 WAZIPOINT Engineering Science & Technology: Calculating the Resistance of a Wire

## Wednesday, April 26, 2023

### Calculating the Resistance of a Wire

In many cases, we will know the length of a wire l and the AWG (American Wire Gauge) or
SWG (British Standard Wire Gauge) or IEC standard size of the wire, but not the resistance. It's easy to calculate the resistance though.

Wikipedia has a list of AWG specifications available here, which includes the resistance per meter in Ohms per kilometer or milli Ohms per meter. They also have it per kilofeet or feet.

#### The formula for calculating resistance

R = V / I
Knowing the total current and the voltage across the whole circuit, we can calculate the total resistance using
Ohm's Law: R = V / I.

## Wire Resistance Calculation Procedure

1. Identify the resistivity (ρ), length (L), and radius (r) of the wire;
2. Calculate the cross-sectional area of the wire using the formula for the area of a circle: A=πr2;
3. Calculate the resistance (R) of the wire using the formula for resistance: R=ρLA R = ρ L A.

We can calculate the resistance of the wire Rwire by multiplying the length of the wire by the resistance per meter.

An example
We have 500m of a 20AWG wire. What will be the total resistance?
Rwire=0.5km⋅33.31Ω/km=16.655Ω

### Relation between Cable Resistance and Cable Length

The relation between cable length and cable resistivity is given by the resistivity formula mentioned above. Resistance is directly proportional to the cable length. This means that any change in the cable length of the material will change its value of resistance.

If the cable resistance of any material is mentioned by R and the length of the cable is mentioned by L, the relationship between the cable resistance and the cable length will be as follows:

R∝L

This means that-

• When the length of the material (L) is increased, its value of resistance (R) also increases.
• When the length of the material (L) decreases, its value of resistance (R) will also decrease.

#### Cable or Wire resistance formulas

 Resistance of the wire R=ρ⋅lA$�=\frac{\rho ·�}{�}$   =lσ⋅A$=\frac{�}{\sigma ·�}$ Length of the wire l=R⋅Aρ$�=\frac{�·�}{\rho }$   =R⋅A⋅σ$=�·�·\sigma$ Wire cross-sectional area A=lR⋅σ$�=\frac{�}{�·\sigma }$   =l⋅ρR$=\frac{�·\rho }{�}$

The relation between cable length and cable resistance can be summarized formula is as below:

For a wire of length L = m = ft
and area A =  cm2
corresponding to radius r = cm
and diameter  inches for common wire gauge comparison
with resistivity = ρ =  x 10^ ohm meters
will have resistance R = ohms.

#### Relation between Resistance, Resistivity, and Electric Current

Resistance
Resistance is the measure of opposition to current flow in a circuit. Its SI unit is the ohm.

Resistivity
Resistivity is the resistance generated by the substance per unit distance for a unit cross-section. Its SI unit is ohm-m.

Electric Current
Electric current is the rate of flow of electrons inside a conductor. Its SI unit is ampere.

### Copper Wire Resistance Chart as AWG system

The copper wire resistance in ohm per meter and for quick reference you will get per 1o meter, per 100 meter ,and per 1000 meter.

