Wire Gauge Converter

A wire gauge converter turns a number from one naming convention into every other naming convention, the same way a length converter turns inches into millimetres. The numbers people deal with in the workshop or the project notebook are written as labels, "AWG 14", "SWG 18", "2.5 mm²", "1.6 mm diameter", "0.064 inch", but each of those labels means a specific diameter, a specific cross-sectional area, a specific resistance per metre, and a specific current-handling range under the same standard. Wiring that up across all six representations at once is what this calculator does. The anchor references are ASTM B258 for the AWG diameter formula, IEC 60228 for the international conductor cross-section conventions, and the standard resistivity of annealed copper of 1.724 × 10⁻⁸ Ω·m at 20 °C (the IACS 100 % IACS reference). The ampacity column is guidance, not a specification, and the explicit caveat about insulation, bundling, and ambient temperature sits in plain view rather than in a footnote.

The reason a converter like this exists at all is that the wire-gauge labels the world uses are not universal. American Wire Gauge (AWG) is the dominant standard in North America, the British Standard Wire Gauge (SWG) is preserved in legacy British equipment, aftermarket guitar pickups and parts catalogues, and Birmingham Wire Gauge (BWG) is the standard for steel tubing and sheet metal rather than electrical copper. By historical accident, "wire gauge" sounds like one family of measurements, but the diameters attached to the same gauge number are different between systems. AWG 14 is 1.628 mm in diameter, SWG 14 is 2.032 mm, BWG 14 is 2.108 mm. Picking the gauge system that matches the wire's physical label, and then translating the value into every other representation, is the cleanest way to avoid the most common wiring mistake of all.

How to Use This Calculator

1. Pick the standard the wire is labelled with. AWG covers most North American electronics and chassis wiring, SWG covers older British equipment and aftermarket pickup windings, BWG covers steel tubing, mm and inch cover metric and imperial engineering drawings, and mm² covers European electrical drawings.
2. Type the labelled value into the input box. Integer gauge numbers are accepted for AWG, SWG, and BWG; decimal values are accepted for mm, inch, and mm².
3. Read the equivalent-values panel. The panel reports the canonical diameter in mm / inch / mil, the cross-sectional area in mm², the nearest integer AWG, and the nearest tabulated SWG and BWG.
4. Read the resistance panel. DC resistance per km and mΩ per metre is given for solid copper at 20 °C. R in Ω/km and R in mΩ/m are numerically the same value, so the same number appears under both labels with the right unit symbol attached.
5. Use the ampacity table for chassis-wiring guidance. The AWG nearest your input is highlighted in green with its chassis-wiring ampacity range restated below the table.
6. Cross-reference to the other gauge systems. If your input is in AWG, the panel also reports the nearest SWG and BWG for the same diameter, useful for older documentation and parts-list verification.

The Three Gauge Systems

AWG, SWG, and BWG are three different conventions that came out of the same industrial-revolution window of the nineteenth century, each defined by its own national committee.

American Wire Gauge (AWG) was introduced by J. R. Brown in 1857 for the manufacturing of telegraphic cables and was formalised as ASTM B258 in 1957 (reaffirmed multiple times; current edition B258-14). The defining equation is exact:

d_n = 0.127 × 92^((36 − n) / 39) millimetres

with negative indices used to denote gauges thicker than AWG 0 (AWG 4/0 = index −3 = 11.684 mm diameter). The exponent (36 − n) / 39 means each two-gauge step roughly doubles the cross-sectional area, and the 0.127 mm (5 mil) constant anchors the table at the AWG 36 end. AWG is the dominant standard for North American electronics, chassis wiring, and almost any spec sheet you read.

British Standard Wire Gauge (SWG) was the British hardware industry's answer to the same problem, formalised as British Standard BS 3737 and adopting the historical Standard Wire Gauge table. SWG diameters are tabulated in millimetres rather than given by a closed-form equation. The defining values for the common sizes are SWG 14 = 2.032 mm, SWG 16 = 1.626 mm, SWG 18 = 1.219 mm, SWG 20 = 0.914 mm, SWG 22 = 0.711 mm, and SWG 24 = 0.559 mm. SWG is preserved in legacy British equipment and aftermarket guitar-pickup wire, but it is rarely used for new designs.

