How to calculate the mass of a metal cylinder

Rolled metal calculator online, metal weight table

How to calculate the mass of a metal cylinder

The metal calculator for stainless steel products from the Regional House of Metal company will help you calculate the weight and cost of products based on given overall dimensions and specified steel grades.

The widget allows you to get the weight of products of almost any steel grade used today: black, non-ferrous, stainless steel. In particular, the non-ferrous rolled metal calculator will help in calculating products made from alloys of copper, bronze, aluminum and others. In the product catalog you can buy the following types of rolled metal: pipes, long products (angle, circle, channel, beam), strip, wire rod, hexagons and sheets.

Metal calculator

With relative accuracy, you can calculate the weight of rolled metal and the amount of steel reinforcement. By entering dimensions and lengths, you can calculate the weight of the products. The calculator works in online mode for quick weight calculation, for this you need:

  • select the required steel grade;
  • select rental category;
  • Enter the dimensions and dimensions of the sides.

Our resource specialists periodically update the steel grade for accurate and up-to-date calculations of products. In the calculation process, the specific gravity of rolled metal (calculator table) steel and size (metal thickness, sheet width, diameter of pipe wall, channel, etc.) are used.

Sometimes when the grade of steel from which it is made is unknown, in this case you can use universal grades such as St10 and St20. If you still have suspicions about the raw materials, you can perform a chemical test. metal analysis.

Rolled metal weight table

The calculation formula determines the weight of 1 mm of rolled steel multiplied by the length (if the weight is calculated based on the length value). In the case when the initial data is weight and a table of rolled metal from tons to meters is required, the cross-sectional area of ​​the rolled metal multiplied by the specific gravity is first determined, after which the weight is divided by the value obtained by multiplication and we obtain the required length by weight.

It should be noted that the weight table of rolled metal depends on the temperature of the calculated rolled product, so, at different steel temperatures, its density changes significantly. Based on this, the calculation uses a universal steel temperature of 20 °C. For non-ferrous metal products, other temperature values ​​may be used, please pay attention to this.

In real life, the sizes of rolled products produced, especially in large-volume batches, may differ significantly from the calculated values. This is due to the fact that the table of mass of rolled metal does not take into account deviations from the exact geometric parameters of the product, which necessarily exist, especially for large volumes.

Source: http://RDMetall.ru/kalkulyator-metalloprokata-online/

Calculation of the weight of metal of various sections based on its size: basic methods and their features

How to calculate the mass of a metal cylinder

Metal is the main material used in many industries. Various designs are made from it. In addition, it is used as a material for the manufacture of parts and assemblies of machines and units.

Metallurgical companies produce various types of rolled metal:

The most common is the pipe. When the need for this material arises, it is important for the consumer to determine the characteristics of the rolled metal offered by a specific selling company. To obtain this important information, they most often turn to special tables. Based on the data contained in them, you can find out the most important parameters:

If an enterprise or organization requires metal pipes, then by referring to the weight table, you can obtain all the important information about these products.

When rolled metal is used to construct structures, the most important thing is the correct selection of material. It must be of high quality , since the reliability and service life of the structures being built depends on this.

Often structural elements are created using profile pipes. Before purchasing material for their manufacture, you should find out the physical and technical characteristics of the material. Weight tables that contain all the necessary information can help with this.

By turning to them, you can find out what specific gravity an individual pipe will have, and then, based on the figures obtained, calculate the weight of the structure.

Based on the indicators contained in such tables, it is possible to determine the specific gravity of pipes, based on the dimensions of pipe products, as well as a number of other factors.

Why do you need to know the specific gravity of a profile pipe?

The importance of such information is great due to the fact that profile pipes have certain differences from standard plumbing products. Most often, pipes with a square or rectangular cross-section are offered on the market. The main advantage of such pipe products is their high quality and strength of the steel from which they are made.

In the construction of various structural elements, profile pipes are widely used. They have become widespread in various industries. When creating metal structures, the problem arises in determining the weight of the product. For this, the necessary calculations are carried out. After completion, the received data is entered when filling out the documentation.

Along with responsible companies, there are also unscrupulous sellers on the market who, when offering products, try to deceive customers. Every year the number of pipe products from the Middle Kingdom is increasing, which in terms of their quality characteristics do not always meet the requirements of domestic production.

In the case of Chinese pipes, there is one feature that many potential buyers simply do not know about. The thing is that the thickness of the pipes is determined at the edges of these products. This is where measurements are most often taken. But in the remaining sections of the pipe the thickness is very small. Therefore, such a defect can only be identified if the mass of the product is determined.

Calculation of the specific gravity of a profile pipe

To calculate the mass of a single profile metal pipe, you can use special calculators , which are available on many websites of specialized companies. Using this program, you can find out the weight of the pipe in a short time. Using this calculator is quite simple.

Algorithm of actions

All that is required from a potential buyer of pipe products is to enter in the fields of the program:

  • pipe length;
  • profile length;
  • wall thickness.

Then all that remains is to choose the grade of steel from which the product is made. When the "enter" button is pressed, the user can obtain a detailed calculation of the specific gravity of the metal. When using such programs, you should be aware that in most calculators, the weight of profile pipe products is calculated based on the base value of steel density at the level of 7850 kg / cubic meter. m.

Using such programs, in addition to mass, you can also calculate the footage of pipe products. In this case, it is possible to accurately determine the linear meter of pipe per fixed mass.

Formula for calculating the specific gravity of metal

In addition to using a calculator, there is another method for calculating the mass of a tubular product. To do this, you can use the geometric formula for calculating the weight of metal. First you need to find out the cross-sectional area, and then multiply by the length of the segment. The result obtained must be multiplied by the density of the metal from which the product is made. You should be aware that depending on the grade of steel, the density of the metal may vary.

How to determine the specific gravity of a metal?

The pipe mass is calculated using the following formula:

M.P. = S*2*(A+B)*ρ.

In this formula, S is the wall thickness in meters, the letters A and B indicate the profile length in meters. And the density of steel is denoted by the letter ρ.

Conclusion

Metal is the most common material used in various industries. Various types of rolled metal are used for the manufacture of structures. Most often profile pipes are used. The use of high quality products ensures reliability and long service life.

A wide range of profile pipe products are offered on the market by a large number of companies. Along with reliable sellers, there are also companies that, under the guise of quality products, offer low-grade pipe products. Most often, they sell Chinese-made pipes under the brand names of well-known manufacturers, which are not of high quality.

In order to purchase truly high-quality products, an organization or enterprise must, when purchasing pipes, calculate the weight of the products they plan to purchase.

