# Wire Resistance Calculator

## Wire Resistance Calculator

Wire Resistance Calculator presented here will help to select proper wire size and length for different applications.

For calculations of Heat Sink Thermal Resistance please visit, Heat Sink Thermal Resistance Calculator.

For calculations of PCB Trace Resistance please visit, PCB Trace Resistance Calculator.

We know that the resistance is the interruption to the flow of charge. The electric potential difference between the two terminals permits the flow of charge, but the resistance resists the flow of charge.

Wire resistance also resists the flow of charge. Hence, wire resistance calculator is needed to calculate wire resistance in AC or DC applications.

Below is the wire resistance calculator;

 Resistivity (µΩm) Conductivity (MS/m) Wire Diameter (mm) Wire Radius (mm) CSA (mm^2) Length of the wire (m) Multiplier Wire Diameter (mm) Wire Radius (mm) CSA (mm^2) Wire Resistance (Ω)

This calculator will help to find the DC resistance of common wire shapes.

### Wire Resistance Formula

Wire resistance calculations can be done by below mentioned formulas;

Formula for calculating DC resistance is;

DC Resistance = Length / (Cross sectional area x Conductivity).

Formula for calculating AC resistance is;

AC Resistance = Length / (Conductivity x Cross sectional perimeter x Skin depth)

We can write above formulas with the help of units;

R = ρ (L/A)

σ = 1/ρ

Therefore;

R = L/(σA)

Where;
ρ = Resistivity of material
L = Length of wire
A = Cross sectional are of wire = πr²
σ = Conductivity of material

Note:

Above formula is usable when the skin depth is small comparative to the dimensions of the cross section.

AC resistance calculations assumes that the current is equally distributed around the perimeter of the used conductor.

In situations where this assumption is not valid (e.g. a wide trace very close to a ground plane), the AC resistance will be slightly higher than the calculated value.

This assumption is not valid in the circumstances like; a wide trace which is very close to a ground plane, then the AC resistance in this case will be slightly higher than the calculated value.

Conductivity, σ is the reciprocal of the resistivity i.e. 1/ρ.

Hence a pure conductor has infinite conductance and almost zero ohmic resistance.

A conductor that has a high conductivity will have a low resistivity.

### Wire Resistance

The relation between the resistance and the wire length is proportional. The total length of the wire will affect the total resistance. If the wire is longer, then there will be more resistance. The resistance of a thin wire is more than the resistance of a thick wire, because a thin wire has less electrons for flow of current.

The cross-sectional area of the wires will affect the amount of resistance. The relation between the resistance and the wire cross section is inversely proportional. Broader wires have a larger cross-sectional area. The wider the wire, there will be less resistance for the flow of electric charge.

Wire material also affects the resistance. Some materials are good conductors as compare to others and offers less resistance to flow of the charge. For example, silver is the best conductor but because of its cost it is never used in household wires. Copper and aluminium are the least expensive materials with better conductivity, that’s why they are used in the wires of household circuits.

The conducting ability of a material is frequently represented by its resistivity. The resistivity of a material is reliant on the material's electronic structure and its temperature. For most of the materials, resistivity increases with the increase in the temperature.

Below table shows list of resistivity values of different materials at 20°C temperature.

Material         Resistivity (ohm meter)

Silver                1.59 x 10E-8

Copper             1.7 x 10E-8

Gold                  2.2 x 10E-8

Aluminium      2.65 x 10E-8

Tungsten          5.6 x 10E-8

Iron                    9.71 x 10E-8

Platinum           10.6 x 10E-8

Nichrome          100 x 10E-8

Carbon               3.5 x 10E-5

Glass                   1 to 10000 x 10E9

Hard Rubber     1 to 100 x 10E13

### Conclusion

Wire resistance resists the flow of charge. In an application for proper flow of electrical charge, a proper wire should be selected. The wire resistance calculator presented here, will help to select proper wire size and length for applications.