Wire Gauge Converter — AWG to mm², Diameter, Ω/km

What the calculator does

Wire is sized three ways in the equipment that arrives in Pakistan: by AWG number on American, Chinese and much Far-Eastern equipment, by cross-section in mm² on anything to IEC standards, and by SWG or strand count on older British-pattern wiring and drawings. The converter takes any one of an AWG number, a cross-section in mm² or a bare-conductor diameter in mm and gives the other two, exactly, from the definition of the gauge rather than a lookup table. It then finds the IEC 60228 metric size nearest to that area and the smallest metric size that is at least that area, which is the one to use when an AWG specification has to be met with local cable.

For the conductor it also gives the DC resistance per kilometre for copper or aluminium at 20 °C and at the temperature you choose, the resistance of a run and of its loop, the mass of metal per kilometre and for the run, and the size of the other metal that would have the same resistance. It does not give the current the wire may carry; that depends on the insulation, the installation and the ambient, and the cable sizing calculator handles it.

Formula

Diameter of gauge n: d = 0.127 mm × 92^{(36 − n) ÷ 39}
Area: A = π × d² ÷ 4
Gauge from diameter: n = 36 − 39 × log(d ÷ 0.127) ÷ log 92
Resistance: R = ρ ÷ A × 1 000 (Ω/km, A in mm²) at T °C: × (1 + α × (T − 20))
Mass: kg/km = A (mm²) × density (g/cm³)

The American Wire Gauge is defined in ASTM B258 by two fixed diameters, 0.4600 inch for 0000 (4/0) and 0.0050 inch for 36 AWG, with 39 equal ratio steps between them. Each step therefore multiplies the diameter by 92^1/39 = 1.1229 and the area by 1.2610, so three gauge steps double the area (× 2.005), six double the diameter, and ten multiply the area by ten (× 10.16). The number goes down as the wire gets bigger because it began as the count of drawing passes. Sizes above 0000 are given in kcmil, thousands of circular mils, where 1 kcmil = 0.5067 mm². The gauge describes a solid conductor; a stranded conductor of the same nominal gauge has the same nominal area and a slightly larger overall diameter.

Resistivity is 0.017241 Ω·mm²/m for annealed copper of 100 % IACS conductivity and 0.02826 Ω·mm²/m for electrical-grade aluminium, both at 20 °C, with temperature coefficients of 0.00393 and 0.00403 per °C. Densities are 8.89 g/cm³ for copper and 2.70 g/cm³ for aluminium, and because one mm² of conductor over one kilometre is one litre of metal, kg/km is the area in mm² times the density.

Worked example

A packaging machine imported from the United States has its motor circuits wired in 10 AWG copper, and the panel has to be extended with local cable over a 10 m run at 20 °C.

Diameter: 0.127 × 92^{(36 − 10) ÷ 39} = 0.127 × 92^0.6667 = 0.127 × 20.38 = 2.588 mm.
Area: π × 2.588² ÷ 4 = 5.26 mm². That sits between the 4 and 6 mm² IEC sizes; the nearest is 6 mm² and the next size up is also 6 mm², so 6 mm² local cable meets the 10 AWG specification with 14 % more copper. A 4 mm² "equivalent" would have 24 % less.
Resistance: 0.017241 ÷ 5.26 × 1 000 = 3.28 Ω/km at 20 °C; for the 10 m run 0.0328 Ω, and 0.0655 Ω for the loop there and back. At 20 A the loop drops 1.3 V, 0.57 % of 230 V.
Mass: 5.26 × 8.89 = 46.8 kg of copper per kilometre, 0.468 kg for the 10 m. The same resistance in aluminium needs 5.26 × 0.02826 ÷ 0.017241 = 8.62 mm², so 10 mm² aluminium.

The other gauges seen on imported equipment work out the same way: 12 AWG = 3.31 mm² (next metric size up 4 mm²), 14 AWG = 2.08 mm² (2.5 mm²), 16 AWG = 1.31 mm² (1.5 mm²), 18 AWG = 0.823 mm² (1.0 mm²; 0.75 mm² is nearer but smaller), 20 AWG = 0.518 mm² (0.75 mm²; 0.5 mm² is nearer but smaller), 22 AWG = 0.326 mm² and 24 AWG = 0.205 mm², both below the smallest IEC size of 0.5 mm². In the other direction 2.5 mm² is 13.2 AWG: 13 AWG (2.62 mm²) is the first gauge at least that big, and among the even gauges that are actually stocked it is 12 AWG (3.31 mm²), while 14 AWG has 17 % less copper.

