Wire (cable) cross-section by diameter: formula, table

Often, before purchasing cable products, there is a need to independently measure its cross-section in order to avoid deception on the part of manufacturers, who, due to savings and setting a competitive price, may slightly underestimate this parameter.

Variety of cable products and wires

It is also necessary to know how the cable cross-section is determined, for example, when adding a new energy-consuming point in rooms with old electrical wiring that does not have any technical information. Accordingly, the question of how to find out the cross-section of conductors always remains relevant.

General information about cable and wire

When working with conductors, it is necessary to understand their designation.
There are wires and cables that differ from each other in their internal structure and technical characteristics. However, many people often confuse these concepts. A wire is a conductor that has in its design one wire or a group of wires woven together and a thin common insulating layer. A cable is a core or a group of cores that has both its own insulation and a common insulating layer (sheath). Each type of conductor will have its own methods for determining cross sections, which are almost similar.

The role of cross-sectional indicator in wire selection

If you choose a cable with an insufficient cross-section, you risk overloading and overheating the conductor, which can quickly melt the insulation. And this, in turn, is fraught with a short circuit and fire.

At the same time, choosing a cable with an excessively large cross-section is absolutely not beneficial for you, as a buyer, because its price directly depends on this indicator.

The “Rules for the Installation of Electrical Equipment” (PUE) uses a special table for this purpose: it shows the cable cross-section that is designed for a specific load for single-core, two-core and three-core cables when laid in the ground or in the air. But first things first.

Conductor materials

The amount of energy that a conductor transmits depends on a number of factors, the main one of which is the material of the current-carrying conductors. The following non-ferrous metals can be used as the core material of wires and cables:

1. Aluminum. Cheap and lightweight conductors, which is their advantage. They are characterized by such negative qualities as low electrical conductivity, a tendency to mechanical damage, high transient electrical resistance of oxidized surfaces;
2. Copper. The most popular conductors, which have a high cost compared to other options. However, they are characterized by low electrical and transition resistance at the contacts, fairly high elasticity and strength, and ease of soldering and welding;
3. Aluminum copper. Cable products with aluminum cores coated with copper. They are characterized by slightly lower electrical conductivity than their copper counterparts. They are also characterized by lightness, average resistance and relative cheapness.

Some methods for determining the cross-section of cables and wires will depend specifically on the material of their conductor component, which directly affects the throughput power and current strength (method of determining the cross-section of conductors by power and current).

Thickness of popular cable brands

Quite often it is necessary to know the thickness, or more correctly, the outer or outer diameter of a particular brand of cable in order to select suitable cable support systems or the required diameter of protective pipes. We list in the tables below the thicknesses of the most frequently requested brands: KG, VVGng, SIP

Cable thickness KG

Cable thickness VVGng

Why is cable calculation necessary?

When choosing the cross-section of wires, you cannot follow the “by eye” principle. As current flows through the wires, it heats them up. The higher the current, the more heating occurs. This relationship is easy to prove with a couple of formulas. The first of them determines the active current strength:

where I is current, U is voltage, R is resistance.

The formula shows: the greater the resistance, the more heat will be generated, i.e., the more the conductor will heat up. Resistance is determined by the formula:

R = ρ · L/S (2), where ρ is the resistivity, L is the length of the conductor, S is its cross-sectional area. The smaller the cross-sectional area of ​​the conductor, the higher its resistance, and therefore the higher the active power, which indicates stronger heating. Based on this, calculation of the cross-section is necessary to ensure the safety and reliability of the wiring, as well as the competent distribution of finances.

Determining diameter using a ruler

The option is probably the simplest. But the accuracy of such measurements leaves much to be desired. Based on the fact that it is almost impossible to determine the diameter of a too thin wire by measuring with a ruler, this method is acceptable for relatively thick wires.

For these purposes, paper or thread is used. The whole point of the measuring process comes down to wrapping a piece of thin paper (or thread) around the wire being measured so that the ends of this piece of paper (or thread) meet. The place where the different ends of the paper come into contact is marked, after which it is removed and measured with a ruler. So, you get the circumference, which you subsequently substitute into the formula and find out the desired value.

D=L/2π,

where: D – diameter, L – circumference, π – constant value equal to 3.14.

Having information about the diameter, you can substitute it into the appropriate formula and find out the cross-sectional area.

