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Ω
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Ω/kft
2.0525
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mm²
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Ω
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Ω/kft
2.0525
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The wire resistance calculator determines the electrical resistance of a wire based on its length, gauge (AWG), conductor material, and temperature. Wire resistance is a fundamental parameter in electrical engineering — it governs voltage drop, power dissipation, signal attenuation, and fault current levels. Every electrical calculation involving real conductors must account for their resistance.
The resistance of a conductor is given by R = ρ × L / A, where ρ is the resistivity of the material in Ω·m, L is the length in meters, and A is the cross-sectional area in m². Copper has one of the lowest resistivities of any economical conductor: ρ = 1.724 × 10⁻⁸ Ω·m at 20°C. Aluminum's resistivity is 2.82 × 10⁻⁸ Ω·m — about 64% higher. Silver, with ρ = 1.59 × 10⁻⁸ Ω·m, is marginally better than copper but far more expensive.
The AWG (American Wire Gauge) system defines wire diameters by the formula: d = 0.005 × 92^((36-AWG)/39) inches. Each 3 AWG steps doubles the wire diameter, and each 6 AWG steps doubles the cross-sectional area (and halves the resistance per unit length). AWG 36 = 0.005 inches diameter; AWG 0000 (4/0) = 0.46 inches.
Temperature significantly affects conductor resistance. The temperature coefficient of resistance α for copper is 0.00393/°C — meaning a 10°C rise increases resistance by about 4%. For a motor winding that heats from 20°C to 80°C (a common operating temperature), resistance increases by about 24%. This affects starting current calculations, motor protection settings, and voltage drop calculations under load.
Applications of wire resistance calculation include: fault current analysis (Zf = sum of all conductor resistances in the fault loop), motor winding resistance measurement (to detect shorted turns or verify winding integrity), battery cable sizing for automotive and marine applications, resistance heating element design, and grounding system resistance calculations.
AWG-to-diameter: d(inches) = 0.005 × 92^((36-AWG)/39). Cross-sectional area: A = π/4 × d². Temperature-corrected resistivity: ρ(T) = ρ₂₀ × (1 + α × (T - 20)). Resistance: R = ρ(T) × L / A. Results are computed in SI units internally with conversions to practical units for output.
Higher resistance means more voltage drop and power loss for a given current. Lower AWG numbers (thicker wire) give lower resistance. Aluminum requires a larger gauge than copper to achieve the same resistance. For high-temperature applications (motors, transformers), always use the operating temperature, not room temperature, to accurately predict voltage drop under load.
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A 50-foot AWG 16 copper extension cord has 0.655 Ω one-way resistance. Round-trip resistance = 1.31 Ω. At 15A, this drops 19.6V — significant power loss.
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200 ft of AWG 18 winding wire at 75°C has 5.62 Ω — compare to room temperature 4.54 Ω to verify temperature rise in motor diagnostic testing.
Copper resistivity at 20°C: ρ = 1.724 × 10⁻⁸ Ω·m (or 1.724 µΩ·cm). This makes copper the most conductive common metal after silver. Annealed copper used in electrical wiring has slightly higher conductivity than work-hardened copper.
R(T) = R₂₀ × (1 + α × (T - 20)). For copper, α = 0.00393/°C. A temperature rise of 50°C increases resistance by 19.7%. This is important for motor starting currents, fault current calculations, and temperature rise tests.
The AWG system originated from wire drawing: each drawing pass slightly reduces wire diameter. Higher AWG numbers indicate more passes (thinner wire). AWG 40 (0.079 mm) is hair-thin; AWG 4/0 (11.68 mm) is thumb-thick.
A short circuit has resistance equal to the sum of all conductor resistances in the fault loop — source, supply conductors, and return conductors. Fault current = V / Z_total, where Z includes source impedance plus conductor resistance.
Use a milliohmmeter (low-resistance ohmmeter) or a 4-wire (Kelvin) measurement to eliminate contact resistance. For long runs, measure resistance at one end with the far end shorted, then subtract the short-circuit resistance of the measurement leads.
At 50/60 Hz, skin effect is negligible for conductors up to about AWG 2. For larger conductors and high-frequency applications, skin effect increases effective resistance. At 1 MHz, even AWG 12 copper has significant skin effect, with current flowing only in the outer few hundredths of a millimeter.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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