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Full changelogEngine 1.26.4

Wire Gauge & Voltage Drop

PCB & Copper

The wire gauge for a current and allowable drop, or the drop, loss and current density of a gauge you choose.

Inputs

A
Source to load only; the return is counted below
V
3 % on a branch and 5 % end to end is the usual budget
%
Temperature
60 °C is a warm harness, 90 °C a hot one
°C

Results

1 passed · 1 to check
Recommended gauge 

1.309 mm², Ø 1.291 mm bare
16AWG
Voltage drop Vdrop

1.34 % of 12 V over 4 m of conductor
161.2mV
Resistance of the path R

13.43 mΩ/m at 25 °C
53.73mΩ
Current density J

rule limit 2.82 A/mm² · 3.7 A for this gauge
2.292A/mm²
All results (1)
Power lost in the wire P
483.6mW
drop at 3 A over 4 m

Accuracy

Verified against

2 independent cases. See the working.

This is a design aid. The engineer remains responsible for the design and for checking the standard itself.

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

Circuit

The principle

Sizing a wire asks two questions. Voltage drop is exact: resistivity, cross-section and Ohm's law. Heating is not a formula: it depends on the insulation rating, the bundle, the ambient and the cooling, which is why codes publish tables.

AWG diameter (ASTM B258)
d=0.127 mm⋅9236−n39d = 0.127\,\t{mm}\cdot 92^{\frac{36-n}{39}}
Every 3 gauges halves the area; every 6 gauges halves the diameter.
Cross-section
A=πd24A = \frac{\pi d^{2}}{4}
Resistance at temperature
R=ρ20[1+α (T−20)] lAR = \frac{\rho_{20}\left[1 + \alpha\,(T - 20)\right]\, l}{A}
ρ₂₀ = 1.724 × 10⁻⁸ Ω·m and α = 0.00393 /°C for annealed copper. l is the total conductor length: supply and return both count.
Drop, loss, density
Vdrop=IRP=I2RJ=IAV_{drop} = I R \qquad P = I^{2} R \qquad J = \frac{I}{A}
  • nnAWG number; 1/0 = 0, 2/0 = -1, 3/0 = -2, 4/0 = -3
  • lltotal conductor length, ×2 for a supply-and-return pair
  • ρ20ρ₂₀resistivity of copper at 20 °C
  • ααtemperature coefficient of copper resistivity
  • JJcurrent density; the cmil/A rules are its reciprocal
More detail

The rules of thumb

Two old handbook figures: 700 cmil/A (about 2.8 A/mm²) for bundled or enclosed wiring, and 160 cmil/A (about 12 A/mm²) for a single wire in free air. They suit hookup wire and harnesses, but they are not a standard.

Where a code applies, its table wins. The NEC for building wiring, SAE AS50881 for vehicle and aircraft harness, UL 758 for appliance wiring. Each is stated for a specific insulation rating and installation.
3 A at 12 V, 2 m each way, 18 AWG, 60 °C
18 AWG is 0.823 mm², 20.95 mΩ/m at 20 °C and 24.24 mΩ/m at 60 °C. 4 m of it is 97 mΩ, so the drop is 0.29 V, 2.4 % of 12 V. Current density is 3.6 A/mm², over the 2.8 A/mm² bundled rule: fine for a lone wire, marginal in a loom.
The gauge for the same run under the bundled rule and a 3 % budget
The density rule asks for at least 1.06 mm², and 16 AWG (1.31 mm²) is the first gauge that meets it. Its drop over 4 m at 60 °C is 0.18 V, or 1.5 %. The answer is 16 AWG, set by the density, not the drop.
References: ASTM B258, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires. NFPA 70 (NEC), on ampacity and voltage drop. SAE AS50881, Wiring, Aerospace Vehicle. The cmil/A rules appear in most electronics reference handbooks. Related: Trace Resistance & IR Drop for the same question on a PCB.

Engine version ⁨1.26.4⁩