Calculator for calculating cross-section by diameter

To simplify calculations, a calculator has been developed for calculating cable cross-section by diameter. It is based on formulas that can be used to find the cross-sectional area of ​​single-core and stranded wires.

You need to measure the cross-section by measuring the core without insulation, otherwise nothing will work. When it comes to calculating tens and hundreds of values, an online calculator can significantly simplify the life of electricians and electrical network designers due to convenience and increased speed of calculations. It is enough to enter the value of the core diameter, and, if necessary, indicate the number of wires if the cable is multi-core, and the service will show the required wire cross-section.

What is the deception?

If you don’t know and understand what a 4-square wire looks like or what its diameter is, you can easily be deceived. This deception can come from both the contractor’s electrician and negligent manufacturers. What exactly does it involve?

For example, you entrusted all obligations for selecting wiring for your apartment to a specialist. He must go to the supermarket and use the funds allocated by you to purchase a wire network that meets your requirements and conditions for using electricity. Since you understand absolutely nothing about the sizes, sections, and carrying capacities of wires, you completely rely on the responsible contractor.

In turn, he can conscientiously fulfill your instructions and purchase the cable you need, or he can take advantage of your trust for selfish purposes and buy a cheaper, and, accordingly, lower-grade product. He will simply take the difference and put it in his pocket. The wiring will, of course, be installed. But you will live in peace and not even suspect the threats of the poor quality of your wiring and the fact that you were simply deceived.

Another way to be deceived is to trust the cable industry manufacturers completely and completely. Even despite the fairly high competition, in the conditions of which all suppliers of cable products try to work to the maximum and in no case lose their customers, they often resort to various kinds of tricks. One of the most common such tricks is saving on metal by reducing the conductor diameter. Just think: the manufacturer only needs to reduce the cross-section of a 10-square-meter wire by just a couple of mm2 (what diameter will it correspond to?) in order to break even by significantly reducing the cost of selling hundreds of kilometers of this cable! He feels good, but you may be left with nothing. Or, it would be more correct to say, at the burnt-out wiring. After all, the resistance of the purchased conductor will be much lower than that stated in the markings and documentation.

That is why it is so important to have at least minimal information about what the wires should be like, what the difference is in diameter and cross-section in the cable, and on what basis calculations are made.

Three main ways to determine wire diameter

There are several methods, but each of them is based on determining the diameters of the core with subsequent calculations of the final results.

Method one. Using instruments. Today there are a number of instruments that help measure the diameter of a wire or wire strand. This is a micrometer and caliper, which come in both mechanical and electronic (see below).

This option is primarily suitable for professional electricians who are constantly installing electrical wiring. The most accurate results can be obtained using a caliper. This technique has the advantage that it is possible to measure the wire diameter even on a section of a working line, for example, in a socket.

After you have measured the diameter of the wire, you need to make calculations using the following formula:

It must be remembered that the number “Pi” is 3.14, so if we divide the number “Pi” by 4, we can simplify the formula and reduce the calculation to multiplying 0.785 by the diameter squared.

Method two. We use a ruler. If you decide not to spend money on a device, which is logical in this situation, then you can use a simple proven method for measuring the cross-section of a wire or wire?. You will need a simple pencil, ruler and wire. Strip the core of insulation, wind it tightly onto a pencil, and then use a ruler to measure the total length of the winding (as shown in the figure).

Then divide the length of the wound wire by the number of cores. The resulting value will be the diameter of the wire cross-section.

But the following must be taken into account:

• the more cores you wind on a pencil, the more accurate the result will be; the number of turns should be at least 15;
• press the coils tightly against each other so that there is no free space between them, this will significantly reduce the error;
• take measurements several times (change the measuring side, the direction of the ruler, etc.). Several results obtained will again help you avoid a large error.

Please note the disadvantages of this measurement method:

1. You can only measure the cross-section of thin wires, since it will be difficult for you to wind a thick wire around a pencil.
2. To begin with, you will need to purchase a small piece of the product before making the main purchase.

The formula discussed above is suitable for all measurements.

Method three. We use the table. In order not to carry out calculations using the formula, you can use a special table that indicates the diameter of the wire? (in millimeters) and conductor cross-section (in square millimeters). Ready-made tables will give you more accurate results and will significantly save your time, which you will not have to spend on calculations.

How to measure cable cross-section

It is impossible to directly measure the cross section. However, you can determine the cable cross-section in various ways.

