Deutsche Version 
Cross section is just a twodimensional view of a slice through an object. An often asked question: How can you convert the diameter of a round wire d = 2 × r to the circle cross section surface or the crosssection area A (slice plane) to the cable diameter d? Why is the diameter value greater than the area value? Because that's not the same. Resistance varies inversely with the crosssectional area of a wire. The required crosssection of an electrical line depends on the following factors: 1) Rated voltage. Net form. (Threephase (DS) / AC (WS)) 2) Fuse  Upstream backup = Maximum permissible current (Amp) 3) On schedule to be transmitted power (kVA) 4) Cable length in meters (m) 5) Permissible voltage drop (% of the rated voltage) 6) Line material. Copper (Cu) or aluminum (Al) 
The "unit" is usually millimeters but it can also be inches, feet, yards, meters (metres),
or centimeters, when you take for the area the square of that measure.
Litz wire (stranded wire) consisting of many thin wires need a 14 % larger diameter compared to a solid wire.
Cross sectional area is not diameter. 
Cross section is an area. Diameter is a linear measure. That cannot be the same. The cable diameter in millimeters is not the cable crosssection in square millimeters. 
The cross section or the cross sectional area is the area of such a cut. It need not necessarily have to be a circle. Commercially available wire (cable) size as cross sectional area: 0.75 mm^{2}, 1.5 mm^{2}, 2.5 mm^{2}, 4 mm^{2}, 6 mm^{2}, 10 mm^{2}, 16 mm^{2}. 
There are four factors that affect the resistance of a conductor: 1) the cross sectional area of a conductor A, calculated from the diameter d 2) the length of the conductor 3) the temperature in the conductor 4) the material constituting the conductor 
There is no exact formula for the minimum wire size from the maximum amperage. It depends on many circumstances, such as for example, if the calculation is for DC, AC or even for threephase current, whether the cable is released freely, or is placed under the ground. Also, it depends on the ambient temperature, the allowable current density, and the allowable voltage drop, and whether solid or litz wire is present. And there is always the nice but unsatisfactory advice to use for security reasons a thicker and hence more expensive cable. Common questions are about the voltage drop on wires. 
Voltage drop Δ V
The voltage drop formula with the specific resistance (resistivity) ρ (rho) is:
I = Current in ampere l = Wire (cable) length in meters (times 2, because there is always a return wire) ρ = rho, electrical resistivity (also known as specific electrical resistance or volume resistivity) of copper = 0.01724 ohm×mm^{2}/m (also Ω×m) (Ohms for l = 1 m length and A = 1 mm^{2} cross section area of the wire) ρ = 1 / σ A = Cross section area in mm^{2} σ = sigma, electrical conductivity (electrical conductance) of copper = 58 S·m/mm^{2} 

The derived SI unit of electrical resistivity ρ is Ω × m, shortened from the
clear Ω × mm² / m.
The reciprocal of electrical resistivity is electrical conductivity.
Electrical conductor 
Electrical conductivity Electrical conductance 
Electrical resistivity Specific resistance 
silver  σ = 62 S·m/mm²  ρ = 0.0161 Ohm∙mm²/m 
copper  σ = 58 S·m/mm²  ρ = 0.0172 Ohm∙mm²/m 
gold  σ = 41 S·m/mm²  ρ = 0.0244 Ohm∙mm²/m 
aluminium  σ = 36 S·m/mm²  ρ = 0.0277 Ohm∙mm²/m 
constantan  σ = 2.0 S·m/mm²  ρ = 0.5000 Ohm∙mm²/m 
Difference between electrical resistivity and electrical conductivity
The conductance in siemens is the reciprocal of the resistance in ohms. 
To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. 
The value of the electrical conductivity (conductance) and the specific electrical resistance (resistivity) is a temperature dependent material constant. Mostly it is given at 20 or 25°C. 
Resistance = resistivity x length / area
The specific resistivity of conductors changes with temperature. In a limited temperature range it is approximately linear: where α is the temperature coefficient, T is the temperature and T_{0} is any temperature, such as T_{0} = 293.15 K = 20°C at which the electrical resistivity ρ (T_{0}) is known. 
Convert resistance to electrical conductance
Conversion of reciprocal siemens to ohms
1 ohm [Ω] = 1 / siemens [1/S]
1 siemens [S] = 1 / ohm [1/Ω]
To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. 
1 millisiemens = 0.001 mho = 1000 ohms
Mathematically, conductance is the reciprocal, or inverse, of resistance: The symbol for conductance is the capital letter "G" and the unit is the mho, which is "ohm" spelled backwards. Later, the unit mho was replaced by the unit Siemens − abbreviated with the letter "S". 
Table of typical loudspeaker cables
Cable diameter d  0.798 mm  0.977 mm  1.128 mm  1.382 mm  1.784 mm  2.257 mm  2.764 mm  3.568 mm 
Cable nominal cross section A  0.5 mm^{2}  0.75 mm^{2}  1.0 mm^{2}  1.5 mm^{2}  2.5 mm^{2}  4.0 mm^{2}  6.0 mm^{2}  10.0 mm^{2} 
Maximum electrical current  3 A  7.6 A  10.4 A  13.5 A  18.3 A  25 A  32 A   
Always consider, the cross section must be made larger with higher power and higher length of
the cable, but also with lesser impedance. Here is a table to tell the possible power loss.
Cable length in m 
Section in mm^{2} 
Resistance in ohm 
Power loss at  Damping factor at  
Impedance 8 ohm 
Impedance 4 ohm 
Impedance 8 ohm 
Impedance 4 ohm 

