How is the cubic capacity of roundwood calculated? Log cubator: how to calculate the volume of rounded logs

By mathematical standards, a round timber is a cylinder. The volume of a cylinder is calculated as the area of its circumference multiplied by the length of the cylinder itself (read logs).

where: number Pi- 3,14159265358979; R- radius of the circle; H- the length of the cylinder. But since the comparison of a log with a cylinder is purely conditional, in real calculations the diameter of the log is measured at its midpoint. Naturally, without bark. From school we were taught that the area of a circle is calculated as the number Pi (3.14159) multiplied by the radius of the circle squared. Or another option is, again, the number Pi multiplied by the diameter of the circle to the fourth power. These are purely theoretical calculations of the volume (cubic capacity) of one individual log. What if we are talking about large volumes of timber, the so-called timber stacks, where there are hundreds of cubes of round timber? In this case, of course, no one will calculate m3 of each log. To simplify the work of storekeepers, raters, technologists and other employees of woodworking enterprises, who, as part of their duties, have to deal with wood measurements, they use a round timber cube. This is nothing more than tables approved by GOST, containing calculations of the volume of round timber, depending on the thickness of its top. Experienced loggers and woodworkers poke the timber in increments of 2 cm, usually in even sizes. It is worth noting that specialists who constantly deal with forests can, by eye, with great accuracy, determine the diameter of a log without using rulers or tape measures. And then there are mathematical calculations of the pointing of the forest:

there are so many logs of this diameter,
so much different diameter
and so on.

After that, the volume values of a log of each diameter are taken from the forest cubicle and multiplied by the number linear meters.

For example, a log with a diameter of 20 mm has a volume of 0.23 m3, and there were 100 such logs 6 m long in a stack. Thus, the result is obtained based on the cube size of the lumber: V = 0.23 m3 * 100 pieces = 23 m3 - i.e. the stack will contain 23 m3 with a top diameter of 20 mm.

The volume of logs of other diameters is calculated in a similar way, using the values of a 6-meter-long round timber cube.

Round timber cube table

Part I - the length of the measured timber log ranging from 4 to 8.5 linear meters.

Diameter/cm	Length/m
Diameter/cm

Part II - the length of the measured timber log ranging from 9 to 13.5 linear meters.

Diameter/cm	Length/m
Diameter/cm

Converting warehouse cubic meter of timber to dense

Timber stored in piles in open areas is counted in cubic meters (m3). This is the so-called warehouse cubic meter of timber, measured with all the voids and gaps between the logs.

Essentially, folded m3 is measurements of the stack according to its external dimensions: width, height and length. When implemented, round lumber such a concept as a dense cubic meter of wood is used. What it is? This can be thought of as a stack of timber without voids or any gaps between the logs. That is, like a solid volume of wood. How is the volume of round timber converted into a dense cubic meter? A stack of timber, sorted by length, is measured by its outer dimensions. The values are multiplied and the resulting warehouse m3 is obtained. Next, a special conversion factor is used (see table). As a result of multiplying the resulting volume of folded cubic capacity by the coefficient from the table, the value of the dense forest cube * is obtained.

To build a house, bathhouse or other wooden building with your own hands, you need to know how to calculate the cubic capacity of a log. This will allow you to purchase exactly as much building material, how much is required to complete the upcoming work, so you can properly plan your budget and save a certain amount of money.

The volume of round timber is measured in cubic meters. At the design stage of a future building, it is necessary to take into account that the diameter of the logs used for construction external walls at home may be different. Its value depends on the air temperature in the region during the cold season. So, if in winter the temperature does not drop below -22°C, then round timber with a cross-section of 150 mm can be used. In severe frosts, for a comfortable stay in the house, it is necessary to choose thicker building materials. At the same time, their cubic capacity will depend on the cross-section of the logs.

apply a mathematical formula;
use a cubeturner.

Formula for calculating the volume of logs

The algorithm for calculating the cubic capacity of logs is quite simple and understandable even to a novice master. First, the total amount of timber is calculated for the existing project. Then the cubic capacity of one element is calculated, after which the obtained values are multiplied among themselves.

If we consider a log from a geometric point of view, it looks like a cylinder. Therefore, to calculate its cubic capacity, you can use the formula for calculating the volume of a cylinder: V = π*r²*l, where: V is the volume; π is a mathematical constant equal to 3.14; r is the radius of the round timber; l is the length of the log.

