Understanding the electrical resistance of a wire is fundamental to circuit design, cable sizing, fault analysis, and heating-element engineering. This calculator implements the exact R = ρ L / A formula with a full linear temperature correction, so you get the true DC resistance of any conductor from first principles rather than from a lookup table that may not match your operating conditions.
How it works
The resistance of a uniform conductor is given by:
R = ρ(T) × L / A
where:
- ρ(T) is the resistivity of the material at the operating temperature T (Ω·m)
- L is the length of the conductor (m)
- A is the cross-sectional area (m²)
Because resistivity changes with temperature, the calculator first applies the linear correction model before computing R:
ρ(T) = ρ₀ × [1 + α × (T − 20°C)]
where ρ₀ is the resistivity at the 20°C reference and α is the temperature coefficient of resistivity (1/°C). For copper (annealed), ρ₀ = 1.724 × 10⁻⁸ Ω·m and α = 3.93 × 10⁻³ /°C.
Once R is known, the tool derives:
- Conductance: G = 1 / R (siemens)
- Voltage drop: V = I × R (if you supply a current)
- Power dissipated in the wire: P = I² × R
For a two-conductor circuit (out and return path), tick the round-trip checkbox and the displayed total resistance is 2R.
Worked example
A 25-metre run of 2.5 mm² annealed copper cable (two conductors) carrying 16 A at 60°C:
- ρ(60°C) = 1.724 × 10⁻⁸ × [1 + 3.93 × 10⁻³ × (60 − 20)] = 1.724 × 10⁻⁸ × 1.1572 = 1.995 × 10⁻⁸ Ω·m
- R (one conductor) = 1.995 × 10⁻⁸ × 25 / (2.5 × 10⁻⁶) = 0.1995 Ω
- R (round-trip) = 2 × 0.1995 = 0.399 Ω
- Voltage drop = 16 A × 0.399 Ω = 6.38 V on a 230 V circuit = 2.77% — within the IEC 60364-5-52 4% limit
| Material | ρ₀ (Ω·m at 20°C) | Relative to copper |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 0.92× |
| Copper (annealed) | 1.72 × 10⁻⁸ | 1.00× |
| Gold | 2.44 × 10⁻⁸ | 1.42× |
| Aluminium | 2.65 × 10⁻⁸ | 1.54× |
| Nichrome | 1.10 × 10⁻⁶ | 63.8× |
Formula note
The linear temperature model holds well for pure metals from about −50°C to their melting point. For precision work above ~200°C, higher-order corrections exist but are beyond the scope of this tool. The AWG diameter formula used internally is d = 0.127 × 92^((36 − AWG) / 39) mm, the same closed-form expression used in the IPC-2221 standard. All SI unit conversions use exact factors (1 inch = 0.0254 m, 1 foot = 0.3048 m, 1 mile = 1609.344 m).