Article — Wire Resistance Calculator
Wire resistance calculator: sizing conductors right
Wire resistance is the opposition a conductor offers to current flow. It follows R = ρL/A — resistivity times length over cross-section area. Copper at 20°C has ρ = 1.68 × 10⁻⁸ Ω·m, so a 10 m run of 2 mm² copper has R ≈ 0.084 Ω. Resistance rises with length, falls with cross-section, and grows roughly 0.4% per °C of temperature increase.
Every wire wastes some electrical energy as heat. That waste shows up as a voltage drop along the wire (V = IR) and as power loss inside it (P = I²R). For a household circuit, those numbers are usually small. For a 200 m underground feed to a workshop, they can decide whether your motor starts or just hums.
What is wire resistance?
Wire resistance comes from electrons scattering off the lattice of metal ions as they drift through a conductor. The longer the path, the more scattering events; the wider the path, the more parallel routes for current to spread across. Both effects show up in the simple geometric formula R = ρL/A.
Resistivity ρ is the material property — how much a unit cube of that metal opposes current. Resistance R is the property of a specific wire — what ρ becomes when you stretch it to a real length and shrink it to a real cross-section. Conductivity σ = 1/ρ is the reciprocal, often more convenient when comparing "how well does this material carry current".
Silver has the lowest resistivity of any common metal — 1.59 × 10⁻⁸ Ω·m, just 5% less than copper. But silver costs more than 100× as much. That's why copper is the standard for electrical wiring, with silver reserved for high-grade contacts, audio terminals, and specialty switchgear.
The wire resistance formula
The full set of formulas needed to size a real conductor:
Resistance R = ρ · L ÷ AAWG to mm d = 0.127 · 92^((36 − AWG)/39)Area from diameter A = π · (d/2)²Temperature R(T) = R₀ · [1 + α(T − 20)]Voltage drop V_drop = I · RPower loss P = I² · RUnits have to match. Plug ρ in Ω·m, L in metres, and A in square metres for the standard equation. If you have A in mm², multiply by 10⁻⁶ to convert. The calculator handles all conversions internally, but you'll want to know the formula for sanity checks.
Wire resistance by material
Resistivity at 20°C for common materials, with notes on where each is used:
- Silver 1.59 × 10⁻⁸ Ω·m — premium contacts, antennas.
- Copper 1.68 × 10⁻⁸ Ω·m — universal default for wiring.
- Gold 2.44 × 10⁻⁸ Ω·m — connectors, corrosion-resistant contacts.
- Aluminum 2.65 × 10⁻⁸ Ω·m — overhead transmission lines, building feeders.
- Tungsten 5.5 × 10⁻⁸ Ω·m — incandescent filaments, electron tubes.
- Nichrome 1.1 × 10⁻⁶ Ω·m — heating elements (65× copper's resistivity).
- Constantan 4.9 × 10⁻⁷ Ω·m — precision resistors (α ≈ 0).
- Stainless steel 6.9 × 10⁻⁷ Ω·m — heating elements in harsh environments.
Copper wins by being inexpensive, ductile, corrosion-resistant, and well-understood after a century and a half of mass use. Aluminum is roughly 60% the conductivity but a third the weight, which makes it the default for utility-scale transmission where wire weight matters more than connection complications.
AWG versus mm² sizing
North America uses American Wire Gauge; most of the rest of the world uses mm² cross-section. The conversion is logarithmic — every 3-step change in AWG roughly halves the area. Conversions for common sizes:
- AWG 14 ≈ 2.08 mm² — 15 A residential circuits.
- AWG 12 ≈ 3.31 mm² — 20 A receptacles.
- AWG 10 ≈ 5.26 mm² — 30 A appliances.
- AWG 8 ≈ 8.37 mm² — 40–50 A circuits.
- AWG 6 ≈ 13.3 mm² — 55–65 A subpanels.
- AWG 4 ≈ 21.2 mm² — 70–85 A feeders.
- AWG 1/0 ≈ 53.5 mm² — 150 A residential service.
Voltage drop and wire resistance
The same physics that limits wire resistance limits how far you can run a circuit before the voltage drop becomes unacceptable. Residential code typically allows 3% drop; commercial 5%. The standard rule: V_drop = I · R, but R has to include both legs of the circuit (out and back).
Worked example: 30 m run feeding a 30 A circuit at 240 V, looking for under 3% drop (7.2 V max). Round trip is 60 m. R_max = V_drop / I = 7.2 / 30 = 0.24 Ω. Needed area: A = ρL / R = 1.68 × 10⁻⁸ × 60 / 0.24 = 4.2 × 10⁻⁶ m² = 4.2 mm². AWG 10 (5.26 mm²) just clears it; AWG 8 gives margin.
A 30 m feeder runs out 30 m and back 30 m, so the total wire length for resistance is 60 m. Calculating with only 30 m halves the resistance and doubles the apparent capacity — leading to undersized conductors that overheat under load.
Temperature effects on wire resistance
Resistance rises linearly with temperature: R(T) = R₀ · [1 + α(T − 20°C)]. The temperature coefficient α depends on the metal. Copper sits at 0.00393/°C — about 0.4% per degree.
The effect is bigger than people expect. A 10 Ω copper coil at 20°C climbs to 12.4 Ω at 80°C — a 24% increase. For heating elements, that's a built-in current limiter: as the element heats up, resistance rises, current drops, heat output stabilises. Constantan and Manganin are alloys deliberately formulated to have near-zero α, which makes them the materials of choice for precision resistors and shunts where temperature stability matters.
When designing for a long-duration high-current load, derate the wire size by the temperature factor. A wire that sees 50°C continuous (above 20°C reference) carries roughly 12% more resistance and dissipates 12% more heat as I²R loss. Codes account for this implicitly through conduit-fill and ampacity tables.
Common wire-resistance mistakes
Six errors that trip up DIY electricians and sometimes professionals:
- Sizing by ampacity only — passes code on amperage but fails on voltage drop for long runs.
- Forgetting the round trip — total wire length is twice the one-way distance.
- Mixing AWG and mm² incorrectly — AWG 12 is 3.31 mm², not 12 mm².
- Ignoring temperature derating — wires in conduit, attics, or sun-exposed sites need bigger sizes.
- Aluminium without proper terminations — Al oxidises; use rated lugs and antioxidant compound.
- Skin effect at high frequency — at 50/60 Hz it's negligible, but past a few hundred kHz the effective conductor area shrinks and resistance rises.
Superconductors have exactly zero resistance below their critical temperature. The first one discovered was mercury, in 1911, with T_c = 4.2 K. Today's high-temperature ceramic superconductors work above liquid nitrogen temperature (77 K), enabling MRI magnets, particle accelerators, and experimental power transmission cables.