Wire Resistance Calculator

Wire resistance is calculated using Pouillet's Law: R = ρ × L / A, where ρ is the material's resistivity (in Ω·m), L is the wire length (in meters), and A is the cross-sectional area (in m²). For a round wire, A = π × (d/2)², where d is the diameter. This calculator handles all that math automatically once you enter your inputs.

Resistance is directly proportional to wire length — doubling the length doubles the resistance. This is because a longer wire presents more collisions between electrons and the conductor's atoms, impeding current flow more. In practical wiring, keeping runs short reduces voltage drop and power loss.

Resistance is inversely proportional to cross-sectional area. A thicker wire (larger area) has lower resistance because more electrons can flow in parallel. Halving the area doubles the resistance. This is why high-current applications require thicker gauge wires.

The four factors are: (1) Material — each conductor has a unique resistivity ρ; (2) Length — longer wire = higher resistance; (3) Cross-sectional area — thicker wire = lower resistance; and (4) Temperature — most metals increase in resistivity as temperature rises, described by R(T) = R₂₀ × [1 + α × (T − 20)].

Resistivity (ρ) is an intrinsic material property measured in Ω·m that describes how strongly a material opposes electric current flow, regardless of shape or size. Resistance (R) is the actual opposition of a specific wire and depends on resistivity, length, and area. Think of resistivity as a material constant and resistance as the real-world result.

As temperature increases, atoms in the metal vibrate more intensely, causing more collisions with charge-carrying electrons and increasing resistivity. The relationship is approximately linear: R(T) = R₂₀ × [1 + α × (T − 20°C)]. Copper, for example, has α ≈ 0.00393 /°C, meaning each degree of temperature rise increases resistance by about 0.393%.

Copper has a resistivity of approximately 1.68×10⁻⁸ Ω·m at 20°C, making it one of the best electrical conductors available. Its electrical conductivity (σ = 1/ρ) is about 5.96×10⁷ S/m. Annealed copper is slightly less conductive (ρ ≈ 1.72×10⁻⁸ Ω·m) due to its softer, more disordered crystal structure.

Conductance (G) is the reciprocal of resistance: G = 1/R, measured in Siemens (S). While resistance measures how strongly a wire opposes current, conductance measures how easily it allows current to flow. A wire with a resistance of 0.01 Ω has a conductance of 100 S. The conductance formula in terms of geometry is G = σ × A / L, where σ is electrical conductivity.