Wire Resistance Calculator

Compute DC resistance for 7 different materials (Copper, Aluminum, Silver, Gold, Iron, Steel, Nichrome). Includes temperature correction, unit conversion, and in-depth educational content.

Resistance formula: R = ρ · L / A (for given material and cross-section)

Temperature correction: RT = R20 · [1 + α · (T - 20)]

α values: Cu 0.00393, Al 0.00403, Ag 0.0038, Au 0.0034, Fe 0.0050, Steel ≈0.003, NiCr 0.00017 (per °C).

°C
100 ft 12 AWG Cu 200 ft 10 AWG Al 50 m 8 AWG Ag 10 m 14 AWG NiCr

Understanding Wire Resistance

Electrical resistance is the opposition to the flow of electric current. It determines voltage drop and power dissipation (I²R losses) in circuits. For a uniform conductor, resistance depends on four key factors:

? Physical Origin

Resistance arises from collisions between conduction electrons and the vibrating atoms (phonons) and impurities in the material. Higher temperature increases atomic vibrations, thus increasing resistance.

? Fundamental Formula

R = ρ · L / A

  • R = resistance (ohms, Ω)
  • ρ = resistivity of the material (Ω·m) – a material property at a given temperature
  • L = length of the conductor (m)
  • A = cross-sectional area (m²)

For AWG wires, cross-sectional area is standardized. The table below shows typical resistivities at 20°C.

? Material Properties at 20°C
Material ρ (10⁻⁸ Ω·m) α (10⁻³ /°C) Conductivity (relative to Cu)
Silver (Ag) 1.59 3.8 108%
Copper (Cu) 1.724 3.93 100%
Gold (Au) 2.44 3.4 71%
Aluminum (Al) 2.65 4.03 65%
Iron (Fe, pure) 9.71 5.0 18%
Steel (mild) ≈14.3 ≈3.0 12%
Nichrome (80/20) 110 0.17 1.6%

* α values are approximate; exact values depend on purity and alloy composition.

?️ Temperature Correction

Resistance changes linearly with temperature over a moderate range:

RT = R20 · [1 + α · (T - 20)]

where R20 is resistance at 20°C, α is temperature coefficient, and T is conductor temperature in °C. This calculator applies this correction when enabled.

? AWG and Cross-sectional Area

American Wire Gauge (AWG) sizes follow a geometric progression. Smaller gauge numbers correspond to larger diameters. The resistance per 1000 ft for copper and aluminum at 20°C is pre‑tabulated. For other materials, resistance is scaled from copper using the resistivity ratio (ρmaterial/ρCu).

⚡ Practical Applications
  • Voltage drop: ΔV = I × R – excessive drop causes equipment malfunction.
  • Power loss: P = I² × R – wasted energy as heat.
  • Short-circuit calculations: Resistance determines fault current magnitude.
  • Heating elements: Nichrome's high resistivity and low α make it ideal for heaters.
? Skin Effect (AC Resistance)

At high frequencies (>60 Hz), current tends to flow near the conductor surface, increasing effective resistance. This calculator provides DC resistance; for AC applications at power frequencies (50/60 Hz), the difference is negligible for AWG sizes up to 4/0.

? Example Calculation

What is the resistance of 500 ft of 10 AWG copper wire at 50°C?

  1. From table: R20 (10 AWG Cu) = 0.9989 Ω/1000ft.
  2. For 500 ft: R20 = 0.9989 × (500/1000) = 0.49945 Ω.
  3. Temperature correction: α = 0.00393, ΔT = 30°C → factor = 1 + 0.00393×30 = 1.1179.
  4. R50 = 0.49945 × 1.1179 = 0.558 Ω.

Our calculator gives the same result.

Frequently Asked Questions

In North America, wire resistance is commonly tabulated per 1000 feet (kft) for easy voltage drop calculations (VD = 2×L×I×R/1000). This calculator provides both Ω/kft and Ω/km for convenience.

They are calculated from the copper base using resistivity ratios. This yields excellent accuracy for pure metals. For alloys (steel, nichrome), typical values are used; actual resistance may vary with exact composition. Always consult manufacturer data for critical applications.

Use it when the wire operates at a temperature significantly different from 20°C, e.g., in hot environments or when current causes self-heating. For short circuits, resistance at final temperature is needed.

Stranded and solid conductors of the same AWG have essentially the same DC resistance. Stranding affects flexibility and skin effect slightly, but DC resistance is unchanged.