If there are different wire lugs, you can try which lug fits the cable to determine the size. If the cable does not fit into the ferrule, then the cable cross-section is larger and you need to choose a larger ferrule.

If the cable fits too loosely into the ferrule, use a smaller ferrule. Of course, only copper material should be inserted into the cage.

• Another possibility is to measure the diameter of the cable with a micrometer and calculate the cross-section from it. To do this, you need to measure the diameter of the copper conductor. This method is very reliable for single-wire conductors.
• However, when using flexible stranded cables, it is important not to compress these thin wires too much and thereby obtain an incorrect measurement, and also to note that there is a certain amount of air between the individual strands of these wires.
• It is therefore recommended to take measurements directly next to the insulation.

To avoid getting into trouble, you need to choose the cable carefully so that it is of the required thickness. Since the cable contains several cores, it is necessary to calculate the cross-section, taking into account the diameter of all cores.

The procedure for calculating the power cross section

In general, the calculation of the cable cross-section for power occurs in 2 stages. To do this you will need the following data:

• Total power of all devices.
• Network voltage type: 220 V – single-phase, 380 V – three-phase.
• PUE 7. Rules for electrical installations. Edition 7.
• Conductor material: copper or aluminum.
• Wiring type: open or closed.

Step 1. The power consumption of electrical appliances can be found in their instructions or take the average characteristics. Formula for calculating total power:

ΣP = (P₁ + Р₂ + … + Рₙ) · Кс · Кз,

where P1, P2, etc. is the power of connected devices, Kc is the demand factor, which takes into account the probability of turning on all devices at the same time, Kz is the safety factor in case of adding new devices in the house. KS is defined as follows:

• for two simultaneously switched on devices – 1;
• for 3-4 – 0.8;
• for 5-6 – 0.75;
• for larger quantities – 0.7.

In calculating the cable load, it makes sense to take the short circuit as 1.15-1.2. For example, you can take a total power of 5 kW.

Step 2. At the second stage, it remains to determine the cross-section of the conductor based on the total power. For this purpose, a table for calculating the cable cross-section from the PUE is used. It provides information for both copper and aluminum conductors. With a power of 5 kW and a closed single-phase electrical network, a copper cable with a cross-section of 4 mm2 is suitable.

conclusions

Before wiring your home, be sure to familiarize yourself with the existing types of wires. Electricians also recommend examining copper wire for color before purchasing, since manufacturers can save on material and use an alloy. This contributes to a significant increase in electrical resistance, which, in turn, does not allow the use of the permissible load level for a particular section.

Experts also advise measuring only the core when making calculations. No matter how thin the insulation on a wire is, no matter how flexible it is, you will have to remove it one way or another to get accurate data. Otherwise, the extra millimeters will give you a reason to use an unacceptably small cross-section of wire for wiring, the load for which will ultimately be excessive. This, in turn, is fraught with consequences.

Length calculation rules

Calculation of the cable cross-section along the length assumes that the owner has determined in advance how many meters of conductor will be required for the electrical wiring. This method is usually used at home. For the calculation you will need the following data:

• L – conductor length, m. For example, the value taken is 40 m.
• ρ – resistivity of the material (copper or aluminum), Ohm/mm2 m: 0.0175 for copper and 0.0281 for aluminum.
• I – rated current, A.

Step 1. Determine the rated current using the formula:

I = (P Ks) / (U cos ϕ) = 8000/220 = 36 A,

where P is the power in watts (the total of all appliances in the house, for example, the value is 8 kW), U is 220 V, Ks is the simultaneous switching factor (0.75), cos φ is 1 for household appliances. In the example, the value turned out to be 36 A.

Step 2. Determine the cross-section of the conductor. To do this you need to use formula (2):

R = ρ · L/S.

The voltage loss along the length of the conductor should be no more than 5%:

dU = 0.05 220 V = 11 V.

Voltage loss dU = I R, hence R = dU/I = 11/36 = 0.31 Ohm. Then the cross-section of the conductor must be no less than:

S = ρ · L/R = 0.0175 · 40/0.31 = 2.25 mm2.

In the case of a three-core cable, the cross-sectional area of ​​one core should be 0.75 mm2. Hence, the diameter of one core must be at least (√S/ π) · 2 = 0.98 mm. Cable BBGng 3×1.5 satisfies this condition.

Requirements for packaging of KG cable

Cables can be supplied on drums or in coils. The diameter of the drum neck or the internal diameter of the coil must be no less than 12 external diameters of the cable.

