Wire Resistance Calculator

About the Wire Resistance Calculator

The electrical resistance of a wire is determined by four factors: the conductor material's resistivity (ρ), the wire length (L), the cross-sectional area (A), and the temperature. The fundamental formula R = ρL/A tells the whole story: longer wires have more resistance, thicker wires have less, and materials with lower resistivity conduct better.

Temperature significantly affects resistance in metals. Copper's resistance increases about 0.393% per degree Celsius above 20°C. A copper wire that measures 1.000 Ω at 20°C will measure 1.314 Ω at 100°C. This temperature coefficient is critical for precision measurements, heating element design, and temperature sensing (RTDs use this effect intentionally).

This calculator computes wire resistance from AWG gauge or custom diameter, with 7 conductor materials including copper, aluminum, silver, gold, nichrome, and steel. Temperature correction is applied automatically. Results include resistance per meter, per foot, and per kilometer, plus cross-sectional area in mm² and circular mils. A visual shows how resistance changes from -40°C to 100°C.

When This Page Helps

Wire resistance affects voltage drop, power loss, heating, and signal integrity. Incorrectly estimated resistance can cause excessive voltage drop, wasted energy, or even fire. This calculator handles all the physics — material resistivity, area from AWG or diameter, temperature correction — so you get an accurate resistance value for real operating conditions.

How to Use the Inputs

1. Choose wire size input: AWG gauge or custom diameter.
2. Select the AWG gauge or enter the diameter with units (mm, inches, or mils).
3. Select the conductor material (copper, aluminum, silver, gold, nichrome, steel, or custom).
4. Enter the wire length and select units (meters, feet, or kilometers).
5. Set the operating temperature (affects resistance).
6. Read total resistance, per-unit resistance, and area.
7. Check the temperature effect chart to see how resistance varies with temperature.

Example Calculation

Tips & Best Practices

• Copper resistivity at 20°C: 1.724 × 10⁻⁸ Ω·m. Aluminum: 2.65 × 10⁻⁸ (53% more). Silver: 1.59 × 10⁻⁸ (8% less, but much more expensive).
• For round-trip (2-wire) resistance, multiply the result by 2 or double the length. Voltage drop calculations need round-trip resistance.
• Nichrome has ~64× the resistance of copper, making it ideal for heating elements. Its very low temperature coefficient means resistance stays nearly constant when hot.
• Each 6 AWG step doubles the cross-sectional area and halves the resistance. AWG 12 is ~2× the area of AWG 18.
• Stranded wire has slightly higher resistance than solid wire of the same gauge because strands don't pack perfectly (filling factor ~90%).
• At high frequencies, skin effect reduces the effective cross-section. The skin depth δ = √(ρ/(πfμ)). At 1 MHz in copper, δ ≈ 66 μm.

Resistivity of Common Materials

Resistivity varies enormously: silver (1.59 × 10⁻⁸ Ω·m) is the best metallic conductor, followed by copper (1.72), gold (2.44), and aluminum (2.65). Nichrome (1.10 × 10⁻⁶) is 64× more resistive than copper — intentionally chosen for heating elements. Carbon steel (1.43 × 10⁻⁷) is 8× more resistive than copper but much stronger, used in structural cables. Superconductors reach exactly zero resistance below their critical temperature.

Wire Gauge Standards Around the World

AWG (American Wire Gauge) is standard in North America. Europe uses mm² cross-sectional area directly (e.g., 2.5 mm², 4 mm², 6 mm²). SWG (Standard Wire Gauge, British) uses a different numbering. IEC 60228 defines standard conductor sizes in mm² used internationally. Converting between systems requires a reference table because the relationships are not linear.

Power Loss in Transmission Lines

Power lost in a wire equals I²R. A 100 m run of AWG 10 copper carrying 30 A: R = 2 × 100 × 3.277 mΩ/m = 0.655 Ω, power loss = 30² × 0.655 = 589 W. At $0.12/kWh, that is $619/year if running 24/7. This is why utilities use high voltage (reducing current for the same power) and why voltage drop calculations matter.

Frequently Asked Questions

• How does temperature affect wire resistance?

  Metals have a positive temperature coefficient — resistance increases with temperature. For copper: α = 0.00393/°C. At 100°C, resistance is about 31% higher than at 20°C. This is why wires run hotter under heavy load: more current → more I²R heating → higher resistance → even more heating.

• What are circular mils?

  Circular mil (cmil) is an area unit used in North American wire sizing. It equals the area of a circle 1 mil (0.001 inch) in diameter. 1 cmil = 5.067 × 10⁻⁴ mm². AWG 10 = 10,380 cmil. The formula: cmil = d(mils)². It simplifies wire calculations because you skip π/4.

• Why is aluminum wire used despite higher resistance?

  Aluminum is lighter (2.7 vs 8.9 g/cm³) and cheaper than copper. For the same weight, aluminum actually has lower resistance. Overhead power lines use aluminum (with steel core for strength). For building wiring, aluminum requires special connectors to prevent oxidation issues.

• What is the AWG system?

  American Wire Gauge defines wire sizes by a number: larger numbers = thinner wire. AWG 0000 (4/0) is the thickest at 11.7 mm diameter. AWG 40 is the thinnest common size at 0.08 mm. Each step changes diameter by a factor of 92^(1/39) ≈ 1.123, and area by ~1.261.

• How do I calculate voltage drop using wire resistance?

  V_drop = I × R_total (round-trip). For a 15 A load on 30 m of AWG 12 copper: R = 2 × 0.1565 = 0.313 Ω, V_drop = 15 × 0.313 = 4.7 V (3.9% on 120 V). This exceeds the NEC's 3% recommendation — consider AWG 10.

• What is skin effect and when does it matter?

  At high frequencies, current concentrates near the wire surface (skin effect). The effective cross-section decreases, increasing AC resistance. In copper at 60 Hz, skin depth is ~8.5 mm (insignificant for building wire). At 1 MHz, it is 66 μm (significant — only the outer shell conducts). At 1 GHz, it is 2.1 μm.