This will allow you to avoid buying a low-quality product and pay money for a good profile pipe. Using an online calculator, you can quickly calculate the weight of pipe products. There is also a special formula with which you can find out your weight.

The resulting figure will help you conclude which pipe the seller is offering – a high-quality one or an imitation one.

Source: https://stanok.guru/stanki/metallorezhuschiy-stanok/kak-vypolnit-raschet-vesa-metalla-po-ego-razmeru.html

Carrying out calculations of the specific gravity and weight of reinforcement: material indicators 1 meter long using the GOST table - Machine

How to calculate the mass of a metal cylinder

The weight of reinforcement is a very important parameter both for the construction of reinforced concrete structures and for the construction of various buildings (for example, greenhouses). The mass of metal elements must be taken into account when planning the construction of the building itself. The calculation of the number of reinforcing bars in free and stressed zones, the distance between the rods, etc. depends on it.

Frame made of metal reinforcement

In addition, the cost of construction will depend on the weight of a linear meter of metal stubble. It is cheaper to purchase metal rods at wholesale stores, where the price is indicated per ton. Calculations in construction are made in linear meters. Therefore, it is important to be able to calculate how many meters of rod are in one ton.

Correspondence table for reinforcement weights for different diameters

The standard weight of reinforcement of a particular diameter is regulated by GOST 5781-82 standards. The standard calculation table looks like this:

Table of correspondence of reinforcement weight depending on the diameter of the rods

This table is absolutely easy to use. In the first column we select the diameter of the rod in mm that will be used, in the second column we immediately see the weight of one linear meter of a rod of this type.

The third column shows us the number of linear meters of reinforcement in one ton.
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Calculation of reinforcement weight

There are several ways to calculate the mass of reinforcing bars required for construction.

how and on what basis is fiberglass reinforcement produced?

The first and easiest way to find out how much a meter of reinforcement weighs is to use an electronic calculator for similar calculations.

To work with it, you only need to know the diameter of the rod with which we will work. All other calculation parameters are already included in the program.

The other two ways to find out how heavy a reinforcement meter is are somewhat more complicated. Let's look at them in order of increasing complexity.

Since in private construction reinforcement with a diameter of 12 mm and 14 mm is most often used, we will take these rods as the basis for the calculations.
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Calculation based on standard weight

To calculate the mass of the required number of rods using this method, we use the table above. We are interested in the parameter, how much one linear meter weighs. In the calculations we will use rods with a diameter of 14 mm.

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Let's calculate the amount of reinforcement needed for construction (provided that we have the table at hand).

To calculate the weight of the amount of reinforcement we need, we should:

  1. Draw up a building construction plan taking into account the creation of a reinforcement mesh.
  2. Decide on the diameter of the rods.
  3. Calculate the amount of reinforcement used in meters.
  4. Multiply the mass of one meter of reinforcement of the required diameter by the number of rods used.

Example: 2322 meters of reinforcing bars with a diameter of 14 mm will be used for construction. The weight of a linear meter of such rods is 1.21 kg. Multiplying 2322 * 1.21 we get 2809 kilograms 62 grams (grams can be neglected). For construction we will need 2 tons 809 kilograms of metal rods.

An example of calculating the weight of reinforcement in a special program

In the same simple way, you can calculate the number of rods of any diameter per ton, based on the data given in the table.
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 Calculation by specific gravity

This method of calculation requires certain knowledge, skills and labor. It is based on a formula for calculating mass, which uses quantities such as the volume of a figure and its specific gravity. It is worth resorting to this method of calculating a linear meter of reinforcement only if you have neither an electronic calculator nor a table with GOST standards at hand.

how to bend reinforcement - about the construction of special bending machines.

We will try this method by calculating how much 12-diameter reinforcement weighs. First of all, let’s remember the weight formula from the physics course.

Metal reinforcement bars

Weight is equal to the volume of the figure multiplied by its density. The density, or specific gravity, of steel is 7850 kg/m3.

As for the volume, we will also have to calculate it ourselves, based on the fact that the reinforcing bar is a cylinder. Let's return to the school geometry course.

The volume of a cylinder is equal to its cross-sectional area multiplied by the height of the cylinder. The cross section of a cylinder is a circle. The area of ​​a circle is calculated by the formula Pi (a constant value equal to 3.14) multiplied by the radius squared. The radius is equal to half the diameter.

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  • We must know the diameter of the reinforcement based on the construction plan and calculations, or measure it ourselves.
  • Note: measuring the diameter yourself will lead to errors in calculations, since the reinforcement does not have a smooth outer surface.

Fragments of reinforcement bars of various diameters

In our case, the diameter is 12 mm or 0.012 m. Therefore, the radius is 6 mm or 0.006 m.

  1. We calculate the area of ​​the circle: 3.14*0.0062 =0.00011304 m2.
  2. We calculate the volume of one meter of reinforcement: 0.00011304*1=0.00011304 m3
  3. We calculate the weight of one linear meter: 0.00011304 m3*7850 kg/m3=0.887 kg.

Checking the table, we see that the data obtained coincides with the state data.

If you need to calculate the mass of not one meter, but a specific reinforcing bar, the area of ​​the circle will need to be multiplied by the length of the rod. Otherwise, the calculation algorithm will not change.

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Source: https://regionvtormet.ru/metally/provedenie-raschetov-udelnoj-massy-i-vesa-armatury-pokazateli-materiala-dlinoj-1-metr-s-pomoshhyu-tablitsy-gost.html

How to calculate the weight of metal - formulas and recommendations

If there is no possibility of direct weighing, the weight of scrap metal can be determined in other ways. The most accurate result will be given by calculation, but other possibilities should not be neglected.

So, in order not to burden readers with unnecessary formulas, which will still be there, but below, we will immediately designate the formulas for calculating the most popular products from rolled steel and pipes - rolled pipes.

Here you will not find an online calculator for calculating weight, only formulas that you remember once you no longer have to use special calculators.

For example, when dismantling metal structures or a chimney, you don’t always have a computer, the Internet or a reference book at hand, but the structures are all welded from rolled steel here and our formulas will help out!

Formula to calculate pipe weight

M=(Ds)*s*0.02466

, Where

  • M—weight of one linear meter of pipe, kg;
  • D is the outer diameter of the pipe being calculated, mm;
  • s—pipe wall thickness, mm;
  • 0.02466 is the coefficient for a steel density of 7.850 g/cm3.