Standard cable lengths must be at least 150 m for sections up to 35 mm2 inclusive and at least 125 m for sections from 50 mm2 and above. In one delivery batch, a certain percentage (no more than 20) of cables with a length of at least 20 m is allowed. No more than 5 pieces of cable can be wound on a drum. Cable lengths when supplied in coils are agreed upon between the manufacturer and the consumer.

Calculation for stranded wire

Stranded wire (stranded) consists of single-core wires twisted together. Anyone who is even a little familiar with mathematics understands perfectly well that it is necessary to count the number of these wires in a stranded wire. After this, the cross-section of one thin wire is measured and multiplied by their total number. Let's consider the following options.

Calculation using a caliper

The measurement is carried out with a caliper with a conventional scale (or micrometer). Experienced craftsmen always have this tool at hand, but not everyone is a professional electrician.

To do this, using the VVGng cable as an example, cut the thick sheath with a knife and spread the wires in different directions.

Then select one core and strip it with a knife or scissors. Next, measure this core. The size should be 1.8 mm. Please refer to the calculations to prove the measurement is correct.

The resulting figure of 2.54 mm² is the actual cross-section of the core.

Measuring with a pen or pencil

If you don’t have a caliper at hand, you can use improvised methods using a pencil and ruler. First, take the wire to be measured, strip it and wind it around a pencil or pen so that the turns lie close to each other. The more turns, the better. Now let's count the number of wound turns and measure their total length.

For example, we got 10 turns with a total winding length of 18 mm. It is easy to calculate the diameter of one turn; to do this, divide the total length by the number of turns.

As a result of all the calculations made using the formula, you will obtain the required diameter of the core. In this case it is 1.8 mm. Since the diameter of one core is known, it is not difficult to calculate the cross-section of the entire VVGng wire using the already known formula. You can see that the results were equal.

Using tables

How can you find out and measure the cable cross-section if you don’t have a caliper, a ruler, or a micrometer at hand? Instead of racking your brains over complex mathematical formulas, just remember that there are ready-made tables of values ​​for measuring cable cross-section. There are, of course, very complex tables with many parameters, but, in principle, to begin with it is enough to use the simplest of the two columns. The diameter of the conductor is entered in the first column, and the ready-made values ​​​​of the wire cross-section are given in the second column.

Wiring cross-section table for closed wiring

There is another “approximate” method that does not require measuring the thickness of individual wires. You can simply measure the cross-section (diameter) of the entire thick scroll. This method is usually used by experienced electricians. They can find out the cable cross-section both “by eye” and with the help of tools.

Determining diameter using a micrometer

Calculating the diameter of a wire is the simplest thing that can be done not only by a novice in installing electrical wiring, but even by a person who has nothing to do with this area. To measure the diameter, simply use one of the most common methods.

The first method is to use a micrometer or caliper. This method is considered the most relevant and often used in practice. This is due to the fact that such devices provide the most accurate measurement indicators. The measurement process itself is carried out by moving the latch to the open position. The micrometer handle must be unscrewed to a distance that will allow the wire to easily fit into the groove between the probes. After this, the handles of the device are activated: they twist the device until the ratchet operates. That's all, you can record the received data.

Parallel connection of electrical wiring wires

There are hopeless situations when you urgently need to lay wiring, but there is no wire of the required cross-section available. In this case, if there is a wire with a smaller cross-section than necessary, then the wiring can be made from two or more wires, connecting them in parallel. The main thing is that the sum of the sections of each of them is not less than the calculated one.

For example, there are three wires with a cross-section of 2, 3 and 5 mm², but according to calculations, 10 mm² is needed. Connect them all in parallel and the wiring will handle up to 50 amps. Yes, you yourself have repeatedly seen the parallel connection of a large number of thin conductors to transmit large currents. For example, welding uses a current of up to 150 A and in order for the welder to control the electrode, a flexible wire is needed. It is made from hundreds of thin copper wires connected in parallel.

In a car, the battery is also connected to the on-board network using the same flexible stranded wire, since when starting the engine, the starter consumes current from the battery up to 100 A. And when installing and removing the battery, the wires must be taken to the side, that is, the wire must be flexible enough . The method of increasing the cross-section of an electrical wire by connecting several wires of different diameters in parallel can be used only as a last resort. When laying home electrical wiring, it is permissible to connect in parallel only wires of the same cross-section taken from the same reel.