AWG sizes 0000 to 24

AWG	Diameter (mm)	Area (mm²)	Copper Ω/km at 20 °C	Nearest IEC size (mm²)	Next IEC size up (mm²)
0000 (4/0)	11.7	107	0.161	120	120
000 (3/0)	10.4	85.0	0.203	95	95
00 (2/0)	9.27	67.4	0.256	70	70
0 (1/0)	8.25	53.5	0.322	50	70
1	7.35	42.4	0.407	50	50
2	6.54	33.6	0.513	35	35
3	5.83	26.7	0.646	25	35
4	5.19	21.2	0.815	25	25
5	4.62	16.8	1.03	16	25
6	4.12	13.3	1.30	16	16
7	3.66	10.5	1.63	10	16
8	3.26	8.37	2.06	10	10
9	2.91	6.63	2.60	6	10
10	2.59	5.26	3.28	6	6
11	2.30	4.17	4.13	4	6
12	2.05	3.31	5.21	4	4
13	1.83	2.62	6.57	2.5	4
14	1.63	2.08	8.29	2.5	2.5
15	1.45	1.65	10.4	1.5	2.5
16	1.29	1.31	13.2	1.5	1.5
17	1.15	1.04	16.6	1	1.5
18	1.02	0.823	20.9	0.75	1
19	0.912	0.653	26.4	0.75	0.75
20	0.812	0.518	33.3	0.5	0.75
21	0.723	0.410	42.0	0.5	0.5
22	0.644	0.326	53.0	0.5	0.5
23	0.573	0.258	66.8	0.5	0.5
24	0.511	0.205	84.2	0.5	0.5

Every row computed from the ASTM B258 definition and rounded to three significant figures; published tables that round the inch diameter to four decimals differ in the last digit (20 AWG is listed as 0.519 mm² in some). Nearest is on a ratio basis. Only even gauges are normally stocked as building wire; the odd ones exist and are used in magnet wire. Below 0.5 mm² IEC 60228 has no size.

SWG and imperial stranded sizes still met in Pakistan

SWG	Diameter (mm)	Area (mm²)	About the same as
8	4.064	12.97	6 AWG (13.3 mm²)
10	3.251	8.30	8 AWG (8.37 mm²)
12	2.642	5.48	10 AWG (5.26 mm²), 6 mm²
14	2.032	3.24	12 AWG (3.31 mm²)
16	1.626	2.08	14 AWG (2.08 mm²)
18	1.219	1.17	17 AWG (1.04 mm²), 1 mm²
20	0.914	0.656	19 AWG (0.653 mm²)
22	0.711	0.397	21 AWG (0.410 mm²)

Diameters are the defined values of BS 3737, the British Standard Wire Gauge (16 SWG is 0.064 inch), with the areas computed from them; SWG is not a geometric series and its numbers do not line up with AWG, so 16 SWG is 2.08 mm² while 16 AWG is 1.31 mm². The stranded sizes of pre-metric British practice name the strands as count/diameter in thousandths of an inch: 3/029 is three strands of 0.029 inch (0.737 mm) = 1.28 mm²; 7/029 = 2.98 mm²; 7/036 = 4.60 mm²; 7/044 = 6.87 mm²; 7/052 = 9.59 mm²; 7/064 = 14.5 mm². A 7/029 carries more copper than a 2.5 mm², a 3/029 less than a 1.5 mm².

Assumptions and limitations

Solid-conductor geometry. The diameter is that of a solid round conductor of the given gauge or area. A stranded conductor of the same nominal size has the same nominal copper area but an overall diameter about 2–5 % larger, because of the gaps between strands; measure a strand and multiply by the count, or take the diameter over the strands and expect the area to come out high.
The metric equivalence is by area, not by current. Nearest and next-up sizes compare copper cross-sections only. The current a conductor may carry is fixed by its insulation temperature rating and the installation, and a 12 AWG conductor rated for 20 A under NEC rules and a 4 mm² conductor rated under IEC 60364-5-52 are rated by different tables for different conditions; convert the size, then rate the cable by the rules that apply to the installation.
DC resistance of pure metal. The resistance is for 100 % IACS copper or electrical-grade aluminium. IEC 60228 specifies conductors by maximum resistance, and its class 2 stranded values are a few per cent above the solid figure here (7.41 Ω/km for 2.5 mm² against 6.90 computed); class 5 flexible conductors are higher again, and tinned wire slightly higher still. At 50 Hz the AC resistance of conductors up to about 50 mm² is the DC value for practical purposes.
Temperature correction is linear. The factor 1 + α(T − 20) is accurate over the −40 to 120 °C range offered; the coefficient is that of the pure metal.
No ampacity, no voltage-drop limit. The resistance of the loop lets you compute a voltage drop for a known current, but the limit and the installation derating are in the voltage drop and cable sizing calculators.