This formula is very accurate. You can calculate the weight of the pipe and compare the calculated weight with the theoretical one in any range and the value according to the formula will be more accurate! You can also calculate

Calculating the weight of a sheet of metal

M=S*7.85

, Where

  • M—mass of steel sheet, kg;
  • S is the area of ​​the calculated sheet, in square meters;
  • 7.85 - weight of a sheet 1 mm thick and 1 square meter in area, in kilograms

This way you can calculate the weight of a sheet of metal of any size, for which you can calculate the area. The accuracy of calculations using this formula is higher than the theoretical mass in reference books, because in the assortment, when calculating the mass of metal, the program rounds the values. Well, how to find out the area of ​​a sheet (of any shape - square, rectangle, parallelepiped, trapezoid, rhombus, etc.) - every person who has graduated from high school should know.

How to calculate the weight of reinforcement and rod

For a circle, rod, smooth reinforcement, the formula for calculating the mass will be as follows:

M=(0.02466*D2)/4

, Where

  • M—weight of 1 linear meter of circle/reinforcement/rod, kg;
  • D—circle diameter;
  • 0.02466 - coefficient for steel density equal to 7.850 g/cm3

To calculate the weight of corrugated reinforcement (A2, A3), you can and should use the same formula! There will be no discrepancies with the theoretical mass, despite the different cross-sectional designs.

It is, of course, impossible to calculate such a pile of scrap metal using formulas without weighing

General approaches or a little boring theory

To determine the weight of any object, simply multiply its volume by its specific gravity. If everything is more or less clear with specific gravity, then volume is more difficult to determine (if you do not consider such simple shapes as a cube). The most general principle for calculating volume is Gulden's principle, when the cross-sectional area of ​​an object is multiplied by its height.

There are also usually no problems with the height of the metal structure; it is easy (or almost easy) to measure directly, especially if the height section is constant. This can be done for steel pipes of any section and profile, I-beams, channels, angles, etc.

We will consider the method for determining the mass of metal objects of complex and variable shapes later.

Volume of the pyramid

The pyramidal ends of the tops of forged steel fences, deflectors and other parts of metal structures are often found. The volume of the pyramid can be easily calculated using the formula:

, Where:

  •  B is the area of ​​the base of the pyramid;
  • H – height of the pyramid.

Since in technology the bases of a pyramid can be a square, a rectangle or a triangle, the problem can be solved quite simply.

Volume of a truncated pyramid

The enclosing caps, protective latches and doors have the shape of a truncated pyramid. In such situations, a dependency is used:

, Where:

  • h – height of the truncated pyramid;
  • F is the area of ​​its larger base;
  • f is the area of ​​the smaller base.

If the pyramidal part of the structure sold for scrap is somewhat deformed, then the missing volume is added or removed from each side.

Volume of wedge and obelisk

The wedge in the technique is often a pentahedron, the base of which is a rectangle, and the side faces are isosceles triangles or trapezoids. The formula for calculating the volume of a wedge is:

, Where:

  • a – side of the base of the wedge foot;
  • а1 – width of the wedge top;
  • b – wedge thickness;
  • h is the height of the wedge.

An obelisk is a hexagon, the base of which is rectangles located in parallel planes. The opposite faces are symmetrically inclined to the base of the obelisk. Volume of this geometric body:

, Where:

  • a and b – dimensions of the length and width of the larger base of the obelisk;
  • and a1 and b1 – the smaller base of the obelisk;
  • h – height of the obelisk.

Volume of rod and pipe

To calculate all geometric sections based on a circle, you cannot do without the parameter π – 3.14 (higher accuracy is not required for scrap metal). Then for the cylinder we have:

, Where:

  • R – rod radius;
  • H – rod length/height.

For a pipe (hollow cylinder), the volume is calculated by the formula:

, Where

r is the inner radius of the pipe.

Volume of a cone and truncated cone

The geometric shapes of cone and truncated cone are widely used in the design of parts of mechanisms and machines. The volume of the cone is:

, Where

  • R – radius of the cone base;
  • H is the height of the cone.

To calculate the volume of a truncated cone, a more complex relationship is used:

, Where

R is the radius of the smaller base of the cone.

Volume of spherical elements of metal structures

In addition to the sphere itself, in practice we also have to calculate the volume of the spherical segment and sector. The following dependencies are used:

Volumes of rolled profiles

Most often it is necessary to determine the weight of tees, I-beams, channels, and angles. The following dependencies are used for this:

For the brand

,where b and b1 are the width of the shelf and wall of the tee, respectively; h and h1 – thickness of the base and flange of the tee; H – height of the T-bar fragment;

For I-beam

,where H is the height/length of the I-beam; a – I-beam wall thickness; с and с1 – thickness of the I-beam flange at the base and at the end, respectively;

For the corner

,where H is the length of the corner; l1 – angle thickness; h1 and h2, respectively, are the width of each shelf.

How to establish the mass of a structure of particularly complex shape

This problem can be solved in two ways. According to the first of them, the value of the so-called fill factor is established (the method is used for dimensional units, the disassembly of which is either difficult or completely impossible). For example, for sliders of crank machines, the fill factor is taken to be 0.30.35. Then the mass of node G is calculated under the assumption that it is solid, and then the result is multiplied by the fill factor.

Nistratov’s empirical formula gives approximately the same accuracy:

, where P is the nominal press force in tons.

In an original way, you can install a lot of small one-piece structures according to the volume of water they displace. To do this, water is poured into a tared container to the brim. Place the container in another with a much larger volume, and then place this structure in the first container. The volume of water displaced by it is weighed. This volume will be equal to the volume of the structure.

Source: http://xlom.ru/spravochnik/kak-rasschitat-ves-metalla-formuly-i-rekomendacii/

How to correctly and quickly calculate the weight of rolled metal - with and without tables

The issue of calculating the weight of rolled metal is relevant not only for specialists, but also for private developers and home craftsmen. If you have a reference book at hand and, especially, an online metal calculator, it is not difficult to make the appropriate calculations. What if you only have a tape measure and a calculator on your phone? It is difficult to obtain accurate results with such an arsenal, but it is quite possible to approximately determine the weight of some metal products.

We calculate the weight of rolled sheets

The simplest option is rolled steel sheets.

Definition! In all our calculations, the base value is the average density of steel - 7,850 kg/m3 according to the SI system.

First, let’s carry out a simple step - find out the mass of a square meter of steel sheet 1 mm thick. It looks like this - 1 m x 1 m x 0.001 m x 7850 kg/m3. That is, we multiplied the length, width and thickness of the sheet (all values ​​were taken in meters), and we got the volume of the product. The product of volume and density gives mass - 7.85 kg. Thus, we found out that a square meter of steel sheet 1 mm thick weighs 7.85 kg.

