overwhelming length of the sheets, they are smaller than they actually are.

Let’s say you need to calculate the cost to purchase a 4.1 x 6 m metal tile with a useful sheet width of 1.1 m and a total length of 2.25 m for a house roof. For this:

1. Divide the length of the roof to the useful width of the leaf of the tile: n = 6 / 1.1 = 5.45. Round this value up to 6. This is the required number of sheets in a row along the width of the roof.
2. From the real length of the sheet (2,250 mm), we deduct the size of the overlap (150 mm) and thereby set the effective length of the sheet (2,100 mm or 2.1 m).
3. We will divide the total length of the roofing of the roofing to the effective length of the sheet: k = 4.2 / 2.1 = 2. Thus, we determine that by the length of the roof, that is, from the cornice to the skate, each row will require two sheets.
4. The number of sheets in a 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, 12 sheets will go to cover the entire roof.

Pilomaterial

We determine how much lumber will be needed to build a wooden frame device that is 6 m wide and 4 m long and supports a single roof slope:

1. The distance between the elements of the frame depends on the weight of the finish roofing material. We choose a light ondulin to cover the roof, which can be placed in the rafters with a step of 60 cm, and set the angle of inclination of the slope of 15 o .
2. We calculate the number of rafter legs, for which we will divide the width of the roof 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.
3. The thickness of the rafter legs is determined by subtracting the sum of the distance between the rafters from the total width of the roof and dividing the resulting number by the number of elements of the frame (6 – 5.4 / 11 = 0, 055 m = 55 mm). And choose the width so that it is 2-3 cm more than the thickness of the heater slab. Judging by a special table (see. Below), rafters are suitable for us with a cross section of 50 x 150 mm or 55 x150 mm.
4. We will make sure that we correctly chose the cross -section of the rafter legs. To do this, we first determine the load on the linear meter of each rafter leg according to the formula Q formula_r = A ∙ Q, where A is a step of the rafters, and Q is the total load on the roof, which consists of the weight of the roof, the pressure of snow and wind. Then we check if the inequality is executed [3.125 ∙ Q_r ∙ (l_Max³)] / [b ∙ h³] ≤ 1, where l_Max – the working length of the largest section of the rafter leg in meters, b is the thickness and n is the width of the board in centimeters. If the inequality is not respected, you need to increase the width of the board or reduce the step of the rafters.
5. Based on the angle of tilt of 15 °, we decide to put the labels on the labels every 60 cm. Determining the length of the roof by the distance between them and adding to the resulting number 1 (board for fastening the skate), we get that 8 rows will be required.
6. We find the width of the knob boards by subtracting the amount of steps between them from the length of the roof and dividing the result into the amount of collapse (400 – 360 /8 = 5 cm). According to the table below, select the optimal element thickness.
7. Since the length of the slope is 4 m and it is necessary to make a wage of 7 cm below and at the top, we come to the conclusion that it is necessary to buy two wind boards with a length of 4.15 m.

Table: Dependence of the section of the rafters on their step and length

Step of installation of rafters (cm)	Rraft length (m)
	3	3.5	4	4.5	5	5.5	6
215	100×150	100×175	100×200	100×200	100×250	100×250	–
175	75×150	75×200	75×200	100×200	100×200	100×200	100×250
140	75×125	75×175	75×200	75×200	75×200	100×200	100×200
110	75×150	75×150	75×175	75×175	75×200	75×200	100×200
90	50×150	50×175	50×200	75×175	75×175	75×250	75×200
60	40×150	40×175	50×150	50×150	50×175	50×200	50×200

Using a specific table, the thickness of the knob boards is calculated based on the distance between the rafters. It ought to be at least 20 mm in our situation.

Table: How the stepal step affects the thickness of the crate

Step of rafters (mm)	Chatting board thickness (mm)
300	–
600	20
900	23
1200	thirty
1500	37

Video: calculation of the size of the rafters and the beams with your own hands

Sofites

Finally, we will gradually ascertain whether more components are required:

1. According to the formula l = b ∙ 2 + d ∙ 2, where in is the length of the pediment, and D is the cornice overhang, we find the perimeter of the overhangs according to the cornice and the pediment: 4 ∙ 2 + 6 ∙ 2 = 20 linear meters. Then we measure the overhang width a (for example, 30 cm) and determine the area of ​​cornice and pedimental overhangs (s = l · a = 20 · 0.3 = 6 m²). Now we think how much metal sophite will need 3 x 0.325 m in size and with an area of ​​0.98 m². To do this, we will divide the total area of ​​the overhangs into the area of ​​metal sophite (6 / 0.98 = 6.2). The resulting number is rounded to 7, t. e. It will take 7 sheets of sofits.
2. We determine the number of J-profiles 3 m long, which are inserted under the overhangs near the walls. Having divided the perimeter of 20 m by the length of one element, set that for the roof device you will have to purchase 7 J-profiles.
3. We calculate the number of frontal ones (installed in the end of the overhangs) and finish (mounted in combination with frontal) planks. 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 frontal and finish strips.

Preliminary calculations regarding your roof’s needs are essential for any building project. It entails evaluating the roof’s dimensions, form, and structural requirements to make sure it offers sufficient durability and protection. You can compute precisely to find the quantity of roofing tiles, shingles, or metal sheets required, as well as the amount of supporting framework.

Planning and budgeting are also aided by accurate roofing calculations. Accurate quantity requirements help you estimate costs more accurately and avoid unforeseen costs later in the project. Whether you’re replacing an old roof or building a new one, this step is crucial to keeping your project budgeted and on schedule.

In addition, roof calculations take local climate and building codes into account. These factors have an impact on choices about the kind of materials to use and the layout of the roof. To guarantee longevity and weather resistance, a well-calculated roof considers these environmental factors.

All things considered, the first phase of roof calculation lays the groundwork for a building project that is successful. It guarantees adherence to building standards, helps with financial planning, and clarifies material requirements. You can have a roof that not only fulfills your functional needs but also improves the overall look and market value of your home by taking the time to make precise calculations.