Frequently asked questions

Why do AWG numbers go down as the wire gets bigger?

Because the gauge number was originally the number of times the wire had been pulled through a die. Each pass through a smaller die makes the wire thinner, so more passes mean a finer wire and a higher number. ASTM B258 later fixed the series as a geometric one with 39 steps from 0000 to 36, but kept the direction. Sizes larger than 0000 abandon the gauge altogether and are quoted in kcmil.

Is 2.5 mm² the same as 14 AWG?

No. 14 AWG is 2.08 mm²; 2.5 mm² is 20 % more copper and corresponds to 13.2 AWG. The two are often called equivalent because both are the standard size for 20 A circuits in their own systems, under their own rules; as conductors they are not the same. Replacing 2.5 mm² with 14 AWG puts 20 % more resistance and 20 % more voltage drop into the circuit; replacing 14 AWG with 2.5 mm² is the safe direction.

What does 7/029 mean?

Seven strands, each 0.029 inch (0.737 mm) in diameter: 7 × π × 0.737² ÷ 4 = 2.98 mm² of copper. It is the imperial British stranded size that preceded the metric 2.5 mm² and it is still how much of the wire trade in Pakistan names cable. The related sizes are 3/029 (1.28 mm²), 7/036 (4.60 mm²), 7/044 (6.87 mm²), 7/052 (9.59 mm²) and 7/064 (14.5 mm²). The name tells you exactly how much copper there should be, which makes an under-gauge cable easy to catch with a micrometer on one strand.

What is MCM or kcmil?

A circular mil is the area of a circle 0.001 inch across, and kcmil (older texts say MCM) is a thousand of them: 1 kcmil = 0.5067 mm². American conductors larger than 0000 AWG (211.6 kcmil, 107 mm²) are named this way: 250 kcmil = 126.7 mm², 350 kcmil = 177 mm², 500 kcmil = 253 mm². To convert, multiply kcmil by 0.5067; the next IEC size up is usually the honest equivalent.

Can I use a 12 AWG cable where 4 mm² is specified?

No, not without checking the design. 12 AWG is 3.31 mm², 17 % less copper than 4 mm², so its resistance and voltage drop are 21 % higher and its current-carrying capacity lower in the same installation. If the 4 mm² was chosen with margin the 12 AWG may still be adequate, but that has to be shown with the cable sizing calculation, not assumed from a conversion table. 10 AWG (5.26 mm²) meets the specification outright.

Why does the converter not give the current rating?

Because the conductor size does not fix it. The same 2.5 mm² copper carries about 27 A clipped to a wall, 24 A in conduit on the wall, 18.5 A in a thermally insulated wall, and less again when grouped with other circuits or in a hot roof space, under IEC 60364-5-52; with 90 °C XLPE insulation each of those rises by about 30 %. The rating is a property of the installation, and the cable sizing calculator applies the tables and the correction factors.

References

ASTM B258-18, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors — the definition of the gauge: 0.4600 in at 0000, 0.0050 in at 36, 39 geometric steps
BS 3737:1964, Specification for Standard Wire Gauge (SWG) — the defined SWG diameters; withdrawn, but still the reference for the gauge
IEC 60228:2004, Conductors of insulated cables — nominal cross-sections, conductor classes 1, 2, 5 and 6, and maximum resistance at 20 °C
IEC 60028:1925, International standard of resistance for copper — the IACS reference: 0.017241 Ω·mm²/m at 20 °C for annealed copper
IEC 60287-1-1:2006, Electric cables — Calculation of the current rating — Part 1-1: Current rating equations (100 % load factor) and calculation of losses — resistivities and temperature coefficients of copper and aluminium
IEC 60364-5-52:2009, Low-voltage electrical installations — Part 5-52: Wiring systems — the current-carrying capacities that a conversion cannot supply

Last reviewed 2026-09-20.