How this instrument works
A conductor loses supply voltage to its own resistance in direct proportion to the current it carries: ΔV = I·R. Resistance itself follows from geometry acting on one material constant, R = ρ·L ⁄ A, so solving that pair for A — instead of for R or ΔV — turns a measurement equation into a sizing equation: given a target drop, how much cross-section does the job need? The 2 in A = 2·I·L·ρ ⁄ ΔV is not an extra correction bolted on afterward; it falls straight out of counting both conductors in the loop, since current leaves along one wire and returns along another, and both share the same resistance budget between them.
Most wire-sizing charts hard-code one number for one metal, usually annealed copper near room temperature, and hide it behind a lookup table. This instrument instead asks for Conductor resistivity, Ω·m, directly, which is what makes it useful past copper's default case: a marine electrician working in tinned copper, whose resistivity sits slightly above bare copper's, or a design engineer specifying nickel-plated conductor for wiring that runs hot inside an oven enclosure, can enter the correct figure for that exact material rather than reach for a table that only covers one. The output lands in square millimetres, the unit that IEC-style cable schedules and most of the world's conduit and lug catalogues are already built around.
What the equation returns is a lower bound on area for voltage drop alone, evaluated at whatever resistivity you supply — and that number is only as good as the resistivity entered. Published values apply at a stated reference temperature, typically 20 °C; a conductor running warm in service carries genuinely higher resistance than its cold rating, so a figure taken from a datasheet without correcting for expected operating temperature will understate the area a real installation needs. Nor does this equation know about current-carrying capacity, insulation rating, or mechanical strength — it answers one question, precisely, and leaves the rest of the specification to whoever is holding the cable schedule.
- Enter One-way wire run length — the one-direction distance between source and load; the equation itself accounts for both conductors in the circuit.
- Enter Load current — the amps the circuit will actually carry in service, not a breaker or fuse rating.
- Enter Conductor resistivity, Ω·m — 1.68 × 10⁻⁸ for annealed copper at 20 °C is a common default; substitute the figure for the actual metal and temperature in service.
- Enter Maximum allowable voltage drop in volts — the absolute figure your design margin or wiring standard permits, not a percentage.
- Read Minimum conductor area in mm² as a floor, then round up to the nearest catalogue size and confirm current-carrying capacity separately.
Worked example — 30 m to a backyard studio at 20 A
A homeowner is running power 30 m one-way from the main panel out to a backyard studio, on a 120 V circuit carrying a genuine 20 A load, and wants to hold the drop to 3.6 V — 3% of supply, a common design margin for a general-use branch circuit. Enter 30 for One-way wire run length, 20 for Load current, 1.68 × 10⁻⁸ for Conductor resistivity, Ω·m (annealed copper at 20 °C), and 3.6 for Maximum allowable voltage drop.
The equation counts both conductors before it multiplies: A = 2 × 20 × 30 × 1.68 × 10⁻⁸ ⁄ 3.6 = 5.6 × 10⁻⁶ m², which the Minimum conductor area field reads out as 5.6 mm². That crosses from a nominal 4 mm² cable into 6 mm² on a metric supplier's shelf — a jump voltage drop demands over this distance even though 20 A itself sits comfortably within 4 mm² copper's current-carrying capacity, which is exactly the situation this instrument exists to catch.
Questions
Why does the equation double the length instead of asking for the full circuit length directly?
Because One-way wire run length is the distance most people can actually measure — panel to load, walked off with a tape — while the physics needs the total path current travels, out and back through both conductors. Doubling it internally keeps the input honest to what is easy to measure and the arithmetic honest to what current actually does, without asking the user to double anything by hand.
Can I use this for aluminium, or any metal other than copper?
Yes — that is the point of asking for resistivity directly rather than assuming one material. Enter aluminium's roughly 2.65 × 10⁻⁸ Ω·m, or a nickel-plated or tinned conductor's slightly higher figure, and the result reflects that exact metal. Nothing in the formula is copper-specific; only the default value in Conductor resistivity, Ω·m happens to be copper's.
Should resistivity be the cold value from a datasheet, or the value at operating temperature?
Operating temperature, if the result is meant to hold up in service. Metallic resistivity climbs with temperature — copper by roughly 0.4% per degree Celsius near room temperature — so a conductor working hot inside an enclosure or a sun-heated conduit run has genuinely higher resistivity than its 20 °C datasheet figure. Entering the cold value understates the area a warm circuit will actually need.
Is 5.6 mm² a size I can actually buy?
Not exactly — it is the smallest area that satisfies the voltage-drop target, and cable is stocked in fixed steps, not continuous sizes. Once Minimum conductor area returns a figure, round up to the nearest size a supplier actually stocks; rounding down defeats the calculation entirely, since even a slightly undersized conductor pushes the real drop back over budget.
Does a larger required area mean the smaller size would have been dangerous?
Not necessarily, and that distinction matters. This equation protects against voltage lost to resistance — dim lights, a motor that struggles to start, a charger that never quite finishes — which is a performance limit, not a safety one. A conductor's current-carrying capacity, governed separately by its insulation and how the heat it generates can escape, sets the safety floor; an installation should satisfy whichever limit calls for the larger conductor.
What happens to the required area if the allowable voltage drop is cut in half?
It doubles. Area sits in the numerator alongside current and length, but voltage drop sits alone in the denominator, so halving Maximum allowable voltage drop while holding everything else fixed doubles Minimum conductor area exactly — tightening a drop budget is never free, and the cost is paid in copper.