About choosing a cable brand for home wiring

Making apartment electrical wiring from aluminum wires at first glance seems cheaper, but operating costs due to low reliability of contacts over time will be many times higher than the costs of electrical wiring made from copper. I recommend making the wiring exclusively from copper wires! Aluminum wires are indispensable when laying overhead electrical wiring, as they are light and cheap and, when properly connected, serve reliably for a long time.

Which wire is better to use when installing electrical wiring, single-core or stranded? From the point of view of the ability to conduct current per unit of cross-section and installation, single-core is better. So for home wiring you only need to use solid wire. Stranded allows multiple bends, and the thinner the conductors in it, the more flexible and durable it is. Therefore, stranded wire is used to connect non-stationary electrical appliances to the electrical network, such as an electric hair dryer, an electric razor, an electric iron and all the others.

After deciding on the cross-section of the wire, the question arises about the brand of cable for electrical wiring. The choice here is not great and is represented by only a few brands of cables: PUNP, VVGng and NYM. PUNP cable since 1990, in accordance with the decision of Glavgosenergonadzor “On the ban on the use of wires such as APVN, PPBN, PEN, PUNP, etc., produced according to TU 16-505. 610-74 instead of APV, APPV, PV and PPV wires according to GOST 6323-79*" is prohibited for use.

Cable VVG and VVGng - copper wires in double polyvinyl chloride insulation, flat shape. Designed for operation at ambient temperatures from −50°С to +50°С, for wiring inside buildings, outdoors, in the ground when laid in tubes. Service life up to 30 years. The letters “ng” in the brand designation indicate the non-flammability of the wire insulation. Two-, three- and four-core wires are available with core cross-sections from 1.5 to 35.0 mm2. If in the cable designation there is a letter A (AVVG) before VVG, then the conductors in the wire are aluminum.

The NYM cable (its Russian analogue is the VVG cable), with copper cores, round in shape, with non-flammable insulation, complies with the German standard VDE 0250. Technical characteristics and scope of application are almost the same as the VVG cable. Two-, three- and four-core wires are available with core cross-sections from 1.5 to 4.0 mm².

As you can see, the choice for laying electrical wiring is not large and is determined depending on what shape the cable is more suitable for installation, round or flat. A round-shaped cable is more convenient to lay through walls, especially if the connection is made from the street into the room. You will need to drill a hole slightly larger than the diameter of the cable, and with a larger wall thickness this becomes relevant. For internal wiring, it is more convenient to use a VVG flat cable.

When laying apartment electrical wiring, as a rule, the question arises about choosing a circuit breaker, or, as it is often called, a machine. This issue and the choice of a meter, RCD, and differential circuit breaker are covered in detail in the website article “About the electric meter, RCD and circuit breakers.”

Number of wires in the conductor

The minimum number of wires in the conductors of cables and wires is regulated by GOST 22483 and is presented in the tables below:

Table 1, GOST 22483. Cores of single-core and multi-core cables and wires of class 1.

Table 2, GOST 22483. Cores of single-core and multi-core cables and wires of class 2.

Notes:

• The minimum number of round core wires is established in the standards or technical specifications for cable products.
• The cross sections indicated in parentheses are not preferred.

Table 3, GOST 22483. Cores of single-core and multi-core cables and wires of class 3.

Table 4, GOST 22483. Cores of single-core and multi-core cables and wires of class 4.

Table 5, GOST 22483. Cores of single-core and multi-core cables and wires of class 5.

Table 6, GOST 22483. Cores of single-core and multi-core cables and wires of class 6.

As a summary of this article and for ease of use, below are tables from the reference book “Electrical Cables, Wires and Cords” (N.I. Belorussov, A.E. Saakyan, A.I. Yakovleva; Edited by N.I. Belorussov - 5th ed., revised and supplemented - M.:, Energoatomizdat, 1988. - 536 pp.; ill.), which summarizes all the above-described parameters of cables and wires.

Table 1.1 of the Directory. Cores of single-core and multi-core cables and wires for stationary installation

Table 1.1 of the Directory. Cores of single-core and multi-core cables and wires for stationary installation (continued)

Table 1.2 of the Directory. Cores of single-core and multi-core cables and wires for non-stationary installation

Table 1.2 of the Directory. Cores of single-core and multi-core cables and wires for non-stationary installation (continued)

Table 1.3 of the Directory. Electrical resistance of 1 km of round core at 20 °C, Ohm, no more