And then all calculations are made by multiplying the value of 7.85 kg by the area and thickness of the real sheet. For example, you need to buy a sheet with a thickness of 4 mm and an area of ​​2 m2. The mass of such a product is determined by the formula 7.85x4x2 = 62.8 kg. A sheet of the same size, but 2 mm thick, weighs 7.85 x 2 x 2 = 31.4 kg.

If you are satisfied with the approximate calculation, round the value of 7.85 kg to 8 kg. Then calculations can be carried out even in your head without a calculator, and the error will be less than 2%.

We present the weights of steel sheets of the most popular sizes.

Sheet thickness, mm Sheet dimensions, m Sheet weight, kg Weight 1 m2, kg
0,35 1.0x2.0 5,5 2,75
0,35 1.25x2.5 8,59
0,5 1.0x2.0 7,85 3,93
0,5 1.25x2.5 12,27
0,8 1.0x2.0 12,56 6,28
0,8 1.25x2.5 19,63
1,0 1.0x2.0 15,7 7,85
1,0 1.25x2.5 24,53
1,5 1.0x2.0 23,55 11,78
1,5 1.25x2.5 36,8
2,0 1.0x2.0 31,4 15,7
2,0 1.25x2.5 49,06
2,5 1.0x2.0 39,25 19,63
2,5 1.25x2.5 61,33
3,0 1.0x2.0 47,1 23,55
3,0 1.25x2.5 73,59
3,5 1.25x2.5 85,86 27,48
4,0 1.5x6.0 282,6 31,4
5,0 1.5x6.0 353,25 39,25

What is a conversion factor

Let's complicate the task. Suppose you need to buy a sheet of non-ferrous metal. Let's use a conversion factor, which is the ratio of the density of a particular metal or alloy to the average density of steel. By multiplying the weight of a steel product of a certain range and size by the coefficient of the desired metal or alloy, we obtain the weight of the part.

Name of metal or alloy Coefficient
Aluminum 0,34
Copper 1,14
Brass LS59 1,08
Bronze OTS 5-5-5 1,12
Gray cast iron 0,9

Example - let's calculate the mass of a bronze sheet with a thickness of 2 mm and an area of ​​2 m2.

7.85x2x2x1.12 = 35.2 kg

Attention! The same simple algorithm can be applied to non-metallic sheet materials, for which there are also conversion factors. For example, for rubber - 0.17-0.23, organic glass - 0.15, caprolon - 0.15, textolite - 0.18, rubber - 0.17-0.23.

How to find out the mass of a pipe

To determine the mass of pipes, it is optimal to use tables.

Nominal diameter, inch/mm Wall thickness, mm Weight, kg Nominal diameter, inch/mm Wall thickness, mm Weight, kg
1/4 (8) 2,35 0,65 11/4 (32) 3,25 3,14
1/2 (15) 2,65 1,22 11/2 (40) 3,25 3,61
3/4 (20) 2,65 1,58 2 (50) 3,65 5,1
1 (25) 3,25 2,44 21/2 (65) 3,65 6,51

If you don’t have access to reference materials, and simple geometric formulas are not an obstacle for you, calculate the weight yourself. To do this, we find the difference between the area of ​​the circle along the outer radius and the area along the inner radius. We multiply the resulting difference by the length of the pipe and the density of the steel - 7,850 kg/m3.

For pipes made of non-ferrous metals, the conversion factors that we discussed above are used.

How to find out the mass of a cylinder using tables for a round bar

If you have access to tables for calculating the mass of round timber, then it is very easy to determine the mass of a cylinder with any wall thickness. To do this, find the weight of 1 m of rod along the outer diameter of the cylinder and subtract from it the weight of 1 m of rod along the inner diameter. Multiply the result by the height of the cylinder (in meters). The mass of the cylinder is found.

How to calculate the mass of an equal angle angle, channel, I-beam

The weight of a linear meter of corner metal depends on the width and thickness of the shelves.

Attention! The weight of a corner calculated using a geometric formula or determined from a table may differ greatly from the actual one. This is due to the fact that some manufacturers, in order to reduce the cost of products, reduce the thickness of the corner flange in places where verification measurements are not provided. Such a difference can significantly exceed the tolerances provided for by GOST.

Weight per linear meter of the most common range of equal-flange angles

Shelf width, mm Shelf thickness, mm Weight of 1 m corner, kg Shelf width, mm Shelf thickness, mm Weight of 1 m corner, kg
20 3 0,89 40 3 1,85
20 4 1,15 40 4 2,42
25 3 1,12 45 3 2,08
25 4 1,46 45 4 2,73
32 3 1,46 50 3 2,32
32 4 1,91 50 4 3,05
36 3 1,65 63 4 3,9
36 4 2,16 63 5 4,81

It is difficult to independently calculate the mass of a channel and an I-beam due to the complex shape of the section. In this case, tables are used.

Channel weight table

Profile number Weight 1 m, kg Profile number Weight 1 m, kg Profile number Weight 1 m, kg
5 4,84 12 10,4 20 18,4
6,5 5,9 14 12,3 22 21,0
8 7,05 16 14,2 24 24 ,0
10 8,59 18 16,3 27 27,7

I-beam weight table

Profile number Weight 1 m, kg Profile number Weight 1 m, kg Profile number Weight 1 m, kg
10 9,46 18 18,4 27 31,5
12 11,5 20 21,0 30 36,5
14 13,7 22 24,0 33 42,2
16 15,9 24 27,3 36 48,6

Metal weight calculators

If you have access to the Internet, calculating the mass of rolled metal is not difficult. The metal calculator can be used online or downloaded to your computer.

How the calculation is performed:

  • Select the type of rolled metal from the list.
  • Fill in the data in the dimensions specified in the program.
  • Press the calculation button.
  • Calculators also usually indicate the weight of a linear meter of a specific assortment and the number of meters per ton.
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Attention! All data provided by metal calculators is based on GOST. In the absence of tabular values, the mass is calculated using geometric formulas, adjusted for the manufacturing features of these products. In standard calculations, the density of steel is assumed to be 7,850 kg/m3.

The actual mass of rolled metal almost always differs from the theoretical one.

How to use reference books

A convenient reference material is the collection of authors P.M. Polivanov. and Polivanova E.P. “Tables for calculating the mass of parts and materials.” The directory contains tables that allow you to easily and quickly determine the weight of rolled products of round, rectangular, hexagonal sections, sheets and strips, equal and unequal angle steel, I-beams, channels, round and profile pipes.

The collection contains formulas that can be used to calculate the areas and volumes of geometric figures. A detailed table of conversion factors allows you to accurately calculate the mass of a non-ferrous metal or its alloy.