As an example, consider a situation where it is necessary to calculate the cubic capacity of timber for the construction of a bathhouse 6x12x2.4 m. It is planned to use logs 300 cm long and 15 cm in diameter as a building material. First, you need to find out the total amount of round timber. To lay one row along the perimeter of the future building you will need: 6/3 + 12/3 = 6 logs. To increase the height of the walls you should prepare: 240/15 = 16 pcs. Having summed up the obtained values, we find out what you need to buy to build a bathhouse: 16 * 6 = 96 logs. The volume of one element will be equal to: 3.14x(0.15/2)²x3 = 0.0529 m³. For the example given, the total cubic capacity of the required timber will be equal to: 0.0529*96 = 5.08 m³.

The above algorithm can only be used when the building material meets the following requirements:

the logs are cylindrical in shape;
their length and diameter are the same.

If during the construction process it is necessary to use round timber whose butt and top dimensions are different (truncated cone), then the standard formula for calculating the volume of a cylinder will not give a true result. In this case, it is necessary to apply the following formula: V = (π/400000)*l*, where d is the diameter of the apex; D—butt diameter; a is the narrowing coefficient of the round timber. Its size depends on the length and cross-section of the butt. The values of coefficient a are presented in the table.

Using a cubeturner

The timber block is strictly regulated by GOST 2708-75 and is a matrix into which the volumes of round timber are inscribed depending on its geometric parameters. This table consists of rows and columns. The former contain information about the cross-section of the product, and the latter - about its length.

The table is very easy to use and significantly reduces the time of calculations. For example, you need to calculate the volume of a log whose length is 5 m and diameter is 25 cm. At the intersection of the corresponding column and row there is a number of 0.295 m³.

Volume of timber of different diameters

If everything is more or less clear with logs of the same size, then with round timber of different cross-sections the buyer may have certain difficulties. In this case, the volume can be calculated using several methods:

calculate the cubic capacity of each element, and then sum the resulting values;
calculate the amount of space occupied;
find the average diameter of the log and carry out further calculations based on it.

To obtain the most accurate results, it is necessary to use the first method, however, it is the most labor-intensive and can take quite a long time. However, in this case, you can be sure that you will buy exactly as much building material as you need to complete certain tasks.

The second method assumes that the material occupies a space of a certain size, which has the shape of a parallelepiped. It could be the body truck, part of a warehouse, etc. Since voids are formed between the logs when folded, the actual volume of wood should be reduced by approximately 20%.

The calculation algorithm is as follows:

the dimensions of the parallelepiped filled with round timber are calculated (length, width and height);
the available quantities are multiplied among themselves;
the resulting value is multiplied by the hollowness coefficient, that is, by 0.8, which will be the final result.

This method is the simplest and fastest, so it is used quite often.

The averaged method can be used when the cross-section of all logs is almost the same. In this case, from total number 3-5 elements of timber are selected. After this, the diameter of each of the selected round timbers is calculated and the average value is determined. Next, the volume for one element is calculated using a formula or cubature, and then the result is multiplied by the number of logs required.

Conclusion on the topic

Today, there are several ways to calculate the cubic capacity of logs. All of them have a small error, which must be taken into account when purchasing timber. The most precise method It is considered to determine the volume of each element with further multiplication of the resulting values, and the fastest is to calculate the cubic capacity of the occupied space.

Calculation of cubic capacity of occupied space

The simplest method is to define a cubic rectangular space in which the timber is folded. Such a place could be the back of a dump truck or a barn. You can also calculate the geometric dimensions of a woodpile if it is folded into a neat rectangle.

Since the spatial cubic capacity is not completely filled with wood, the determined value is reduced using the voids coefficient. In construction calculations, the void ratio is considered to be 0.8. That is, 20% of the space is occupied by air voids, and 80% by wood.

Cubic size is defined as follows:

The length, width and height of the rectangular space are measured.
The resulting values are multiplied with each other to obtain the volume value.
The resulting value is multiplied by a factor of 0.8, which takes into account the approximate number of voids between round logs.
The resulting value is taken as the required volume of the log.

This method is used to calculate the cubic capacity of round timber, boards, and firewood of different sizes.

