Cross-sectional area to diameter conversion circle electric cable wire diameter and wiring and calculation cross section AGW American Wire Gauge area of a wire formula

Conversion and calculation: Round electric cable, wire, and wiring
• Cable diameter to circle cross-sectional area and vice versa •

Cross section is just a two-dimensional view of a slice through an object.
An often asked question: How can you convert the diameter of a round wire d to the
circle cross section surface or the cross-section area A (slice plane) to the cable diameter d?

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The "unit" can be inches, feet, yards meters (metres), centimeters, or millimeters.

Litz wire consisting of many thin wires need a 14 % larger diameter compared to a massive wire.

Cross section is an area.
Diameter is a linear measure.
That cannot be the same.

Calculation of the cross section A, entering the diameter d:

r = radius of the wire or cable
d = diameter of the wire or cable

Calculation of the diameter r, entering the cross section A:
Formula calculate diameter from cross-sectional area

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 three-phase current, whether the cable is released freely, or is placed
under the ground. Also, it depends on 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 rho ρ ist:

Δ V = I · R = I · (2 · e · ρ / A)

I = Current in ampere
e = Wire length in meters (times 2, because there is always a return wire)
ρ = Rho, specific resistance for copper = 0,0178 ohm·mm²/m
(Ohms for 1 m length and 1 mm² cross section area of the wire) ρ = 1 / κ
A = Cross section area in mm²
κ = kappa, specific conductance for copper = 56 S·m/mm²

metal	spec. conductance	spec. resistance
copper	56	0,0178
aluminium	36	0,0277
silber	62	0,0161

Calculator: Ohm's law

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 mm²	0.75 mm²	1.0 mm²	1.5 mm²	2.5 mm²	4.0 mm²	6.0 mm²	10.0 mm²
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 mm²	Resistance in ohm	Power loss at		Damping factor at
Cable length in m	Section in mm²	Resistance in ohm	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

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 used
only in the USA. Sometimes you find AWG numbers also in catalogues and technical data in Europe.

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 mm²	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 mm²	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 mm²	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 mm²	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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