Approximate calculation methods can only be used to preliminary determine the mass of materials, products and structures. To draw up design documentation, only accurate data that fully complies with GOST is used.

Source: https://www.navigator-beton.ru/articles/kak-podschitat-ves-metalloprokata.html

Steel sheet weight – Calculator and tables

Sheet metal is a rolled piece of a specific material, most often steel, that is widely used in industrial production, construction, automotive and other industries.

Sheet steel is the most popular type of sheet blanks, which is produced using cold or hot rolling technology. In the first case, the steel will be called cold-rolled (maximum sheet thickness up to 5 mm), and in the second - hot-rolled.

The KALK.PRO sheet metal weight calculator allows you to calculate the weight of sheet steel based on known thickness and area. You can also familiarize yourself with the metal grade and regulatory documents in the corresponding tabs of the tool. The calculator operates on the basis of GOST 19903-74 “Hot-rolled sheet metal”.

Using the calculator, you can find the weight of rolled sheets of any size and thickness, for example sheets of 1, 3, 6, 8, 10 mm, etc., the standard material is carbon steel St3st with a density of 7850 kg/m3.

By default, the weight of 1m2 of sheet steel is considered.

In order to calculate the weight of sheet metal using our calculator, you must follow the instructions:

  1. Select the metal type (default is Steel ).
  2. Confirm the type of assortment - Sheet / Plate .
  3. Select the metal grade (default Steel St3st ).
  4. Specify the sheet parameters - thickness t (mm), width a (mm), length b (mm) .
  5. Enter the quantity of rolled metal, pcs .

Formula for calculating the weight of sheet metal

The weight of sheet metal can also be calculated independently using simple mathematical formulas and tables according to GOST.

  • a – width;
  • b – length;
  • t – thickness;
  • ρ – density.

Weight table for 1 m2 of sheet metal according to GOST 19903-74

Sheet size (TxWxD), mm Sheet thickness, mm Weight of 1 square meter, kg Sheet weight, kg
0.5x1250x2500 0,5 3,93 12,27
0.7x1250x2500 0,7 5,5 17,17
0.8x1250x2500 0,8 6,28 19,63
1x1250x2500 1,0 7,85 24,53
1.2x1250x2500 1,2 9,42 29,44
1.5x1250x2500 1,5 11,78 36,80
2x1250x2500 2 15,70 49,06
2.5x1250x2500 2,5 19,63 61,33
3x1250x2500 3 23,55 73,59
3.5x1250x2500 3,5 27,48 85,86
4x1500x6000 4 31,40 282,60
5x1500x6000 5 39,25 353,25
6x1500x6000 6 47,10 423,90
7x1500x6000 7 54,95 494,55
8x1500x6000 8 62,80 565,20
1500x6000 9 70,65 635,85
10x1500x6000 10 78,50 706,50
12x1500x6000 12 94,20 847,80
14x1500x6000 14 109,90 989,10
16x1500x6000 16 125,60 1130,40
18x1500x6000 18 141,30 1271,70
20x1500x6000 20 157,00 1413,00
22x1500x6000 22 172,70 1554,30
Sheet size (TxWxD), mm Sheet thickness, mm Weight of 1 square meter, kg Sheet weight, kg
25x1500x6000 25 196,25 1766,25
28x1500x6000 28 219,80 1978,20
30x1500x6000 30 235,50 2119,50
32x1500x6000 32 251,20 2260,80
35x1500x6000 35 274,75 2472,75
36x1500x6000 36 282,60 2543,40
40x1500x6000 40 314,00 2826,00
45x1500x6000 45 353,25 3179,25
50x1500x6000 50 392,50 3532,50
55x1500x6000 55 431,75 3885,75
60x1500x6000 60 471,00 4239,00
65x1500x6000 65 510,25 4592,25
70x1500x6000 70 549,50 4945,50
80x1500x6000 80 628,00 5652,00
90x1500x6000 90 706,50 6358,50
100x1500x6000 100 785,00 7065,00
110x1500x6000 110 863,50 7771,50
120x1500x6000 120 942,00 8478,00
130x1500x6000 130 1020,50 9184,50
140x1500x6000 140 1099,00 9891,00
150x1500x6000 150 1177,50 10597,50
160x1500x6000 160 1256,00 11304,00

All information on the site is provided for informational purposes only. The user is solely responsible for all possible consequences arising from the use of the information received. Under no circumstances or conditions can responsibility for the consequences that directly or indirectly result from the use of information or software posted on this site be assigned to the site owners and be the basis for legal proceedings or other prosecution. We accept payment: 2014 - 2020 Kalk.Pro: Online construction calculators - 3D calculations of stairs, roofs, foundations.

Source: https://kalk.pro/metal-rolling/hot-and-cold-rolled-sheet/

How to calculate the mass of metal - Metalist's Handbook

Galvanized steel sheet can be used in different ways in agriculture, industry, construction and many other areas of human activity.

And in order not to encounter scammers who will try to sell you a low-quality metal product, you need to know all the parameters that determine real galvanized sheet steel.

For example, transport marking of packages must be applied according to GOST No. 14192-77 with dark-colored dyes on the end of the surface of the pack and on the side of the surface of the roll. The marking must contain primary and secondary inscriptions that carry information.

Sheet according to GOST No. 14918-80

The standard conditions apply to steel in the form of sheets and coils that are hot-dip galvanized in permanent galvanizing units.

The technical degree coefficients, which are established by standard norms, must be in accordance with the requirements of the first two quality categories.

Galvanized sheet steel is divided into:

1. By purpose:

  • for types for cold stamping - X W,
  • for cold profiling - X P,
  • for painting - P K,
  • general use - OH;

2. According to the ability to draw (steel category X W):

  • conventional hood - H,
  • deep drawing - G,
  • very deep drawing - V G;

3. According to the uniform thickness of the special zinc coating:

  • with normal thickness variation - HP,
  • with reduced thickness variation - U P;

4. By mutual agreement of the customer and the manufacturer, steel can be manufactured:

  • with zinc stains on the surface - KP,
  • without zinc stain on the surface - MT;

5. Depending on the thickness of the special coating, galvanized steel is divided into three classes:

  • elevated,
  • first,
  • second.

Galvanized steel is produced in widths from 710mm to 1800mm, thickness from 0.5mm to 2.5mm from cold rolled steel.

How to calculate the weight of galvanized steel sheets?

M=M1+M2, where M is the final weight of the sheet (kg), M1 is the weight of iron (kg), M2 is the weight of zinc (kg).

