# Calculation of cable cross-section for power and current: formulas and examples

Are you planning to do power grid upgrade or additionally stretch the power line to the kitchen to connect a new electric stove? This will be useful minimum knowledge of the conductor cross section and the effect of this parameter on the power and current strength.

Agree that the incorrect calculation of the cable cross section leads to overheating and short circuit or to unnecessary costs.

It is very important to carry out calculations at the design stage, since the failure of the hidden wiring and the subsequent replacement is associated with significant costs. We will help you deal with the intricacies of the calculations, to avoid problems in the further operation of electrical networks.

In order not to burden you with complex calculations, we picked up clear formulas and computational options, provided information in an accessible form, providing explanations to the formulas. Also, thematic photos and video materials were added to the article, allowing to visually understand the essence of the issue under consideration.

The content of the article:

• Calculation of the power consumers
• Stage # 1 - calculation of reactive and active power
• Stage # 2 - search for simultaneity and margin ratios
• Stage # 3 - perform the calculation by the geometric method
• Stage # 4 — calculate the power section in practice
• Calculation of the current section
• Stage # 1 - calculation of current strength using formulas
• Stage # 2 - choosing the appropriate section by tables
• Stage # 3 - calculation of the conductor cross section by current on an example
• Voltage drop calculation
• Carry calculation example
• Conclusions and useful video on the topic

## Calculation of the power consumers

The main purpose of conductors - the delivery of electrical energy to consumers in the required quantity. Since superconductors are not available under normal operating conditions, it is necessary to take into account the resistance of the conductor material.

Calculation of the required section conductors and cables depending on the total power of consumers based on long-term operating experience.

Image Gallery

A photo of Cable cross section is one of the basic values ​​in selecting it for a wiring device. The cross section determines which power current is able to conduct the cable without overheating due to excess power The basis of the cable is a single-wire or multi-wire copper conductor, which in cross section can be round, triangular or rectangular If there are more than two veins in the conductor, then they are most often twisted. The nominal cross-section of multicore products is the sum of the cross-sections of all existing veins. Different types of cable for wiring device Different thickness at the conductors for domestic use The number of lived in different brands of cable Stranded cable options

We begin the general course of calculations by first performing calculations using the formula:

P = (P1 + P2 +.. PN) * K * J,

Where:

• P - power of all consumers connected to the calculated branch in Watts.
• P1, P2, PN - power of the first consumer, second, n-th, respectively, in watts.

Having obtained the result at the end of the calculations using the above formula, it was the turn to turn to the tabular data.

Now we have to choose the necessary section in table 1. Table 1. The cross section of the wires is always necessary to choose the nearest big side (+)

### Stage # 1 - calculation of reactive and active power

Capacities of consumers are listed in the documents for the equipment. Usually in the passports of the equipment indicated active power, along with reactive power.

Devices with an active type of load transform all the received electrical energy, taking into account the efficiency, into useful work: mechanical, thermal, or another kind of it.

Devices with active load include incandescent lamps, heaters, electric stoves.

For such devices, the calculation of power by current and voltage is:

P = U * I,

Where:

• P - power in watts;
• U - voltage in;
• I - current in A.

Devices with a reactive type of load can accumulate energy from the source, and then return. Such an exchange takes place due to the displacement of the sinusoid current and voltage sinusoid. At zero phase displacement, the power P = U * I always has a positive value. Such a graph of the phases of current and voltage have devices with an active type of load (I, i is the current, U, u is the voltage, π is the pi number, equal to 3.14)

Devices with reactive power include electric motors, electronic devices of all sizes and purposes, transformers. When there is a phase shift between a sinusoid of current and a sinusoid of voltage, the power P = U * I can be negative (I, i is the current, U, u is the voltage, π is the pi number, equal to 3.14). A device with reactive power returns the stored energy back to the source

Electric networks are constructed in such a way that they can produce electric power transmission in one direction from the source to the load.

Therefore, the returned energy of the consumer with reactive load is parasitic and is spent on heating conductors and other components.

Reactive power has a dependence on the angle of phase displacement between voltage and current sinusoids. The phase angle is expressed in terms of cosφ.

To find the full power apply the formula:

P = PR / cosφ,

Where PR - reactive power in watts.

Usually in the passport data on the device indicated reactive power and cosφ.

Example: in the passport of the perforator indicated reactive power of 1200 W and cosφ = 0.7. Consequently, the total power consumption will be equal to:

P = 1200 / 0.7 = 1714 W

If cosφ could not be found, for the vast majority of household appliances, the cosφ can be taken as 0.7.