1  0.75  0.042  0.53%  1.05%  98  49 
1.50  0.021  0.31%  0.63%  123  62  
2.50  0.013  0.16%  0.33%  151  75  
4.00  0.008  0.10%  0.20%  167  83  
2  0.75  0.084  1.06%  2.10%  65  33 
1.50  0.042  0.62%  1.26%  85  43  
2.50  0.026  0.32%  0.66%  113  56  
4.00  0.016  0.20%  0.40%  133  66  
5  0.75  0.210  2.63%  5.25%  32  16 
1.50  0.125  1.56%  3.13%  48  24  
2.50  0.065  0.81%  1.63%  76  38  
4.00  0.040  0.50%  1.00%  100  50  
10  0.75  0.420  5.25%  10.50%  17  9 
1.50  0.250  3.13%  6.25%  28  14  
2.50  0.130  1.63%  3.25%  47  24  
4.00  0.080  1.00%  2.00%  67  33  
20  0.75  0.840  10.50%  21.00%  9  5 
1.50  0.500  6.25%  12.50%  15  7  
2.50  0.260  3.25%  6.50%  27  13  
4.00  0.160  2.00%  4.00%  40  20 
The damping factor values show, what remains of an accepted damping factor of 200
depending on the cable length, the cross section, and the impedance of the loudspeaker.
Conversion and calculation of cable diameter to AWG
and AWG to cable diameter in mm  American Wire Gauge
The gauges we most commonly use are even numbers, such as 18, 16, 14, etc. If you get an answer that is odd, such as 17, 19, etc., use the next lower even number. AWG stands for American Wire Gauge and refers to the strength of wires. These AWG numbers show the diameter and accordingly the cross section as a code. They are only used in the USA. Sometimes you find AWG numbers also in catalogues and technical data in Europe. 
American Wire Gauge  AWG Chart
AWG number 
46  45  44  43  42  41  40  39  38  37  36  35  34 

Diameter in inch 
0.0016  0.0018  0.0020  0.0022  0.0024  0.0027  0.0031  0.0035  0.0040  0.0045  0.0050  0.0056  0.0063 
Diameter (Ø) in mm 
0.04  0.05  0.05  0.06  0.06  0.07  0.08  0.09  0.10  0.11  0.13  0.14  0.16 
Cross section in mm^{2} 
0.0013  0.0016  0.0020  0.0025  0.0029  0.0037  0.0049  0.0062  0.0081  0.010  0.013  0.016  0.020 


AWG number 
33  32  31  30  29  28  27  26  25  24  23  22  21 
Diameter in inch 
0.0071  0.0079  0.0089  0.0100  0.0113  0.0126  0.0142  0.0159  0.0179  0.0201  0.0226  0.0253  0.0285 
Diameter (Ø) in mm 
0.18  0.20  0.23  0.25  0.29  0.32  0.36  0.40  0.45  0.51  0.57  0.64  0.72 
Cross section in mm^{2} 
0.026  0.032  0.040  0.051  0.065  0.080  0.10  0.13  0.16  0.20  0.26  0.32  0.41 


AWG number 
20  19  18  17  16  15  14  13  12  11  10  9  8 
Diameter in inch 
0.0319  0.0359  0.0403  0.0453  0.0508  0.0571  0.0641  0.0719  0.0808  0.0907  0.1019  0.1144  0.1285 
Diameter (Ø) in mm 
0.81  0.91  1.02  1.15  1.29  1.45  1.63  1.83  2.05  2.30  2.59  2.91  3.26 
Cross section in mm^{2} 
0.52  0.65  0.82  1.0  1.3  1.7  2.1  2.6  3.3  4.2  5.3  6.6  8.4 


AWG number 
7  6  5  4  3  2  1  0 (1/0) (0) 
00 (2/0) (1) 
000 (3/0) (2) 
0000 (4/0) (3) 
00000 (5/0) (4) 
000000 (6/0) (5) 
Diameter in inch 
0.1443  0.1620  0.1819  0.2043  0.2294  0.2576  0.2893  0.3249  0.3648  0.4096  0.4600  0.5165  0.5800 
Diameter (Ø) in mm 
3.67  4.11  4.62  5.19  5.83  6.54  7.35  8.25  9.27  10.40  11.68  13.13  14.73 
Cross section in mm^{2} 
10.6  13.3  16.8  21.1  26.7  33.6  42.4  53.5  67.4  85.0  107.2  135.2  170.5 
How are high frequencies damped by the length of the cable?
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