Calculation of the volume of individual logs

Figure 1. Measuring two perpendicular diameters in a beam cross-section

If round wood characterized by the same long logs and similar diameter, then you can calculate the volume of selectively 3 logs and reduce them to the average calculated value and multiply it by the amount of log material. In this case, the calculations are performed as follows:

Choose any 3 timbers.
Measure their diameter and length. For ease of calculation, measurements are made in meters.
Calculate the cubic space occupied by each of the round timbers using the formula:

where Pi is a number equal to 3.14,

R – radius, equal to half measured diameter,

L – beam length.

The resulting values of 3 cubic meters of roundwood will be close to each other. They must be added up and the sum divided by 3. Thus, we obtain the value of the average volume of one log.
Next, we multiply the resulting average value by the number of blanks in the machine or storage.

Since logs of similar diameter and standardized length are used for construction, this method widely used to estimate cubic capacity scaffolding.

If the shape of the beam is slightly pressed down, its cross-section will not be round, but slightly oval. How then to determine the diameter value? To do this, measure the size of 2 perpendicular diameters in the section of the beam: the largest and the smallest. Next, the measured values are summed and divided by 2. The resulting value will be the average diameter used in the calculations (Fig. 1).

Volume calculation using tables

Calculating the volume of round timber using tables involves measuring the diameter and obtaining data from ready-made construction tables.

Such directories contain structured information indicating the consumption of lumber of a given diameter for the construction of 1 m² of wall. Such tables are the result of construction calculations and established practice in determining lumber consumption. Therefore, they make it possible to fairly accurately estimate the cubic capacity of scaffolding. A set of tables compiled into a single standardized document is called GOST.

Most often, the tables are calculated for a rounded log from which upper layer and bark, the surface is leveled to a regular cylinder.

If desired, you can use the table data to determine the amount of unedged wood, making allowances for possible inaccuracies. Errors in the results obtained will be associated with changes in the cross-sectional diameter of the round timber along its length.

Independent calculation of the quantity of round timber allows you to verify that the seller has determined the price correctly. It is economically feasible to check a team of contractors by conducting your own approximate calculations of the consumption of construction logs for the construction of the walls of the house.

For many builders, the topic of calculating the number of logs in a cube is familiar. But for an unprepared person this may seem not only very distant, but also incomprehensible. And very often disagreements arise between the builders themselves, as well as between the builders and the customer, about how many logs there should be in a cube.

To deal with this problem, we usually use mathematical method, which in a few minutes can give a clear answer about how many logs are needed for a certain number of cubic meters.

Typically in construction wooden buildings rounded logs are used. But this material may differ in size, that is, in length and diameter. The unit of measurement is usually centimeters. There are one million centimeters in one cubic meter. Thus, first you need to decide on the size of the logs.

In order to measure the size of the logs, you will need a regular centimeter tape measure. All logs, as a rule, should initially be the same size, and later, depending on the project, they are sawn into the necessary elements.

So, by measuring the size of a log using a tape measure, we obtain the length and diameter in centimeters. For example, let's try to calculate how many logs are needed for one cubic meter, if the logs are six meters long and their diameter is eighteen centimeters.

To calculate, you will need the following formula:

Volume = Pi * Radius * Radius * Length.

Six meters in this case equals six hundred centimeters. Pi is always 3.14. We get the radius by dividing the diameter by two. Thus, our formula acquires next view: Volume = 3.14 * (18:2) * (18:2) * 600 = 3.14 * 9 * 9 * 600 = 152604 centimeters. To convert to cubic meters, divide the resulting number by one million: 152604: 1000000 = 0.1526. This result tells us that one log of this size will occupy only a little over 0.15 cubic meters.

Now you need to figure out how many logs are in a meter. This is our main task. To do this, we divide one cubic meter by the result of our calculations - 0.1526. It turns out: Quantity = 1: 0.1526 = 6.55 logs. It turns out that for one cubic meter we need to take about seven logs of a given size.

If we consider the logs larger diameter, for example, twenty-four centimeters, then the calculation results will be different:

Volume = 3.14 * 12 * 12 * 600 = 271296 cubic centimeters = 0.2713 cubic meters.

This means that in one cubic meter there will be: 1: 0.2713 = 3.69 logs. In this case, there will be fewer logs in one cubic meter.