### Stage # 2 - search for simultaneity and margin ratios

K - the dimensionless coefficient of simultaneity, shows how many consumers can be simultaneously connected to the network. It rarely happens that all devices simultaneously consume electricity.

The simultaneous operation of a television and a music center is unlikely. From the established practice, K can be taken equal to 0.8. If you plan to use all consumers at the same time, K should be taken equal to 1.

J - dimensionless safety factor. It characterizes the creation of a power reserve for future consumers.

Progress does not stand still, every year invented all the new amazing and useful electrical appliances. It is expected that by 2050 the growth of electricity consumption will be 84%. Usually J is assumed to be from 1.5 to 2.0.

### Stage # 3 - perform the calculation by the geometric method

In all electrical calculations, the cross-sectional area of ​​the conductor is taken - the core section. Measured in mm2.

It is often necessary to learn how to correctly calculate wire diameter wire conductor.

In this case, there is a simple geometric formula for a monolithic wire of circular cross section:

S = π * R2 = π * D2/4, or vice versa

D = √ (4 * S / π)

For rectangular conductors:

S = h * m,

Where:

• S - core area in mm2;
• R - core radius in mm;
• D - core diameter in mm;
• h, m - width and height, respectively, in mm;
• π - pi number, equal to 3.14.

If you acquire a multicore wire, in which one conductor consists of a set of twisted round wires, then the calculation is carried out according to the formula:

S = N * D2/1,27,

Where N - the number of wires in the vein.

The wires having twisted from several wires of a vein, in general case have the best conductivity, than monolithic. This is due to the peculiarities of the flow of current through a circular conductor.

Electric current is the movement of like charges along a conductor. Like charges repel each other, therefore the charge distribution density is shifted to the surface of the conductor.

Another advantage of stranded wires is their flexibility and mechanical resistance. Monolithic wires are cheaper and are used mainly for fixed installation.

### Stage # 4 — calculate the power section in practice

Task: The total power of consumers in the kitchen is 5000 W (meaning that the power of all reactive consumers is recalculated). All consumers are connected to a single-phase network of 220 V and are powered from one branch. Table 2. If you are planning in the future to connect additional consumers, the table shows the necessary power of common household appliances (+)

Decision:

The coefficient of simultaneity K is taken equal to 0.8. The kitchen is a place of constant innovation, you never know, the safety factor is J = 2.0. The total estimated power will be:

P = 5000 * 0.8 * 2 = 8000 W = 8 kW

Using the value of the estimated power, we look for the nearest value in table 1.

The closest suitable value of the conductor cross-section for a single-phase network is a copper conductor with a cross section of 4 mm2. The same size of wire with aluminum core 6 mm2.

For single-conductor wiring, the minimum diameter is 2.3 mm and 2.8 mm, respectively. In the case of the multicore version, the cross section of the individual conductors is summed.

Image Gallery

A photo of Kitchens usually have the most powerful power consumers and less “voracious” household appliances. Bathrooms and combined bathrooms can also have an impressive amount of electrical equipment. Depending on the power of the technical unit, it is powered from a common or separate power line. Calculations are made for a group of sockets, for consumers of individual lines are selected according to the power To the socket block, powered by one power line, you can connect only low-power devices: mixers, hair dryers, coffee grinders, etc. Connecting to a separate power line require microwaves, hobs and electric ovens. Normal operation of a standard washing machine should be provided by a separate power line. Obligatory laying of a separate power branch require refrigerators and electric stoves In the hygienic premises, separate lines are laid for the jacuzzi, electronic bidet covers, shower cubicles. Room with the maximum number of home appliances Technical equipment of bathrooms and combined bathrooms Connecting high-power consumers Socket unit for low-power equipment The hob requires proper connection. Power line for washing machine Separate power lines for refrigerators Powerful energy users in bathrooms and bathrooms

## Calculation of the current section

Calculations of the required cross-section for current and power of cables and wires will provide more accurate results. Such calculations make it possible to estimate the overall effect of various factors on the conductors, including the thermal load, the type of wires, the type of installation, the operating conditions, etc.

The whole calculation is carried out in the course of the following stages:

• power choice of all consumers;
• calculation of the currents passing through the conductor;
• selection of a suitable cross-section according to the tables.

For this version of the calculation, the power of current consumers with voltage is taken without taking into account the correction factors. They will be taken into account when summing up the current.

