Wire gauge — AWG sizes, conversions, and the Brown & Sharpe formula

Use the wire gauge calculator

Enter your load, run length, and conductor material. The calculator picks the smallest standard AWG (or mm²) that satisfies both NEC 310.16 ampacity and your voltage-drop limit, then prints the recommended breaker and equipment grounding conductor. AC and DC modes are both supported — for low-voltage DC (12 V or 24 V) the same engine applies the doubled voltage-drop coefficient automatically.

What is wire gauge?

Wire gauge is a designation that maps a single number to a conductor's diameter and cross-section area. The two systems used commercially are AWG (American Wire Gauge, also known as Brown & Sharpe), used in the US, Canada, Mexico, parts of Latin America, and Japan; and mm² per IEC 60228, used in Europe, the UK, Australia, New Zealand, and most of the rest of the world. AWG is dimensionless; mm² is the cross-section in square millimetres rounded to a standard ladder of values.

The AWG count was originally a literal count of how many drawing passes the wire took. Manufacturing started with a thick rod and pulled it through progressively smaller dies. Each pass thinned the wire by a small fixed ratio. So a "1 AWG" wire was drawn through one die; a "36 AWG" wire was drawn through thirty-six dies and is very fine. This is why a lower AWG number means a thicker wire.

When the system was formalised by Joseph R. Brown of Brown & Sharpe in 1857, the geometric ratio between consecutive sizes was fixed at the 39th root of 92 — about 1.123. Three useful properties follow: every 6 numbers down doubles the area; every 3 numbers down doubles the resistance per unit length; every 10 numbers down increases the area roughly 10-fold. These ratios make mental arithmetic easy and explain why standard AWG sizes (2, 4, 6, 8, 10, 12, 14) are spaced by 2.

The Brown & Sharpe formula

The diameter of an AWG conductor is given by a single closed-form expression. It works for sizes 36 AWG through 4/0; sizes larger than 4/0 use kcmil instead.

For 4/0 use n = −3, for 3/0 use n = −2, for 2/0 use n = −1, for 1/0 use n = 0. Multiply the diameter by 25.4 to get millimetres. Cross-section area follows from A = π × (D/2)². The ratio between consecutive sizes is 92^(1/39) ≈ 1.123 — a 12.3% change in diameter per AWG step, which is a 26% change in area and a 26% change in resistance per metre.

For ASTM-rated stranded conductors the diameter is slightly larger than the solid equivalent because of strand interstitial gaps, so the listed mm² is for the nominal copper area only. NEC 310.16 ampacity uses solid-equivalent area for both solid and stranded conductors.

How to read wire gauge, step by step

1. Identify which gauge system you are working in. AWG (Brown & Sharpe) for the US, Canada, Mexico, and Japan; mm² (IEC 60228) for Europe, Australia, NZ, and the rest of the world. SWG (Birmingham) is a third, older British system used for crafts and jewellery — never use SWG values for electrical wire.
2. Read AWG numbers correctly: lower number = thicker wire. AWG counts how many drawing passes a wire was pulled through. 36 AWG was drawn 36 times → very fine. 1 AWG was drawn once → thick. The system is geometric: every 6 numbers down doubles the cross-section area, every 3 numbers down halves the resistance per metre.
3. Convert AWG to mm² when crossing standards. Use the conversion table on this page. 14 AWG = 2.08 mm² (not 2.5), 12 AWG = 3.31 mm² (not 4), 10 AWG = 5.26 mm² (not 6). The IEC mm² ladder rounds to convenient values; AWG-derived areas do not fall on the same numbers. Always look up — never round mentally.
4. For sizes above 4/0, use kcmil. AWG runs from 40 down to 4/0. Above 4/0, conductor sizes use kcmil (thousand circular mils). 250 kcmil ≈ 127 mm², 500 kcmil ≈ 253 mm², 1000 kcmil ≈ 507 mm². Service entrances and large feeders work in kcmil.
5. Pair gauge with conductor material. Same AWG of aluminium has 60% more resistance than copper. So an aluminium wire needs to be 1–2 AWG sizes larger than copper for the same ampacity. NEC 310.16 codifies this: 50 A → 8 AWG Cu but 6 AWG Al; 200 A → 2/0 Cu but 4/0 Al.
6. Verify the wire is solid, stranded, or compact as suited. Solid for 14/12/10 AWG residential branch wiring (grips screws firmly). Stranded for 8 AWG and larger, and for any flexible run. Compact-stranded (compressed) for tight conduits — same copper area, smaller outer diameter. Never use copper-clad aluminium (CCA) on a 20 A circuit.