To calculate the number of logs per cubic meter, it is used simple formula, which allows you to calculate the result in a matter of minutes. For calculations, of course, it is better to arm yourself with a tape measure and a calculator.

When implementing construction work for the construction of a residential building, a specialist must perform big number various tasks, one of which is: drawing up and calculating the estimated cost to the final finishing of the premises of a residential building. It is mandatory to calculate the required amount of various building materials, which is quite difficult to do. Therefore, such knowledge - how many boards are in a cube - has a very important for a specialist who is engaged in the construction of a residential building and wants to complete the work as efficiently and quickly as possible.

Buying club: existing types of boards

To calculate exactly how many board pieces are in a cube, you will need to know not only what exactly a board cube means, but it is worth understanding important point that exist different kinds boards and what is possible to purchase on modern market for performing various construction works. It should be noted that the cube of almost all materials, regardless of the type of material, is calculated in the same way, that is, according to one specific method. The types of boards have no influence on the calculation of the cubic capacity of this building material.

Non-grooved types of lumber are: timber, various edged boards, as well as unedged boards (they are an exception when calculating cubic capacity, because this process occurs a little differently). Tongue-and-groove types (which have special grooves for making joints) include: modern lining, blockhouse, flooring material, as well as imitation natural timber. When you choose a tongue-and-groove type of building material to purchase, then you will need to pay attention to the fact that when making calculations, only working width boards without tenons. If we talk about a blockhouse (imitation log), then when calculating the cubic capacity, only the thickness at its highest point is taken.

How many boards are in 1 cube: performing the calculation

Any person, even from his school days, understands how cubic capacity is calculated. For this procedure, it is necessary to calculate quantities such as: length, width and height. A similar principle is used to calculate the cubic capacity of 1 board. When performing such calculations, it is recommended to convert all available values into meters. The cubic capacity of 1 board, which has a cross-section of 150x20 mm. and a length of 6 m, is calculated as follows: 0.15 multiplied by 0.02 and 6, so that the cubic capacity of this board will be 0.018 cubic meters.

Let's apply the volume formula V= L*h*b (where L is length, h is height, b is width).

L= 6.0; h= 0.02; b= 0.15.

Thus, V= 6.0*0.02*0.15 = 0.018 m3.

To determine how many boards are in one cube: divide 1 m3 by cubic capacity (the volume of one board).

1 m 3 / V = N pcs.

1 m 3 / 0.018 m 3 = 55.55 pcs.

Thus, the number of boards in one cube is 55.5 pieces.

Finding out the cost of a certain type of board when the values of its volume is known is quite easy: 0.018 multiplied by the price of 1 cubic meter. When 1 cube of a certain type of board costs, for example, 5,500 rubles, then the cost will be 99 rubles. At this point in the calculation, there is some trick of sellers and managers in construction stores, because the cubic capacity of the material is rounded to some integer values.

Such rounding can lead to such a moment that the price of 1 board (when 1 cube costs 5500) will be completely different values. In addition to all this, it should be noted that various boards for construction, which have a nominal length of 6 meters, the actual length is 6.1 - 6.2 m, which is not taken into account when selling this building material. This also applies to the purchase significant number boards This can be seen quite clearly if we use a 150x20 mm board as an example. The number of boards in a cube is a value of 55.5 pcs. But, in a cube they count 55 pieces, which when performing the calculation will have a value of 0.99 cubic meters. In fact, it follows from this that the overpayment for 1 cubic meter of this popular building material can amount to 1% of the real price. For example, 5500 instead of 4995 rubles.

To calculate the cubic capacity for a continuous type of board, slightly different methods are used. When we are talking about buying 1 board, then measuring its thickness, as well as the total length, is carried out in the same way as when choosing edged building material. In this case, the average width is taken for calculations - between great value and small.

For example, when the width of the board at one end is 25 cm, and at the other 20, then the average value will be approximately 22 centimeters. When it is necessary to calculate the volume of a significant number of similar boards for construction, then you will need to lay them out so that the wide one does not differ from the narrow one, more than 10 cm. The main length of this material in the laid out stack should be approximately the same. After this, using a regular tape measure, an accurate measurement is made of the height of the entire existing stack of boards, and the width is measured (approximately in the very middle). The result obtained will then need to be multiplied by a special coefficient, amounting to a value from 0.07 to 0.09, directly dependent on the existing air gap.