 AWG Copper Wire: Resistance Per 1 Ft (Ohms/Ft): Resistance Per 10 Ft (Ohms/10 Ft): Resistance Per 100 Ft (Ohms/100 Ft): Resistance Per 1000 Ft (Ohms/1000 Ft): 0000 (4/0) AWG 0.04901 milliohms (mΩ) 0.4901 milliohms (mΩ) 4.901 milliohms (mΩ) 0.04901 ohms (Ω) 000 (3/0) AWG 0.06180 milliohms (mΩ) 0.6180 milliohms (mΩ) 6.180 milliohms (mΩ) 0.06180 ohms (Ω) 00 (2/0) AWG 0.07793 milliohms (mΩ) 0.7793 milliohms (mΩ) 7.793 milliohms (mΩ) 0.07793 ohms (Ω) 0 (1/0) AWG 0.09827 milliohms (mΩ) 0.9827 milliohms (mΩ) 9.827 milliohms (mΩ) 0.09827 ohms (Ω) 1 AWG 0.1239 milliohms (mΩ) 1.239 milliohms (mΩ) 12.39 milliohms (mΩ) 0.1239 ohms (Ω) 2 AWG 0.1563 milliohms (mΩ) 1.563 milliohms (mΩ) 15.63 milliohms (mΩ) 0.1563 ohms (Ω) 3 AWG 0.1970 milliohms (mΩ) 1.970 milliohms (mΩ) 19.70 milliohms (mΩ) 0.1970 ohms (Ω) 4 AWG 0.2485 milliohms (mΩ) 2.485 milliohms (mΩ) 24.85 milliohms (mΩ) 0.2485 ohms (Ω) 5 AWG 0.3133 milliohms (mΩ) 3.133 milliohms (mΩ) 31.33 milliohms (mΩ) 0.3133 ohms (Ω) 6 AWG 0.3951 milliohms (mΩ) 3.951 milliohms (mΩ) 39.51 milliohms (mΩ) 0.3951 ohms (Ω) 7 AWG 0.4982 milliohms (mΩ) 4.982 milliohms (mΩ) 49.82 milliohms (mΩ) 0.4982 ohms (Ω) 8 AWG 0.6282 milliohms (mΩ) 6.282 milliohms (mΩ) 62.82 milliohms (mΩ) 0.6282 ohms (Ω) 9 AWG 0.7921 milliohms (mΩ) 7.921 milliohms (mΩ) 79.21 milliohms (mΩ) 0.7921 ohms (Ω) 10 AWG 0.9989 milliohms (mΩ) 9.989 milliohms (mΩ) 99.89 milliohms (mΩ) 0.9989 ohms (Ω) 11 AWG 1.260 milliohms (mΩ) 12.60 milliohms (mΩ) 126.0 milliohms (mΩ) 1.260 ohms (Ω) 12 AWG 1.588 milliohms (mΩ) 15.88 milliohms (mΩ) 158.8 milliohms (mΩ) 1.588 ohms (Ω) 13 AWG 2.003 milliohms (mΩ) 20.03 milliohms (mΩ) 200.3 milliohms (mΩ) 2.003 ohms (Ω) 14 AWG 2.525 milliohms (mΩ) 25.25 milliohms (mΩ) 252.5 milliohms (mΩ) 2.525 ohms (Ω) 15 AWG 3.184 milliohms (mΩ) 31.84 milliohms (mΩ) 318.4 milliohms (mΩ) 3.184 ohms (Ω) 16 AWG 4.016 milliohms (mΩ) 40.16 milliohms (mΩ) 401.6 milliohms (mΩ) 4.016 ohms (Ω) 17 AWG 5.064 milliohms (mΩ) 50.64 milliohms (mΩ) 506.4 milliohms (mΩ) 5.064 ohms (Ω) 18 AWG 6.385 milliohms (mΩ) 63.85 milliohms (mΩ) 638.5 milliohms (mΩ) 6.385 ohms (Ω) 19 AWG 8.051 milliohms (mΩ) 80.51 milliohms (mΩ) 805.1 milliohms (mΩ) 8.051 ohms (Ω) 20 AWG 10.15 milliohms (mΩ) 101.5 milliohms (mΩ) 1015 milliohms (mΩ) 10.15 ohms (Ω) 21 AWG 12.80 milliohms (mΩ) 128.0 milliohms (mΩ) 1280 milliohms (mΩ) 12.80 ohms (Ω) 22 AWG 16.14 milliohms (mΩ) 161.4 milliohms (mΩ) 1614 milliohms (mΩ) 16.14 ohms (Ω) 23 AWG 20.36 milliohms (mΩ) 203.6 milliohms (mΩ) 2036 milliohms (mΩ) 20.36 ohms (Ω) 24 AWG 25.67 milliohms (mΩ) 256.7 milliohms (mΩ) 2567 milliohms (mΩ) 25.67 ohms (Ω) 25 AWG 32.37 milliohms (mΩ) 322.7 milliohms (mΩ) 3237 milliohms (mΩ) 32.37 ohms (Ω) 26 AWG 40.81 milliohms (mΩ) 408.1 milliohms (mΩ) 4081 milliohms (mΩ) 40.81 ohms (Ω) 27 AWG 51.47 milliohms (mΩ) 514.7 milliohms (mΩ) 5147 milliohms (mΩ) 51.47 ohms (Ω) 28 AWG 64.90 milliohms (mΩ) 649.0 milliohms (mΩ) 6490 milliohms (mΩ) 64.90 ohms (Ω) 29 AWG 81.84 milliohms (mΩ) 818.4 milliohms (mΩ) 8184 milliohms (mΩ) 81.84 ohms (Ω) 30 AWG 103.2 milliohms (mΩ) 1032 milliohms (mΩ) 10320 milliohms (mΩ) 103.2 ohms (Ω) 31 AWG 130.1 milliohms (mΩ) 1301 milliohms (mΩ) 13010 milliohms (mΩ) 130.1 ohms (Ω) 32 AWG 164.1 milliohms (mΩ) 1641 milliohms (mΩ) 16410 milliohms (mΩ) 164.1 ohms (Ω) 33 AWG 206.9 milliohms (mΩ) 2069 milliohms (mΩ) 20690 milliohms (mΩ) 206.9 ohms (Ω) 34 AWG 260.9 milliohms (mΩ) 2609 milliohms (mΩ) 26090 milliohms (mΩ) 260.9 ohms (Ω) 35 AWG 329.0 milliohms (mΩ) 3290 milliohms (mΩ) 32900 milliohms (mΩ) 329.0 ohms (Ω) 36 AWG 414.8 milliohms (mΩ) 4148 milliohms (mΩ) 41480 milliohms (mΩ) 414.8 ohms (Ω) 37 AWG 523.1 milliohms (mΩ) 5231 milliohms (mΩ) 52310 milliohms (mΩ) 523.1 ohms (Ω) 38 AWG 659.6 milliohms (mΩ) 6596 milliohms (mΩ) 65960 milliohms (mΩ) 659.6 ohms (Ω) 39 AWG 831.8 milliohms (mΩ) 8318 milliohms (mΩ) 83180 milliohms (mΩ) 831.8 ohms (Ω) 40 AWG 1049 milliohms (mΩ) 10490 milliohms (mΩ) 104900 milliohms (mΩ) 1049 ohms (Ω)