AWG ↔ mm² ↔ kcmil conversion table

Standard AWG sizes used for electrical wire, with their solid-equivalent diameters, areas, and DC resistance per kilometre at 20°C for copper.

Two patterns to memorise: the circular-mil-area in kcmil doubles every 3 AWG numbers (4/0 = 212 kcmil ≈ 8 × the 26.2 of 6 AWG, with 6 → 4/0 spanning 9 numbers ≈ 2³ ≈ 8×). And resistance halves every 3 AWG numbers — 14 AWG is 8.45 Ω/km, 8 AWG (3 down ×2) is 2.10 Ω/km.

AWG vs mm² — how the two systems compare

AWG is a discrete sequence (each integer is a fixed size). mm² is also discrete, but rounded to round numbers like 1.5, 2.5, 4, 6, 10, 16. The IEC mm² ladder does not align exactly with AWG-derived areas — 14 AWG is 2.08 mm², not 2.5; 12 AWG is 3.31 mm², not 4; 10 AWG is 5.26 mm², not 6. So conductor selection across standards needs a real table, not a one-line conversion.

For voltage-drop calculations, what actually matters is the physical mm² area, not the label. A 12 AWG wire has 3.31 mm², so its drop is greater than a 4 mm² European wire of the same length and current. This is why the calculator on this page works in physical units internally and only labels the result in AWG or mm² at the end.

Variants and edge cases

Solid vs stranded

For a given AWG, a stranded conductor has slightly larger overall diameter than the solid equivalent — the strands have small gaps between them. The nominal copper area is still the AWG-defined value. Stranded wire is more flexible (essential above 8 AWG and on portable cords) but slightly larger in conduit fill. NEC Chapter 9 Tables 4 & 5 use stranded outer-diameter for conduit fill; the resistance-per-metre value is for the same copper area regardless of stranding.

Compact and compressed strands

"Compact" and "compressed" strandings reduce the gaps between strands by mechanical compaction. Compact 4/0 Cu has the same copper area as ordinary 4/0 stranded but ~10% smaller outer diameter — useful in tight conduits. Resistance and ampacity are unchanged.

Sizes above 4/0

The AWG geometric series stops at 4/0 (n = −3). Above that, conductors use kcmil (thousand circular mils). 250 kcmil ≈ 127 mm², 500 kcmil ≈ 253 mm², 1000 kcmil ≈ 507 mm². For very large feeders (>2000 kcmil), parallel sets of 500 or 750 kcmil are nearly always preferred over a single huge cable, both for cost and bending radius.

Solid copper vs copper-clad aluminium (CCA)

CCA is a steel or aluminium core with a thin copper skin. NEC permits CCA only for specific low-current applications and bans it for general residential branch circuits. CCA has higher resistance per AWG than solid copper — never use a CCA wire on a 20 A circuit just because its label says "12 gauge."

Specialty applications: solar PV, speaker, and 12 V DC

For above-roof PV string runs, NEC Article 690 typically calls for 10 AWG XHHW-2 or PV-rated cable on the DC side; many residential strings use 10 gauge PV wire (10 AWG copper, ~5.26 mm²) sized for 1.56× short-circuit current. Speaker cable in home audio uses 12 AWG for runs over 15 m and 16 AWG for short runs — the common audiophile-grade cable is just stranded copper sized by the same Brown & Sharpe geometry as branch wiring. For 12 V DC and 24 V automotive or marine systems, voltage drop dominates: a 20 A draw at 12 V on 14 AWG drops about 1 V per 5 m one-way, so DC wire-gauge sizing usually ends up two to four AWG numbers larger than the ampacity table alone would suggest.

A short history of AWG

AWG was created by Joseph R. Brown at Brown & Sharpe in 1857 to replace the chaotic mix of wire-gauge systems then used by US manufacturers. Each manufacturer had its own gauge — even the same numbered size meant different diameters at different mills. Brown's idea was to fix a single geometric progression with mathematically clean ratios, so any size could be derived from a formula instead of a chart.

The choice of 92 as the base was picked so that the diameter ratio between size 4/0 and size 36 came out to exactly 92 — both sizes being the most common in industry at the time (4/0 for power, 36 for very fine instrument wire). The 39th root then made the spacing fine enough to give one number per practical size step. ASTM standardised the system in 1893, and it has been unchanged since.