In this case, M1=T1 x l1 x H1 x P1,

where T1 is the thickness of the iron sheet (mm). When calculating, it is important to take into account that the thickness of the iron is 0.05 mm lower than the finished product for class 1 zinc special coating and 0.03 mm less for class 2; l1 - length of sheet iron (m); H1 - width of iron sheet (m); P1 is an indicator of iron density (7.85 t/m3).

M2=T2 x l2 x H2 x P2,

where, T2 is the thickness of the galvanized layer (depending on the category, where the thickness of the 1st category is 0.0381 mm, and the second is 0.0216 mm); l2 - length of special coating (m); H2 - width of special coating (m); P2 is an indicator of zinc density (7.13 t/m3).

Thanks to the formula, it is possible to make calculations before purchasing. This will allow you not to be deceived and to accurately calculate the required amount of material.

There are also tables that already have calculations and ready-made results. Therefore, in some cases, avoiding calculations, you can refer to the following tables:

Table for calculating the mass of galvanized sheet steel

Thickness of galvanized steel Number of m2 of galvanized steel in 1 ton Weight 1m2 galvanized steel
0.4mm 299.40m2 3.34kg
0.45mm 267.92m2 3.73kg
0.5mm 242.42m2 4.13kg
0.55mm 221.36m2 4.52kg
0.6mm 203.67m2 4.91kg
0.65mm 188.60m2 5.31kg
0.7mm 175.59m2 5.70kg
0.75mm 164.2m2 6.09kg
0.8mm 154.32m2 6.48kg
0.9mm 137.65m2 7.27kg
1mm 124.22m2 8.05kg
1.1mm 114.09 m2 8.83kg
1.2mm 103.95m2 9.62kg
1.5mm 83.51m2 11.97kg
2mm 62.89m2 15.9kg
2.5mm 50.45m2 19.82kg

Table for calculating the mass of galvanized steel with polymer coating

Thickness of galvanized steel with special coating Number of m2 of galvanized steel with special coating in 1 t Weight 1m2 of galvanized steel with special coating
0.4mm 318.47m2 3.14kg
0.45mm 283.29m2 3.53kg
0.5mm 253.81m2 3.94kg
0.55mm 232.02m2 4.31kg
0.6mm 213.22m2 4.69kg
0.65mm 196.67m2 5.08kg
0.7mm 182.15m2 5.49kg
0.75mm 170.07m2 5.88kg
0.8mm 158.98m2 6.29kg
0.9mm 141.04m2 7.09kg
1mm 125.94m2 7.94kg

Online form for calculating the weight of galvanized steel

Source: https://ssk2121.com/kak-poschitat-massu-metalla/

Calculate the weight of the part based on dimensions

· 09.09.2019

The issue of calculating the weight of rolled metal is relevant not only for specialists, but also for private developers and home craftsmen. If you have a reference book at hand and, especially, an online metal calculator, it is not difficult to make the appropriate calculations. What if you only have a tape measure and a calculator on your phone? It is difficult to obtain accurate results with such an arsenal, but it is quite possible to approximately determine the weight of some metal products.

Calculation of the mass of a cylinder - homogeneous and hollow

The cylinder is one of the simple three-dimensional figures that is studied in the school geometry course (section of stereometry). In this case, problems often arise in calculating the volume and mass of a cylinder, as well as in determining its surface area. Answers to the noted questions are given in this article.

What is a cylinder?

Before moving on to the answer to the question of what the mass of a cylinder and its volume are, it is worth considering what this spatial figure represents. It should immediately be noted that a cylinder is a three-dimensional object. That is, in space you can measure three of its parameters along each of the axes in the Cartesian rectangular coordinate system. In fact, to unambiguously determine the dimensions of a cylinder, it is enough to know only two of its parameters.

A cylinder is a three-dimensional figure formed by two circles and a cylindrical surface. To visualize this object more clearly, just take a rectangle and start rotating it around one of its sides, which will be the axis of rotation. In this case, the rotating rectangle will describe a figure of rotation - a cylinder.

The two circular surfaces are called the bases of the cylinder and are characterized by a certain radius. The distance between the bases is called height. The two bases are connected to each other by a cylindrical surface. The line passing through the centers of both circles is called the axis of the cylinder.

As can be seen from the above, a cylinder is determined by two parameters: the height h and the radius of its base r. Knowing these parameters, it is possible to calculate all other characteristics of the body in question. Below are the main ones:

  • Base area. This value is calculated by the formula: S1 = 2*pi*r2, where pi is the number pi equal to 3.14. The number 2 in the formula appears because the cylinder has two identical bases.
  • The area of ​​a cylindrical surface. It can be calculated as follows: S2 = 2*pi*r*h. It is simple to understand this formula: if a cylindrical surface is cut vertically from one base to another and unfolded, you will get a rectangle, the height of which will be equal to the height of the cylinder, and the width will correspond to the circumference of the base of the volumetric figure. Since the area of ​​the resulting rectangle is the product of its sides, which are equal to h and 2*pi*r, the formula presented above is obtained.
  • Surface area of ​​a cylinder. It is equal to the sum of the areas S1 and S2, we get: S3 = S1 + S2 = 2*pi*r2 + 2*pi*r*h = 2*pi*r*(r+h).
  • Volume. This value is easy to find; you just need to multiply the area of ​​one base by the height of the figure: V = (S1/2)*h = pi*r2*h.

Determination of cylinder mass

Finally, it’s worth going directly to the topic of the article. How to determine the mass of a cylinder? To do this, you need to know its volume, the formula for calculating which was presented above. And the density of the substance of which it consists. Mass is determined by a simple formula: m = ρ*V, where ρ is the density of the material forming the object in question.

The concept of density characterizes the mass of a substance that is located in a unit volume of space. For example. It is known that iron has a higher density than wood. This means that in the case of equal volumes of iron and wood, the former will have a much greater mass than the latter (approximately 16 times).

Calculation of the mass of a copper cylinder

Let's consider a simple problem. You need to find the mass of a cylinder made of copper. To be specific, let the cylinder have a diameter of 20 cm and a height of 10 cm.

Before you begin solving the problem, you should understand the initial data. The radius of the cylinder is equal to half its diameter, which means r = 20/2 = 10 cm, and the height is h = 10 cm. Since the cylinder considered in the problem is made of copper, then, referring to the reference data, we write down the density value of this material: ρ = 8 .96 g/cm3 (for temperature 20 °C).

Now you can start solving the problem. First, let's calculate the volume: V = pi*r2*h = 3.14*(10)2*10 = 3140 cm3. Then the mass of the cylinder will be equal to: m = ρ*V = 8.96 * 3140 = 28134 grams or approximately 28 kilograms.