### Stage # 1 - calculation of current strength using formulas

For those who have forgotten the school course of physics, we offer the basic formulas in the form of a graphic scheme as a visual crib: "Classic wheel" clearly demonstrates the relationship of the formulas and the interdependence of the characteristics of electric current (I - current strength, P - power, U - voltage, R - core radius)

We write down the dependence of the current strength I on the power P and the line voltage U:

I = p / ul,

Where:

• I - current strength, taken in amperes;
• P - power in watts;
• Ul - linear voltage in volts.

Line voltage in the general case depends on the power supply source, it can be single- and three-phase.

The relationship of linear and phase voltage:

1. Ul = U * cosφ in the case of single-phase voltage.
2. Ul = U * √3 * cosφ in the case of three-phase voltage.

For household electrical consumers take cosφ = 1, so the linear voltage can be rewritten:

1. Ul = 220 V for single phase voltage.
2. Ul = 380 V for three phase voltage.

Further we summarize all consumed currents according to the formula:

I = (I1 + I2 +... IN) * K * J,

Where:

• I - total current in amperes;
• I1..IN - current of each consumer in amperes;
• K - coefficient of simultaneity;
• J - safety factor.

The coefficients K and J have the same values ​​that were used in the calculation of the total power.

There may be a case when a current of unequal power flows through a three-phase network through different phase conductors.

This happens when single-phase and three-phase consumers are connected to the three-phase cable simultaneously. For example, powered three-phase machine and single-phase lighting.

A natural question arises: how in such cases the cross-sectional wire section is calculated? The answer is simple - calculations are made on the most loaded core.

### Stage # 2 - choosing the appropriate section by tables

In the rules of operation of electrical installations (PES) are a number of tables for selecting the desired cross section of the cable core.

The conductivity of the conductor depends on the temperature. For metallic conductors with increasing temperature increases the resistance.

When a certain threshold is exceeded, the process becomes auto-supported: the higher the resistance, the the higher the temperature, the higher the resistance, etc. until the conductor burns out or causes a short closure

The following two tables (3 and 4) show the cross section of conductors depending on the currents and the method of installation. Table 3. First, it is necessary to choose the way of laying the wires; it depends on how efficiently the cooling takes place (+)

The cable differs from the wire in that the cable has all the conductors, equipped with its own insulation, twisted in a bundle and enclosed in a common insulating sheath. More details about the differences and types of cable products are written in this article. Table 4. The open method is indicated for all values ​​of the conductor cross-section, however, in practice, sections below 3 mm2 are not openly laid out for reasons of mechanical strength (+)

When using tables, the following factors are applied to the permissible continuous current:

• 0.68 if 5-6 lived;
• 0.63 if 7-9 lived;
• 0.6 if 10-12 lived

Reduction factors are applied to the values ​​of the currents from the "open" column.

Zero and grounding conductors are not included in the number of conductors.

According to the standards of the PES, the choice of the cross section of the zero conductor according to the permissible continuous current is made as at least 50% of the phase conductor.

The following two tables (5 and 6) show the dependence of the permissible continuous current when laying it in the ground. Table 5. Depending on the permissible continuous current for copper cables when laying in the air or ground

Current load when laying open and when recessed into the ground differ. They are taken equal if laying in the ground is carried out using trays. Table 6. Depending on the permissible continuous current for aluminum cables when laying in the air or ground

For the device of temporary power supply lines (carrying, if for private use), the following table applies (7). Table 7. Permissible continuous current when using portable hose cords, portable hose and mine cables, flood cables, flexible portable wires. Only copper conductor is used.

When laying cables in the ground in addition to the heat dissipation properties, resistivity must be taken into account, as reflected in the following table (8): Table 8. Correction coefficient depending on the type and specific resistance of the soil to the permissible continuous current, when calculating the cable cross-section (+)

Calculation and selection of copper conductors up to 6 mm2 or aluminum up to 10 mm2 It is conducted as for a continuous current.

In the case of large sections, it is possible to apply a reduction factor:

0.875 * √Тpv

Where Tpv - the ratio of the duration of the on-cycle duration.

The duration of the inclusion is taken at the rate of no more than 4 minutes. In this case, the cycle should not exceed 10 minutes.

When choosing a cable for distributing electricity in wooden house Particular attention is paid to its fire resistance.