How many boards are in 1 cube: special tables

To calculate the exact number of boards of a certain width and length in 1 cubic meter, various tables are used. Below are several such specialized tables, which indicate the cubic capacity of the common and in demand types of this material today. It is possible to calculate the volume of various boards of different sizes, for example, material for erecting a fence on your site, using the existing formula presented above.

Table of the amount of edged boards in 1 cubic meter

Board size	Volume of 1st board (m 3)	Number of boards in 1m 3 (pcs.)	Number of square meters in 1m2
Twenty
Board 20x100x6000	0.012 m 3	83 pcs.	50 m2
Board 20x120x6000	0.0144 m 3	69 pcs.	50 m2
Board 20x150x6000	0.018 m 3	55 pcs.	50 m2
Board 20x180x6000	0.0216 m 3	46 pcs.	50 m2
Board 20x200x6000	0.024 m 3	41 pcs.	50 m2
Board 20x250x6000	0.03 m 3	33 pcs.	50 m2
Twenty-five
Board 25x100x6000	0.015 m 3	67 pcs.	40 m2
Board 25x120x6000	0.018 m 3	55 pcs.	40 m2
Board 25x150x6000	0.0225 m 3	44 pcs.	40 m2
Board 25x180x6000	0.027 m 3	37 pcs.	40 m2
Board 25x200x6000	0.03 m 3	33 pcs.	40 m2
Board 25x250x6000	0.0375 m 3	26 pcs.	40 m2
Thirty
Board 30x100x6000	0.018 m 3	55 pcs.	33 m2
Board 30x120x6000	0.0216 m 3	46 pcs.	33 m2
Board 30x150x6000	0.027 m 3	37 pcs.	33 m2
Board 30x180x6000	0.0324 m 3	30 pcs.	33 m2
Board 30x200x6000	0.036 m 3	27 pcs.	33 m2
Board 30x250x6000	0.045 m 3	22 pcs.	33 m2
Thirty-two
Board 32x100x6000	0.0192 m 3	52 pcs.	31 m2
Board 32x120x6000	0.023 m 3	43 pcs.	31 m2
Board 32x150x6000	0.0288 m3	34 pcs.	31 m2
Board 32x180x6000	0.0346 m 3	28 pcs.	31 m2
Board 32x200x6000	0.0384 m 3	26 pcs.	31 m2
Board 32x250x6000	0.048 m 3	20 pcs.	31 m2
Sorokovka
Board 40x100x6000	0.024 m 3	41 pcs.	25 m2
Board 40x120x6000	0.0288 m3	34 pcs.	25 m2
Board 40x150x6000	0.036 m 3	27 pcs.	25 m2
Board 40x180x6000	0.0432 m 3	23 pcs.	25 m2
Board 40x200x6000	0.048 m 3	20 pcs.	25 m2
Board 40x250x6000	0.06 m 3	16 pcs.	25 m2
Fifty
Board 50x100x6000	0.03 m 3	33 pcs.	20 m2
Board 50x120x6000	0.036 m 3	27 pcs.	20 m2
Board 50x150x6000	0.045 m 3	22 pcs.	20 m2
Board 50x180x6000	0.054 m 3	18 pcs.	20 m2
Board 50x200x6000	0.06 m 3	16 pcs.	20 m2
Board 50x250x6000	0.075 m 3	13 pcs.	20 m2

Table of the amount of timber in 1 cubic meter

Beam size	Volume of 1st piece (m³)	Quantity of timber in 1m³ (pcs.)
100×100×6000	0.06 m 3	16 pcs.
100×150×6000	0.09 m 3	11 pcs.
150×150×6000	0.135 m 3	7 pcs.
100×180×6000	0.108 m 3	9 pcs.
150×180×6000	0.162 m 3	6 pcs.
180×180×6000	0.1944 m 3	5 pieces.
100×200×6000	0.12 m 3	8 pcs.
150×200×6000	0.18 m 3	5.5 pcs.
180×200×6000	0.216 m 3	4.5 pcs.
200×200×6000	0.24 m 3	4 things.
250×200×6000	0.3 m 3	3 pcs.