Birmingham Wire Gauge (BWG) was developed in Birmingham, England around the same period as SWG but for steel rather than electrical copper. BWG diameters are also tabulated. The defining values include BWG 14 = 2.108 mm, BWG 16 = 1.651 mm, BWG 18 = 1.245 mm, BWG 20 = 0.889 mm, BWG 22 = 0.711 mm (which is the famous coincidence, same numerical gauge, same diameter as SWG 22), and BWG 24 = 0.559 mm. BWG is the standard for steel tube and sheet-metal wall-thickness specifications; you should not use it for electrical copper unless the steel-tubing convention is what was actually intended.

Note how close SWG and BWG are at gauge 22 and gauge 24, and how far AWG is from both for the same gauge number. This is exactly the gap that causes cross-system confusion.

The Conversion Formulas

The AWG-to-diameter formula is exact:

d_n = 0.127 × 92^((36 − n) / 39) mm (ASTM B258)

For SWG and BWG, the diameters are tabulated rather than derived, so the calculator uses the standard published tables and finds the closest tabulated entry when converting back from a physical dimension.

The cross-sectional area follows the standard geometric relation:

A = π × (d / 2)² = π × d² / 4 (square millimetres for d in mm)

The inverse, going from cross-sectional area back to diameter, is d = sqrt(4 × A / π), and the gauge number that corresponds to that diameter uses the natural-log rearrangement of ASTM B258's equation: n = 36 − 39 × ln(d / 0.127) / ln(92). The result is in most cases a non-integer (gauge 13.21, for instance), which means the round-AWG number is just the nearest tabulated diameter and the precise AWG index is only meaningful when the input diameter is itself one of the B258 table entries.

The resistance per km for any solid conductor follows:

R (Ω / km) = ρ × L / A = ρ × 1000 / A(m²) = ρ × 10³ / A(m²)

For annealed copper at 20 °C, ρ = 1.724 × 10⁻⁸ Ω·m (100 % IACS, the International Annealed Copper Standard). Putting the numbers together gives the compact form used in every wire-data table:

R (Ω / km) = 17.24 / A(mm²) (copper at 20 °C)

Numerically, R (Ω/km) and R (mΩ/m) are the same value: 8.286 mΩ/m at AWG 14 reduces to 0.008286 Ω/m, which is 8.286 Ω/km. The relation holds for any size.

For aluminium at 61 % IACS, the same calculation gives roughly 1.6 × higher resistance for the same cross-section, so an AWG 14 aluminium conductor has about 13 mΩ/m. For stranded conductor, the actual copper cross-section is slightly larger than the nominal size because the geometry of the bundle leaves inter-strand air gaps; copper-density corrections of ~3 % are typical when measured resistance is back-converted to a cross-section.

Worked Examples

The numerical-test cases in the FAQ section reproduce published B258 values to within 0.001 mm. Three restated here with the underlying arithmetic:

AWG 14 → 1.628 mm → 2.08 mm². Compute the diameter: d = 0.127 × 92^((36 − 14)/39) = 0.127 × 92^(22/39) = 0.127 × 12.816 = 1.6277 mm. Compute the area: A = π × 1.6277² / 4 = π × 2.6494 / 4 = 2.0809 mm². Compare to the standard published value of 1.628 mm and 2.08 mm² (B258 Table 1): agreement to four significant figures.

AWG 24 → 0.5106 mm → 0.2047 mm². Compute the diameter: d = 0.127 × 92^((36 − 24)/39) = 0.127 × 92^(12/39) = 0.127 × 4.0269 = 0.5114 mm (technically 0.5106 mm once the exact B258 table value is rounded to four figures, but the formula gives 0.5114). Compute the area: A = π × 0.5106² / 4 = π × 0.2607 / 4 = 0.2047 mm². The standard published value is 0.511 mm and 0.205 mm² for AWG 24, so the agreement is again within the rounding tolerance of the published table.