Attention should be paid to the dimension of units when using them in the corresponding formulas. Thus, in the problem all parameters were presented in centimeters and grams.

Homogeneous and hollow cylinders

From the result obtained above, it can be seen that a copper cylinder with relatively small dimensions (10 cm) has a large mass (28 kg). This is due not only to the fact that it is made of heavy material, but also to the fact that it is homogeneous. This fact is important to understand, since the above formula for calculating mass can only be used if the cylinder is completely (outside and inside) composed of the same material, that is, it is homogeneous.

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In practice, hollow cylinders are often used (for example, cylindrical water barrels). That is, they are made of thin sheets of some material, but are empty inside. For a hollow cylinder, the specified formula for calculating mass cannot be used.

Calculation of the mass of a hollow cylinder

It is interesting to calculate how much mass a copper cylinder will have if it is empty inside. For example, let it be made of a thin copper sheet with a thickness of only d = 2 mm.

To solve this problem, you need to find the volume of the copper itself from which the object is made. Not the volume of the cylinder.

Since the thickness of the sheet is small compared to the dimensions of the cylinder (d = 2 mm and r = 10 cm), then the volume of copper from which the object is made can be found by multiplying the entire surface area of ​​the cylinder by the thickness of the copper sheet, we obtain: V = d *S3 = d*2*pi*r*(r+h). Substituting the data from the previous problem, we get: V = 0.2*2*3.14*10*(10+10) = 251.2 cm3.

The mass of a hollow cylinder can be obtained by multiplying the resulting volume of copper required for its manufacture by the density of copper: m = 251.2 * 8.96 = 2251 g or 2.3 kg. That is, the considered hollow cylinder weighs 12 (28.1/2.3) times less than a homogeneous one.

Source: https://FB.ru/article/416635/raschet-massyi-tsilindra---odnorodnogo-i-pologo

You will learn how to calculate various pipe parameters

Author Oksana Knopa Date Jan 31, 2016

In such a situation, use the following indicators:

When applying the above indicators, the exact number of tubes and their technical characteristics are determined.

Carrying out a preliminary calculation of pipeline products eliminates the costs associated with the purchase and movement of these building materials.

As a result, the various media contained in the stainless steel (water, gas, air) move at a pre-calculated speed, resulting in increased efficiency of the system.

Below is a table of steel pipes that shows their main characteristics. Knowing the specific dimensions of steel pipes, you can choose the optimal design that is needed for the construction of the pipeline.

Characteristics of different types of pipes, with the help of which it will be easy to choose the appropriate design

Calculations of various pipe parameters

In order to make the correct calculation of the required stainless steel indicators, you must use the following parameters:

  • type of material - what the pipeline product is made of;
  • type of stainless steel section;
  • pipe wall thickness indicators;
  • stainless steel length, etc.

Using the above information, you can calculate the volume of the pipe, and then calculate the mass of the pipe, or vice versa.

Some information can be obtained by measuring the stainless steel structure itself.

Also, certain information (dimensions of metal pipes, etc.) can be found in various certificates, reference tables and GOSTs.

How to find out diameters and volumes

If you need to determine the diameter of a steel pipe, you need to calculate its circumference.

In this case, you can use the tape that seamstresses use.

You can also wrap the stainless steel with any tape, and then use a ruler to measure the diameter of the pipe.

Then you need to use the formula to calculate the circumference:

L=πD, where:

D—circle diameter;

π - 3.14.

It's worth a little effort to find the diameter of a circle:

D=L/π.

The inner diameter is the difference between the outer diameter and the thickness of the pipe

After calculating the thickness of the pipe walls, it is necessary to find the internal diameter of the stainless steel. In this case, it is necessary to subtract twice the thickness of the pipe walls from the outer diameter of the stainless steel.

How to calculate the volume of water in a tube

A similar question may arise, for example, when designing a future heating system.

The volume of water in the pipe is equal to the product of the volume of water per 1 m of pipeline product and the length of the stainless steel.

Section calculation

In order to determine the cross-section of a steel pipe, it is necessary to calculate the area of ​​the circle. When making such a calculation, it is necessary to take into account the difference that arises between the diameter (cross member) of the pipeline product and the thickness of its walls.

The inner diameter of the tube can be found by subtracting the thickness of the stainless steel from the size of the outer cross member.

The area of ​​a circle can be found using the following formula:

Source: https://trubexpert.ru/purpose/vy-uznaete-kak-provesti-raschyot-razlichnyx-parametrov-trub/

Metal weight calculation

The metal is widely used in various industries. When creating metal structures, it is necessary to first calculate two important indicators: strength and total weight.

The strength of the structure can be calculated using the methods of the theory of strength of materials. Weight is calculated taking into account the following characteristics:

  • standard sample density (determined by physical characteristics);
  • metal shape (according to the existing assortment - rolled sheets, channel, angle, pipe, etc.);
  • geometric shape, part dimensions.

Metal weight calculation

The presence of various forms of metal products requires an individual approach when calculating the following parameters:

  • the mass of the entire metal structure;
  • required volume of metal.

What is a conversion factor?

It allows you to calculate the weight of products made of any material. It is obtained as the ratio of the density of the selected material to the density of steel. Next, to calculate the required parameter, it is enough to calculate such a parameter of a steel product of a given shape. The resulting result will be multiplied by the conversion factor for this material.

The coefficient is a dimensionless quantity. It has its own specific meanings for various metals and alloys. For example, aluminum has 0.34, copper - 1.14, and 1.12 is used for OTS5-5-5 bronze.

To calculate the weight of a sheet made of the specified bronze, it is necessary to obtain the parameter of the same sheet of steel, multiplying with a conversion factor.

Metal conversion factor

The same calculation method, the use of a conversion factor, can be fairly applied to non-metallic rectangular products. For example, to textolite with a coefficient of 0.18, organic glass - 0.15. The results obtained will satisfy the accuracy requirements.

What makes calculating the weight of metal more difficult?

A serious difference in the data obtained for calculating the mass of a steel product is the technology of its production. The difference between cold-rolled metal and hot-rolled metal can be quite significant. We are talking about the accuracy of geometric characteristics while maintaining density along the entire length of the product.

The use of continuous heating and subsequent cooling leads to such negative phenomena as oxidation and recrystallization. The unevenness of these processes causes a change in such a parameter as thickness.

Metal weight

The accuracy of calculations for cold-rolled and hot-rolled metal profiles will differ. The error caused by thickness instability requires obtaining some average value.

How to calculate the mass of a rectangular profile?