Outside the US, the metric mm² system spread with the international cable industry in the 1920s and was codified by IEC in 1953 (IEC 60228). The two systems coexist today — AWG for the Americas and Japan, mm² for everywhere else — and most wire is dual-marked.

Related calculators and references

Frequently asked questions

Why does a lower AWG number mean a thicker wire?

AWG is a count of how many drawing passes were used to make the wire. Each pass through a smaller die thinned the wire. So 36 AWG (the original "smallest" size) was drawn 36 times and is very fine; 1 AWG was drawn just once. The system was geometric, not arithmetic — every six AWG numbers down doubles the area, every three numbers down doubles the resistance.

What is the formula for AWG to mm?

For sizes 36 AWG through 0000 AWG (4/0), the Brown & Sharpe formula gives the diameter exactly: D (inch) = 0.005 × 92^((36 − n) / 39), where n is the AWG number. For 4/0 use n = −3, for 3/0 use n = −2, for 2/0 use n = −1, for 1/0 use n = 0. Multiply by 25.4 to convert to mm. Cross-section area in mm² = π × (D/2)².

How do I convert AWG to mm²?

Use the table on this page or compute it directly. Going down 6 AWG numbers ≈ doubles the cross-section area: 14 AWG ≈ 2.08 mm², 8 AWG ≈ 8.37 mm² (≈4×), 2 AWG ≈ 33.6 mm² (≈4×). Commercial wire follows IEC 60228 standard mm² values (2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, 300, 400) which do not exactly equal the AWG-derived areas.

What is kcmil?

"kcmil" stands for thousand circular mils, the unit AWG numbering uses for conductors larger than 4/0. One circular mil is the area of a circle 1 mil (0.001 inch) in diameter. So 250 kcmil = 250 000 circular mils ≈ 127 mm². Sizes used: 250, 300, 350, 400, 500, 600, 700, 750, 800, 900, 1000, 1250, 1500, 1750, 2000 kcmil.

Is wire gauge the same as Standard Wire Gauge (SWG)?

No. SWG (also called Imperial Standard Wire Gauge or Birmingham Wire Gauge B&W) was a British system for telegraph wire and is still used for jewellery and crafts. AWG (Brown & Sharpe) is the US standard for electrical conductors. Their numbers do not match: 12 SWG = 0.104 in, 12 AWG = 0.0808 in. Always check which standard a chart or product is using.

How does gauge affect ampacity?

Cross-section area drives heat dissipation: larger area = more amps. NEC 310.16 codifies this: 14 AWG carries 15 A, 12 AWG carries 20 A, 10 AWG carries 30 A — roughly doubling current capacity for every six AWG steps down (which doubles area). The relation is not linear because heat dissipation scales with surface area while loss scales with cross-section.

What gauge wire for typical projects?

Lighting and 15 A receptacles → 14 AWG; 20 A kitchen / bathroom receptacles → 12 AWG; electric dryer (30 A) → 10 AWG; range or EV charger (50 A) → 6 AWG; workshop / detached-garage feeders at 70 A → 4 AWG; 100 A subpanel → 3 AWG (or 4 AWG under the dwelling-unit reduction in NEC 310.12); 200 A service entrance → 2/0 AWG copper or 4/0 AWG aluminium. Long runs need a size up — see the calculator on this page.

What is 4 AWG used for?

Wire gauge 4 (5.19 mm diameter, 21.2 mm² area) sits between branch and feeder territory. NEC 310.16 ampacity at 75°C is 85 A copper / 65 A aluminium, which makes it the standard for 60–80 A subpanel feeders, 70 A garage / workshop feeders, large welder branches, and dwelling-unit 100 A service-entrance under NEC 310.12 (which allows 4 AWG Cu for 100 A service feeder with 83% reduced ampacity). It is also the typical EV charger conductor for 60 A continuous (75 A breaker → 4 AWG copper).

Sources and methodology

1. ASTM. ASTM B258 — Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes.
2. NFPA. National Electrical Code (NEC) NFPA 70, 2023 Edition. Chapter 9 Table 8 (conductor properties), Article 310.
3. IEC. IEC 60228:2004 Conductors of insulated cables (mm² standard sizes).
4. NEMA. NEMA WC 70 / ICEA S-95-658 Power Cables Rated 2000 Volts or Less.
5. BS / IET. BS 7671:2018+A2:2022 Requirements for Electrical Installations (Wiring Regulations), Table 4D.
6. Brown, J. R. (1857). Original Brown & Sharpe gauge specification — historical record.