Source: https://guthlabs.ai/docs/instruments/wire-gauge-awg-swg-diameter-area-converter/

instrument / verified-clean

# Wire Gauge (AWG/SWG) ↔ Diameter/Area Converter

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/wire-gauge-awg-swg-diameter-area-converter/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/wire-gauge-awg-swg-diameter-area-converter/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/wire-gauge-awg-swg-diameter-area-converter/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/wire-gauge-awg-swg-diameter-area-converter/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Electrical & Electronics Engineering — Circuits, Power Systems, Electronics Lab

**Tranche**: tranche-7

**Evidence ID**: t7-060

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The AWG diameter equation is valid, and the area and resistance arithmetic above is consistent with the stated assumptions. Verdict is NEEDS_REVIEW because SWG data/algorithm, diameter-standard selection, conductor material, resistivity convention, temperature, valid ranges, and rounding behavior are not specified. The honest label should say that resistance is nominal conductor resistance at a stated temperature and material, not guaranteed installed-cable resistance.

### Formula and scope findings

- The AWG diameter formula is correct for nominal American Wire Gauge: d(mm)=0.127×92^((36−AWG)/39).

- Cross-sectional area is not stated but must be computed as A=πd²/4.

- Resistance requires R=ρL/A, with diameter converted from mm to m before calculating SI resistance.

- No SWG conversion algorithm or SWG table is supplied, although SWG is an advertised input/output standard. AWG and SWG numbers are not interchangeable.

- Diameter-to-gauge conversion is underspecified: the instrument must identify whether the diameter is being interpreted as AWG or SWG, and should define rounding and valid gauge ranges.

- Resistance cannot be determined from gauge alone without conductor material, resistivity convention, and temperature. If the instrument claims copper resistance, that must be stated explicitly.

### Unit assumptions

- AWG diameters are nominal bare-conductor diameters in millimetres, using the standard 0.127 mm AWG-36 reference diameter.

- Area is reported in mm².

- Resistivity values are assumed to be at 20 °C; resistance uses R=ρL/A.

- For resistance calculations, area in mm² is converted to m² by multiplying by 10^-6.

- Ω/km uses L=1000 m; Ω/1000 ft uses the exact conversion 1000 ft=304.8 m.

- The test vectors explicitly assume annealed copper with ρ=1.68×10^-8 Ω·m, a widely tabulated standard value at 20 °C.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define rejection behavior for zero diameter, does not identify the exact valid AWG range, and does not require an explicit AWG-versus-SWG selector or diameter unit. These omissions permit undefined outputs and materially different numeric results.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "standard": "AWG",
    "gauge": 36,
    "material": "annealed copper",
    "temperature_C": 20,
    "requested_resistance_lengths": [
      "1 km",
      "1000 ft"
    ]
  },
  "expected_outputs": {
    "diameter_mm": 0.127,
    "area_mm2": 0.012667687,
    "resistance_ohm_per_km": 1326.21,
    "resistance_ohm_per_1000ft": 404.23
  },
  "reference_data": {
    "awg_row": {
      "gauge": 36,
      "diameter_mm": 0.127,
      "source_convention": "AWG standard, widely tabulated standard value"
    },
    "copper_resistivity_ohm_m_20C": 1.68e-8,
    "source_convention_resistivity": "widely tabulated standard value for copper at 20 °C",
    "pi": 3.141592653589793,
    "source_convention_pi": "mathematical constant",
    "metres_per_1000ft": 304.8,
    "source_convention_length": "exact SI/international-foot conversion"
  },
  "working": "d=0.127 mm (the exact AWG-36 table entry). A=πd²/4=3.141592653589793×(0.127²)/4=3.141592653589793×0.016129/4=0.012667687 mm². Convert area: A=0.012667687×10^-6=1.2667687×10^-8 m². R/km=ρL/A=(1.68×10^-8 Ω·m×1000 m)/(1.2667687×10^-8 m²)=1326.21 Ω/km. R/1000 ft=(1.68×10^-8×304.8)/(1.2667687×10^-8)=404.23 Ω/1000 ft."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`