How this instrument works
The mass of a length of wire is nothing more than the volume of metal it contains times how tightly that metal's atoms pack together. A wire is a cylinder, so its volume is length times cross-sectional area, π(d ⁄ 2)², and multiplying by copper's density converts that geometric volume straight into a mass electricians, cable buyers, and scrap dealers actually price against. The formula weight = L·π(d ⁄ 2)²·ρ_Cu is exact for anything shaped like a uniform round rod — no calculus, no approximation, just a cylinder's volume married to a material constant.
Because area scales with the square of diameter, wire weight is far more sensitive to diameter than to length: shave a wire down by 10 percent in diameter and it loses about 19 percent of its weight per metre, not 10. That quadratic relationship is why gauge tables such as AWG step their diameters in a fixed ratio rather than a fixed increment — each step is built to roughly double or halve the cross-section, and so the weight, in a predictable multiple rather than a flat amount.
The 8,960 kg/m³ figure describes pure, solid copper at room temperature — the value NIST lists for the element. Real conductors can run a little lighter than the formula predicts once manufacturing tolerance on the diameter, alloying, or stranding enter the picture: bronze and brass conductors are not pure copper, and a stranded conductor bundles several thinner wires with small air gaps between them that a single solid-cylinder formula cannot see. For solid, uncoated copper wire, though, the figure this instrument returns is the shipping weight to three significant figures.
- Enter the Wire length — the total run to be weighed, in metres; switch to feet if that's how the spool is marked.
- Enter the Conductor diameter — bare copper only, excluding any insulation jacket — in millimetres.
- If you only know an AWG size or a cross-sectional area in mm², look up its bare diameter first; the formula needs a linear measurement.
- Read Wire weight in kilograms, or switch its unit menu to pounds for a shipping quote.
Worked example — 100 m of 2.05 mm copper wire
Take a 100 m reel of 2.05 mm diameter copper wire, close to AWG 12, a size common in household branch circuits. Halve the diameter to get the radius, 0.001025 m, square it, multiply by π for the cross-sectional area, 3.300636×10⁻⁶ m², and multiply by the 100 m length for a volume of 3.300636×10⁻⁴ m³.
Multiply that volume by copper's density, 8,960 kg/m³, and the reel weighs 2.95736966038 kg — call it 2.957 kg on a scale that reads to the gram. That is the figure a cable supplier would quote for shipping, and it is close to what a 100 m box of solid-core 12 AWG copper wire actually weighs, before any PVC jacket is added.
Questions
Why does the formula use diameter, not radius, if radius is what actually appears in the area term?
Because diameter is what people measure and buy by — wire gauges, calipers, and spool labels all report diameter, not radius. The instrument halves it internally, d ⁄ 2, before squaring, so you never do that conversion by hand; just read the bare-copper diameter off a caliper or a gauge table and enter it directly.
Does this account for the wire's insulation or jacket?
No — the formula weighs only the copper conductor, using its bare diameter. PVC, XLPE, or rubber jackets add their own volume at a much lower density, typically 1.0 to 1.5 g/cm³, so an insulated cable's total weight runs higher than this figure. For a jacketed cable's shipping weight, add the sheath's weight separately or check the manufacturer's datasheet.
Why 8,960 kg/m³ specifically, and not 8,900 or 8,940?
That is NIST's tabulated density for pure copper at room temperature, and it is the figure most wire-weight tables and mill certificates build from. Commercial electrolytic copper, ETP grade, 99.9 percent pure, sits within a few kilograms per cubic metre of that value; alloyed conductors like bronze or brass are noticeably lighter or heavier and need a different density entered by hand.
How much does the weight change if the diameter measurement is slightly wrong?
More than most people expect, because area — and so weight — scales with diameter squared. A diameter reading that is 5 percent too high overstates the weight by about 10 percent; a caliper misread of a few hundredths of a millimetre on a thin wire matters more than it looks. Measure across several points along the wire and average, rather than trusting a spool label alone.
Does this work for stranded wire, not just a solid conductor?
Only approximately. A stranded conductor bundles several thinner wires together, and the gaps between strands mean its overall diameter encloses some air, not solid copper, so a solid-cylinder formula overstates the weight. For stranded wire, use the individual strand diameter and strand count, or look up the conductor's rated cross-sectional area in mm² directly from a wire table.