2.5 mm² → diameter 1.784 mm → gauge ≈ 13.21. Compute the diameter: d = sqrt(4 × 2.5 / π) = sqrt(3.1831) = 1.7841 mm. Compute the gauge: n = 36 − 39 × ln(1.7841 / 0.127) / ln(92) = 36 − 39 × ln(14.05) / 4.5218 = 36 − 39 × 2.6408 / 4.5218 = 36 − 22.78 = 13.21. So a 2.5 mm² cross-section falls between gauge 13 and gauge 14, sitting slightly closer to gauge 13. This is the metric size most commonly used in domestic European electrical wiring (2.5 mm² nominal), which sits just below AWG 13 (2.628 mm², 2.052 mm diameter).

Resistance sanity check for AWG 14. R = 17.24 / 2.0809 = 8.285 mΩ/m. That is the published "8.3 mΩ/m at 20 °C" figure you see in every wire-data table. For AWG 12 with A = 3.31 mm², R = 17.24 / 3.31 = 5.21 mΩ/m, the published "5.2 mΩ/m" figure. The same calculation reproduces every entry in the published resistance table to four significant figures when carried out through the formula rather than read from a precomputed chart.

Where Wire-Gauge Conversion Shows Up

Wire-gauge conversion appears across a wide slice of electrical and electronic work. Knowing which gauge system the wire is labelled with is the first step in every one of these contexts.

Domestic and commercial building wiring. The metric cable cross-section sizes (1.5 mm², 2.5 mm², 4 mm², 6 mm², 10 mm²) used in Europe correspond to AWG sizes from about AWG 16 (1.31 mm²) up to AWG 8 (8.37 mm²). Reading North American documentation against European installation practice requires the conversion every time.

Automotive and vehicle wiring. SAE J1128 specifies low-voltage primary cable for road-vehicle applications, using AWG sizes from AWG 26 (signal) up to AWG 4/0 (battery and inverter). German DIN-style metric wire uses mm² cross-sections. Aftermarket harness sourcing in particular jumps between AWG and metric dozens of times in a build.

Audio and musical-instrument electronics. Aftermarket pickup windings use AWG 42 to AWG 38 for the coil wire and SWG (preserved from British pickup makers) for the lead-out wire. The two systems are close enough for the same numerical gauge to mean the same wire by accident for some sizes, but not for all, and the calculator gives a faster answer than flipping between reference cards.

Robotics and motion control. Stepper motor and DC motor windings use AWG in older designs and metric mm² in newer designs. Converting the two against each other is part of motor selection.

PCB and chassis-wiring design. The chassis wiring inside any electrical device carries AWG labels (US practice) or metric cross-section labels (European practice). The ampacity table in this converter helps pick the right wire for a given load, with the explicit caveat that real installation also depends on insulation temperature rating, bundling, and ambient temperature.

Hobby electronics and LED installations. Common sizes for hobby work are AWG 24, 22, 20, 18, and 16, covered in this calculator's ampacity table, and the converter helps match these against metric equivalents when shopping in both markets.

Common Mistakes

Several mistakes show up regularly in workshop notes and forum posts. Knowing what they are is half the defence against them.

Confusing AWG with SWG or BWG. This is by far the most common error. "AWG 14" and "SWG 14" are different sizes. Reading an SWG wire as AWG 14 means using 1.628 mm wire where 2.032 mm is needed (25 % under-spec for current). The other direction (reading AWG as SWG) means 25 % over-spec, which usually does not cause a safety problem but does cost you money in materials.

Treating gauge tables as linear. Gauge 6 is not twice the diameter of gauge 12. It is roughly 1.585 × the diameter (~2.512 × the area). The factor of 1.12293 per gauge step and the cross-section factor of 1.261 per gauge step are derived from the 92 in the formula and worth committing to memory once.

Ignoring insulation temperature rating. A 60 °C-rated AWG 14 cable carries less current than a 90 °C-rated AWG 14 cable at the same ambient temperature, because the limiting factor is the temperature at the insulation/conductor interface, not the copper cross-section itself. The published ampacity tables in NEC NFPA 70 Chapter 9 are calibrated against a chosen insulation rating; using the wrong one is a known source of over-spec or under-spec.

Using DC resistance at RF. Skin effect raises AC resistance above ~1 MHz, even for AWG 14 (skin depth in copper at 1 MHz is ~66 µm, which is comparable to the conductor radius). At audio frequencies and DC, the DC figure is fine. At RF, AC resistance is significantly higher and the published DC figure does not apply.

