How do I convert AWG to mm²?

Work out the wire diameter from the gauge, then take the area of that circle. American Wire Gauge is a geometric series: the diameter in inches is 0.005 × 92^((36 − n)/39). Turn that into millimetres, and the area is π × (d ÷ 2)². This tool runs the whole chain from the gauge number you enter.

What is the formula behind the gauge numbers?

Every step in AWG multiplies the diameter by the same ratio, the 39th root of 92. Number 36 is pinned at 0.005 inch and number 0000 at 0.46 inch, and the 40 sizes between are geometric steps. Because it is a formula and not a chart, the tool computes each size rather than looking it up.

How do I enter the big sizes like 4/0?

Type them as they are written — 1/0, 2/0, 3/0 and 4/0, or the zero forms 0, 00, 000 and 0000. Internally those are gauge numbers 0, −1, −2 and −3, and the same formula covers them, so 4/0 comes out at about 107 mm².

What is a kcmil and why is it shown?

A circular mil is the area of a circle one mil (a thousandth of an inch) across, and a kcmil is a thousand of them — the unit North American conductors above 4/0 are sized in. It is simply the diameter in mils, squared, divided by 1000, so the tool reports it alongside the mm² figure.

AWG a mm²

Every figure here is the AWG geometry worked out with a calculator — a diameter turned into an area. It is a size conversion only, and says nothing about what current a conductor may carry; that is governed by your code book and the conditions of the run.

Enter a gauge and the tool gives you the conductor diameter, the metric cross-section in mm², and the North American kcmil figure. Enter an area in the second box instead and it reports the gauge that lands closest — useful when a European spec quotes only mm². The gauge is a name and stays a name in both systems; the diameter line leads with inches or millimetres to match the site's Imperial · Metric setting.

Ejemplo resuelto

For 12 AWG, n = 12, so the diameter is 0.005 × 92^((36 − 12) ÷ 39) = 0.005 × 92^(0.615) ≈ 0.0808 in, which is about 2.05 mm. The area is π × (2.05 ÷ 2)² ≈ 3.31 mm². That same diameter is 80.8 mils, so the area is 80.8² ÷ 1000 ≈ 6.53 kcmil.

En la obra

A metric drawing on an AWG shelf. The schedule says 2.5 mm². Type it in the cross-section field and the tool walks the formula backwards to the nearest gauge — and there is no gauge that is 2.5: 14 AWG works out to 2.08 mm² and 12 AWG to 3.31. Which one the job takes is a question for the spec and the book, but at least you know neither is "the same".

The three shortcuts hiding in the formula. Because the diameter changes by 92^(1/39) per gauge number, every 3 numbers doubles the area (92^(3/39) = 1.416 on the diameter, 2.0 on the area), every 6 numbers doubles the diameter, and every 10 numbers is ten times the area. So if 12 AWG is 3.31 mm², 9 AWG is about 6.6 and 2 AWG about 33 — near enough to check a number without a calculator.

The aught sizes. 1/0 is n = 0, 2/0 is −1, 3/0 is −2 and 4/0 is −3. Put 4/0 in: d = 0.005 × 92^(39/39) = 0.46 in = 11.7 mm, area 107 mm². Above 4/0 the trade switches to kcmil, and a kcmil is 0.5067 mm² — 250 kcmil is 127 mm².

Pruebe un ejercicio

Quick referencefor gauge

The definition: d (in) = 0.005 × 92^((36 − n) ÷ 39) · 36 AWG = 0.005 in · 0000 = 0.46 in
Área: mm² = 0.7854 × (d × 25.4)² · kcmil = (d in mils)² ÷ 1,000
Shortcuts: 3 numbers = 2× area · 6 numbers = 2× diameter · 10 numbers = 10× area
Aughts: 1/0 → n = 0 · 2/0 → −1 · 3/0 → −2 · 4/0 → −3
kcmil: 1 kcmil = 0.5067 mm² · 250 kcmil = 127 mm²
What this page does not do: ampacity — size is geometry; what it carries is the code book's

Mistakes to catchbefore you trust the number

Reading a wire's overall (insulated) diameter as the conductor diameter — the gauge formula describes bare copper, and a jacketed 12 AWG measures well over its 2.05 mm.
Typing 0 when you mean 1/0: the tool takes 0, 00, 000, 0000 or 1/0…4/0, but a 0 with no context is one size smaller than 00.
Expecting a metric cable's 2.5 mm² to be 'a 12 AWG'. The nearest-gauge line rounds, and a 2.5 mm² (3.31 mm² for 12) sits between 13 and 14 — the tool says which is nearest, not which is equal.

What an inspector looks forthe electrical inspector

On this part of the job

The size printed on the conductor against the size on the drawing and the size the load calculation assumed. An inspector reads the cable marking, not your notes.
Metric cable used on a job specified in AWG, or the reverse. The nearest gauge is not the same gauge, and whether the substitution is acceptable is a code question, not an arithmetic one.
Terminations rated for the conductor — including lugs sized for the actual conductor, and the right lug for aluminium if that is what is installed.
That a conductor sized up for voltage drop has taken the bonding conductor with it where the rules require.

Have this ready

Cable markings visible at both ends.
The drawing or schedule the sizes were specified on.
Your code book for the conductor properties table.

Every figure an inspector measures against comes from the code your jurisdiction has adopted, the stamped drawing, or the manufacturer's printed instructions — so none of them are printed here. Look the number up in your own book, type it into the tool, and the arithmetic is yours.

La fórmula

d(in) = 0.005 × 92^((36 − n) ÷ 39) · area = π × (d ÷ 2)²

AWG is defined, not tabulated: 36 gauge is fixed at 5 thousandths of an inch, 0000 at 0.46 inch, and each of the 40 steps between multiplies the diameter by the same ratio, the 39th root of 92. Because the sizes follow a rule, this page computes them from the rule rather than storing a gauge chart.

Preguntas

How do I convert AWG to mm²?: Work out the wire diameter from the gauge, then take the area of that circle. American Wire Gauge is a geometric series: the diameter in inches is 0.005 × 92^((36 − n)/39). Turn that into millimetres, and the area is π × (d ÷ 2)². This tool runs the whole chain from the gauge number you enter.
What is the formula behind the gauge numbers?: Every step in AWG multiplies the diameter by the same ratio, the 39th root of 92. Number 36 is pinned at 0.005 inch and number 0000 at 0.46 inch, and the 40 sizes between are geometric steps. Because it is a formula and not a chart, the tool computes each size rather than looking it up.
How do I enter the big sizes like 4/0?: Type them as they are written — 1/0, 2/0, 3/0 and 4/0, or the zero forms 0, 00, 000 and 0000. Internally those are gauge numbers 0, −1, −2 and −3, and the same formula covers them, so 4/0 comes out at about 107 mm².
What is a kcmil and why is it shown?: A circular mil is the area of a circle one mil (a thousandth of an inch) across, and a kcmil is a thousand of them — the unit North American conductors above 4/0 are sized in. It is simply the diameter in mils, squared, divided by 1000, so the tool reports it alongside the mm² figure.

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