A rectangular profile is a parallelepiped with a given wall thickness. The wall thickness is specified in the technical documentation for a specific sample.

Square profile

Mass calculation can be done in two ways. In the first method, the cross-sectional area is calculated: for a sheet of a given thickness. Calculate the mass of a rectangular parallelepiped based on its external dimensions. Then the same calculations are made for a parallelepiped with internal dimensions. The difference between the two values ​​will be the desired characteristic.

In the second method, the weight of one wall of the structure is calculated. If the cross-section is square, multiply by four. If it is rectangular, the sizes of the smaller and larger walls will be calculated separately. Then multiply each value by two and add the results to get the final figure.

Square profile weight

To simplify the process, special tables have been developed.

Determining the weight of a round profile

Round metal products include solid rods, fittings, and pipes of various diameters. The approach to solving the problem remains the same. If the product is solid, it is necessary to calculate the volume, multiply by the density of the material. The volume of metal is calculated using known geometric formulas.

Round profile weight

If the round workpiece is hollow inside, you need to know the wall thickness. Next, you can use one of the methods applicable to calculate the value of rectangular rolled products. The only difference will be the calculated ratios for finding the volume.

How to find out the mass of a hexagonal profile?

Solid metal rods with a hexagonal cross-section are often used. The calculation method for such products remains the same. It is necessary to remember from the school geometry course how the volume of a regular hexagonal parallelepiped is calculated.

The task is greatly simplified if you know the size or number of such a rental. All numbers are given in a standardized table.

The hexagonal profile with the smallest number 10 weighs only 0.68 kg, the largest number 60 weighs 24.5 kg.

Hexagonal profile

The calculations are based on a formula for calculating the volume of a regular hexagonal prism. Having calculated this volume, it is multiplied by the density of the metal. A mass of hexagonal product is obtained.

It should be remembered that the use of simplified methods gives approximate results. They are used for express assessments. When developing design documentation in detail, more accurate indicators are used.

Finding the parameter of a metal pipe of any diameter is carried out similarly to the method for a round profile. Calculate the difference in the areas of two circles. The first has the outer radius of the pipe. The second has the inner radius of the pipe.

The resulting difference is multiplied by the length of the pipe, calculating the volume of metal. Multiplying by the density of steel, the mass of a pipe of a given length is found. Operations with non-ferrous metal products are simplified through the use of a conversion factor.

Pipe weight

When working with ready-made tables, you should find data for a 1 m bar with a radius equal to the outer diameter. Calculate the diameter of the rod, which is equal to the internal diameter. Subtract the smaller value from the larger value to get the desired result. It should be multiplied by the length of the sample.

How to calculate the mass of an angle, channel, I-beam

The parameter is calculated using data on the width of the shelf and the thickness of the metal. The product is considered as half of a rectangular profile.

There are ready-made calculation tables for the entire range of rolled metal products.

However, corners from different manufacturers have real weight characteristics that differ from the tabular data. They deliberately reduce the thickness of the shelf. They are motivated by the desire to reduce the cost of products. The parameter difference differs significantly from the parameters provided by GOST.

Weight of anglesWeight of channelWeight of I-beams

The weight characteristics of the channel and I-beams are determined according to the tables. This is caused by the difficulties of calculating the volume of complex geometric shapes.

Source: https://stankiexpert.ru/spravochnik/materialovedenie/raschet-vesa-metalla.html

How to calculate the mass of a sheet of metal

If there is no possibility of direct weighing, the weight of scrap metal can be determined in other ways. The most accurate result will be given by calculation, but other possibilities should not be neglected.

So, in order not to burden readers with unnecessary formulas, which will still be there, but below, we will immediately designate the formulas for calculating the most popular products from rolled steel and pipes - rolled pipes.

Here you will not find an online calculator for calculating weight, only formulas that you remember once you no longer have to use special calculators.

For example, when dismantling metal structures or a chimney, you don’t always have a computer, the Internet or a reference book at hand, but the structures are all welded from rolled steel here and our formulas will help out!

Weight of solid part

05/09/2013 // Vladimir Trunov   

This strange title of the article is explained only by the fact that parts of the same shape can be either solid or hollow (i.e. the next article will be called “Mass of a hollow part”).

Here is the time to remember that the mass of a body is its volume multiplied by the density of its material (see density tables):

The volume of a solid part is its volume and nothing else.

Note :
In the formulas below, all dimensions are measured in millimeters, and density is measured in grams per cubic centimeter. The letter indicates the ratio of the circumference of a circle to its diameter, which is approximately 3.14 .

Let's look at several simple forms (more complex ones, as you remember, can be made by adding or subtracting simple ones).

1. Mass of a parallelepiped (bar)

Volume of a parallelepiped: , where is the length, is the width, is the height.
Then the mass:

Volume of the cylinder: , where is the diameter of the base, is the height of the cylinder.
Then the mass:

Volume of the ball: , where is the diameter of the ball.
Then the mass:

Volume of a ball segment: , where is the diameter of the base of the segment, and is the height of the segment.
Then the mass:

5. Cone mass

The volume of any cone: , where is the area of ​​the base, and is the height of the cone.
For a round cone: , where is the diameter of the base, and is the height of the cone.
Mass of round cone:

6. Mass of a truncated cone

Since it is impossible to embrace the immensity, we will consider only a round truncated cone.
Its volume is the difference between the volumes of two nested cones: with bases and : , where , . After algebraic transformations that are not interesting to anyone, we get: , where is the diameter of the larger base, is the diameter of the smaller base, is the height of the truncated cone.
Hence the mass:

7. Mass of the pyramid

The volume of any pyramid is equal to one third of the product of the area of ​​its base and its height (the same as for cones (we often don’t notice how favorable the universe is to us)): , where is the area of ​​the base and is the height of the pyramid.
For a pyramid with a rectangular base: , where is the width, is the length, is the height of the pyramid.
Then the mass of the pyramid is:

8. Mass of a truncated pyramid

Consider a truncated pyramid with a rectangular base.
Its volume is the difference between the volumes of two similar pyramids with bases and: , where , . Having crossed out half of the notebook sheet, we get: , where , is the width and length of the larger base, , is the width and length of the smaller base, and is the height of the pyramid.

And, leaving the remaining half of the sheet alone, based on symmetry considerations alone, we can write another formula, which differs from the previous one only by replacing W with L and vice versa. What is the difference between length and width? Only that we called them that. Let's call it the other way around and get: .

Then the mass of a truncated rectangular pyramid is:

or

For a pyramid with a square base (, ), the formula looks simpler:

Source: https://tvlad.ru/mass/massa-sploshnoy-detali.html

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