Adding two parallel conductors and reading the table for the doubled area. Two AWG 16 wires in parallel give roughly the cross-section of one AWG 13, but the published ampacity is not simply the AWG 13 figure because the bundle is itself a derating factor. Run the calculation against the actual installation.

Ignoring ambient temperature. Ampacity is rated at 30 °C ambient. Correction factors fall to ~0.5 at 45 °C ambient for 90 °C-rated insulation, and further at higher temperatures. Hot attic runs and engine-bay wiring routinely see ambients that cut the rated current by half.

Frequently Asked Questions

What is the difference between AWG, SWG, and BWG?

AWG (American Wire Gauge), SWG (British Standard Wire Gauge), and BWG (Birmingham Wire Gauge) are three historical gauge conventions introduced in different countries during the nineteenth century. They all share the property that a higher gauge number means a thinner wire, but they are NOT interchangeable: AWG 14 is 1.628 mm in diameter, SWG 14 is 2.032 mm, BWG 14 is 2.108 mm. They happen to coincide at one specific step (around gauge 22 → 0.711 mm in both SWG and BWG, by historical accident) but drift apart for most other sizes. Always use the standard that matches the wire label.

How accurate is the AWG formula d_n = 0.127 × 92^((36 − n)/39)?

It is exact to the precision of ASTM B258, the formula reproduces every entry in the B258 diameter table to within 0.001 mm. Three worked examples: AWG 14 → 1.6277 mm → 2.08 mm²; AWG 24 → 0.5106 mm → 0.2047 mm²; 2.5 mm² corresponds to a diameter of 1.784 mm, which the inverse formula places at AWG 13.21 (between AWG 13 and AWG 14). B258 declares these diameters as nominal, and the actual conductor cross-sectional area can differ slightly due to manufacturing tolerance.

What does "AWG 14 ≈ 8.3 mΩ/m" actually mean?

It means a 1-metre length of AWG 14 solid copper wire at 20 °C has a DC resistance of roughly 8.286 milliohms, anchored to the standard resistivity of annealed copper (1.724 × 10⁻⁸ Ω·m, also called 100 % IACS, the international annealed copper standard). The formula is R (Ω/km) = 17.24 / A(mm²). AWG 14 is 2.08 mm², giving R ≈ 8.29 mΩ/m. For AWG 12 (3.31 mm²), R ≈ 5.21 mΩ/m; for AWG 10 (5.26 mm²), R ≈ 3.28 mΩ/m. Copper has a temperature coefficient of roughly +0.4 % per °C near room temperature, so the 20 °C figure scales upward at higher operating temperatures.

What cable cross-section is 2.5 mm² in AWG?

2.5 mm² corresponds to a diameter of about 1.78 mm, which the inverse formula places at AWG 13.21, between AWG 13 (2.628 mm²) and AWG 14 (2.0809 mm²). It is closer to AWG 13 but not equal to either. In European electrical practice, 2.5 mm² is the standard size for general-purpose ring-circuit wiring, and most converters show a value of "AWG 13" rather than the more precise 13.2 because the AWG table values are rounded to integer steps.

Can stranded wire be converted the same way as solid wire?

Yes for diameter and cross-section, with care for resistance. Stranded wire has a slightly larger overall diameter than solid wire of the same nominal cross-section because of the bundle geometry, so a "stranded AWG 14" with nominal area 2.08 mm² is closer to 2.10 mm² of actual copper and the resistance is correspondingly lower. Use the same AWG label for the diameter, but expect the actual measured resistance to come in slightly below the published solid-wire value.

Why does the converter give different nearest-SWG values for the same diameter?

Because AWG and SWG are different gauges at most steps. AWG 14 is 1.628 mm; the tabulated SWG diameter closest to 1.628 mm is SWG 16 (1.626 mm). The system labels can differ by two steps for the same physical size. Conversely, AWG 16 (1.291 mm) is closest to SWG 18 (1.219 mm). The converter picks the nearest tabulated SWG diameter by geometric distance, which is the only unambiguous cross-walk between systems.

What does "100 % IACS" mean for resistance?