### Stage # 3 - calculation of the conductor cross section by current on an example

Task: calculate the required section copper cable for connection:

• 4000 W three-phase woodworking machine;
• 6000 W three-phase welding machine;
• household appliances in the house with a total capacity of 25,000 watts;

The connection will be made by a five-core cable (three phase conductors, one zero and one ground), laid in the ground. Cable insulation is calculated for a specific value of the operating voltage. It should be noted that the operating voltage specified by the manufacturer for its product must be higher than the line voltage.

Decision.

Step 1. Calculate the linear voltage of the three-phase connection:

Ul = 220 * √3 = 380 V

Step # 2. Household appliances, machine and welding machine have reactive power, so the power of machinery and equipment will be:

Pthose = 25000 / 0.7 = 35700 W

Pequipment = 10,000 / 0.7 = 14,300 W

Step # 3. Current required to connect household appliances:

Ithose = 35700/220 = 162 A

Step # 4. Current required to connect equipment:

Iequipment = 14300/380 = 38 A

Step # 5. The required current for connecting household appliances is calculated at the rate of one phase. By the condition of the problem there are three phases. Therefore, the current can be distributed in phases. For simplicity, assume a uniform distribution:

Ithose = 162/3 = 54 A

Step # 6. The current attributable to each phase:

If = 38 + 54 = 92 A

Step # 7. Equipment and household appliances will not work at the same time, but we will lay down a stock of 1.5. After applying the correction factors:

If = 92 * 1.5 * 0.8 = 110 A

Step # 8. Although the cable has 5 cores, only three phase conductors are taken into account. According to table 8 in the column three-core cable in the ground we find that the current of 115 A corresponds to the cross section of the core 16 mm2.

Step # 9. According to table 8, we apply the correction factor depending on the characteristics of the land. For a normal type of land, the coefficient is 1.

Step # 10. Not mandatory, we calculate the core diameter:

D = √ (4 * 16 / 3.14) = 4.5 mm

If the calculation was made only for power, without taking into account the features of cable laying, the cross section of the core will be 25 mm2. The calculation of the strength of the current is more complicated, but it sometimes saves considerable money, especially when it comes to stranded power cables.

On the relationship between voltage and current can be more detailed here.

## Voltage drop calculation

Any conductor, except superconductors, has resistance. Therefore, with sufficient cable or wire length, a voltage drop occurs.

PES standards require that the cable conductor cross section be such that the voltage drop is not more than 5%. Table 9. Specific resistance of common metallic conductors (+)

First of all it concerns low-voltage cables of small section.

The calculation of the voltage drop is as follows:

R = 2 * (ρ * L) / S,

U% = (Upad / Uling) * 100,

Where:

• 2 - coefficient due to the fact that the current flows necessarily through two conductors;
• R - conductor resistance, Ohm;
• ρ - resistivity of the conductor, Ohm * mm2/ m;
• S - conductor section, mm2;
• Upad - voltage drop, V;
• U% - voltage drop relative to Uling,%.

Using formulas, you can independently perform the necessary calculations.

## Carry calculation example

Task: calculate the voltage drop for copper wire with a cross-section of a single core of 1.5 mm2. The wire is needed to connect a single-phase electric welding apparatus with a total power of 7 kW. Wire length 20 m. Those wishing to connect a household welding machine to the power supply branch should take into account the current situation for which the cable used is designed. It is possible that the total power of working devices may be higher. The best option is to connect consumers to individual branches.

Decision:

Step 1. Calculate the resistance of the copper wire, using table 9:

R = 2 * (0,0175 * 20) / 1,5 = 0,47 Ohm

Step # 2. The current flowing through the conductor:

I = 7000/220 = 31.8 A

Step # 3. The voltage drop on the wire:

Upad = 31.8 * 0.47 = 14.95 V

Step # 4. Calculate the percentage of voltage drop:

U% = (14,95 / 220) * 100 = 6,8%

Conclusion: a conductor with a large cross section is required to connect the welding machine.

## Conclusions and useful video on the topic

Calculation of the conductor cross section according to the formulas:

Recommendations of experts on the selection of cable products:

The above calculations are valid for industrial-grade copper and aluminum conductors. For other types of conductors, full heat transfer is pre-calculated.

On the basis of these data, the maximum current capable of flowing through the conductor is calculated without causing excessive heating.

If you have any questions about the method of calculating the cable section or have a desire to share personal experience, please leave comments on this article. The block for reviews is located below. #### Installation of open wiring and an overview of possible errorsInstallation Of Wiring

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