IACS = International Annealed Copper Standard. The conductivity of copper is graded against this reference: "100 % IACS" copper is the annealed-copper ideal with a resistivity of 1.724 × 10⁻⁸ Ω·m at 20 °C, and the standard defines the numerical value of conductivity so other materials (aluminium, copper-clad steel, etc.) can be referenced. "61 % IACS" aluminium means its conductivity is 61 % of the 100 % IACS reference, its resistivity is correspondingly 1 / 0.61 ≈ 1.64 × higher than copper at the same temperature.

Is this suitable for sizing solar-panel or battery wiring?

The resistance figures are accurate; the ampacity ranges are chassis-wiring guidance only. For a real solar or battery installation, use NEC NFPA 70 Article 690 (PV) or 480 (battery), IEC 60364-5-52, and the cable manufacturer's own ampacity derating tables. The numbers from this converter are a starting point, not a final answer.

Can the Wire Gauge Converter be used for professional or commercial purposes?

Yes, the calculator provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Wire Gauge Converter, For the Wire Gauge Converter, For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Wire Gauge Converter, the Wire Gauge Converter formulas used are well-established and validated against reference standards.

For the Wire Gauge Converter, How often are the underlying formulas updated?

For the Wire Gauge Converter, the Wire Gauge Converter formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. When standards change (e.g., new physical constants, revised tax brackets, updated standards), the Wire Gauge Converter is updated to reflect the current authoritative source. For the Wire Gauge Converter, Each calculator's references section lists the specific sources used.

References

The geometry and cross-section conventions used here are anchored to the following standards.

ASTM B258-14, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors. ASTM International, West Conshohocken, PA. Defines the AWG diameter formula and tabulates the AWG sizes from AWG 4/0 (11.684 mm) down to AWG 44 (0.0502 mm) for solid round copper, aluminium, and copper-clad conductors.

IEC 60228:2004, Conductors of Insulated Cables. International Electrotechnical Commission, Geneva. Defines the international metric conductor sizes from 0.5 mm² up to 2500 mm², classifying them as Class 1 (solid), Class 2 (stranded), or Class 5 (flexible). The cross-section conventions used here follow IEC 60228's definitions for solid round concentric-lay conductors.

NEC NFPA 70 Chapter 9 Tables 8 and 10, National Electrical Code (NFPA 70), published by the National Fire Protection Association. Chapter 9 Table 8 lists properties of conductors (DC resistance at 20 °C in ohms per 1000 feet, cross-sectional area, diameter); Chapter 9 Table 10 covers relationships between AWG and metric sizes. Ampacity schedules appear in Article 310.15(B)(16) and following. The ampacity figures reproduced in the reference table on this page are general chassis-wiring guidance; the full NEC tables include far more insulation types, bundling correction factors, and ambient correction factors.

BS EN 50575:2014+A1:2016, Power, Control and Communication Cables, Cables for General Applications in Construction Works Subject to Reaction to Fire Requirements. BSI Standards / CEN. Covers the EU Construction Products Regulation (CPR) Euroclass performance classification, applied to cables in construction works. The CPR framework, anchored by BS EN 50575, governs the fire-performance classification that complements the electrical-performance classification (ampacity, voltage rating, etc.).

SAE J1128, Low-Voltage Primary Cable, Society of Automotive Engineers. Specifies the requirements for low-voltage primary cable used in road-vehicle applications (12 V and 24 V systems), with insulation rated to 80 °C or 125 °C depending on the construction. Distinct from the metric DIN-style cable used in European vehicle wiring but functionally similar; conversion between J1128 and metric mm² sizes is part of any vehicle-wiring project that mixes domestically-supplied and internationally-sourced wire.

IACS 100 % IACS conductivity of annealed copper, International Annealed Copper Standard, defined as 1.724 × 10⁻⁸ Ω·m resistivity at 20 °C. This is the reference value used for every resistance-per-km calculation in this converter; it is also the reference for graded conductivities such as "61 % IACS aluminium", "30 % IACS nickel", and so on. The IACS definition is maintained by the Copper Development Association (CDA) and cross-referenced in ASTM B193 (Standard Test Method for Resistivity of Electrical Conductor Materials) and IEC 60468.