Wire Resistance Calculator
Calculate wire resistance using Pouillet's Law R = ρL/A. Select from copper, aluminum, silver, gold, and more. Free online calculator with interactive charts.
About This Calculator
The Wire Resistance Calculator computes the electrical resistance of a wire based on its material, length, and cross-sectional area using Pouillet's Law (R = ρ × L / A). Students, electricians, engineers, and hobbyists can quickly determine the resistance and conductance of any conductor for circuit design, voltage drop analysis, and cable sizing applications.
The calculator uses the resistivity values of common conductor materials at the standard reference temperature of 20°C. Copper and aluminum are the most widely used materials in electrical wiring, while silver offers the lowest resistivity for specialized high-performance applications. The formula R = ρL/A shows that resistance is directly proportional to length and inversely proportional to cross-sectional area — doubling the length doubles the resistance, while doubling the area halves it. Conductance (G = 1/R) is also displayed as the reciprocal measure of how easily current flows through the wire.
Regional Notes
Worldwide (SI): This calculator uses SI units — meters for length, square millimeters for area, and ohms for resistance. Resistivity values are in ohm-meters (Ω·m) at 20°C. For US users working with AWG wire sizes, the diameter can be converted to cross-sectional area using the formula A = π(d/2)² where d is in mm (1 inch = 25.4 mm).
Voltage Drop Considerations: Once you know the wire resistance, you can calculate voltage drop using Ohm's Law (V = IR). In the US, the National Electrical Code (NEC) recommends a maximum 3% voltage drop for branch circuits. In the UK, BS 7671 specifies similar limits. In India, the Indian Electricity Rules and IS 732 apply with comparable voltage drop guidelines.
Frequently Asked Questions
How do I calculate the resistance of a wire?
The resistance of a wire is calculated using Pouillet's Law: R = ρ × L / A, where ρ is the resistivity of the material (Ω·m), L is the length (m), and A is the cross-sectional area (m²). Simply select the wire material, enter the length and cross-sectional area, and the calculator computes the resistance and conductance instantly.
What materials are available in this wire resistance calculator?
The calculator includes common conductor materials with their standard resistivity values at 20°C: silver (1.59×10⁻⁸ Ω·m), copper (1.68×10⁻⁸ Ω·m), gold (2.44×10⁻⁸ Ω·m), aluminum (2.65×10⁻⁸ Ω·m), tungsten (5.60×10⁻⁸ Ω·m), iron (9.71×10⁻⁸ Ω·m), platinum (1.06×10⁻⁷ Ω·m), nichrome (1.10×10⁻⁶ Ω·m), and carbon (3.50×10⁻⁵ Ω·m). Copper and aluminum are the most common for electrical wiring.
How does wire length affect resistance?
The resistance of a wire is directly proportional to its length. Doubling the length of the wire doubles its resistance because electrons must travel a longer distance through the conductor, encountering more collisions with atoms along the way. This is why longer cable runs require thicker wires to maintain acceptable voltage drop.
How does cross-sectional area affect wire resistance?
The resistance of a wire is inversely proportional to its cross-sectional area. A thicker wire (larger area) has lower resistance because there are more paths for electrons to flow. Doubling the cross-sectional area halves the resistance. This follows from the formula R = ρL/A — area appears in the denominator.
What is the resistivity of copper?
The electrical resistivity of copper at 20°C is approximately 1.68 × 10⁻⁸ Ω·m (or 1.68 × 10⁻⁵ Ω·mm). Copper is the most common material for electrical wiring because it combines low resistivity with good mechanical properties and corrosion resistance. Annealed copper has a slightly lower resistivity of about 1.72 × 10⁻⁸ Ω·m at 20°C.
What is conductance and how is it related to resistance?
Conductance (G) is the reciprocal of resistance: G = 1/R. It measures how easily electricity flows through a conductor. The SI unit of conductance is the siemens (S). While resistance describes opposition to current flow, conductance describes the ease of current flow. For a wire, conductance is calculated as G = σ × A / L, where σ = 1/ρ is the conductivity of the material.
Does temperature affect wire resistance?
Yes, temperature significantly affects wire resistance. For most metals, resistance increases with temperature due to increased atomic vibrations that scatter electrons. The temperature coefficient of resistivity for copper is about 0.00404 per °C, meaning the resistance increases by approximately 0.4% for every 1°C rise in temperature. This calculator provides values at the standard reference temperature of 20°C.
Why is silver not commonly used for electrical wiring despite having the lowest resistivity?
Silver has the lowest electrical resistivity of any metal (1.59×10⁻⁸ Ω·m at 20°C), making it the best conductor. However, it is rarely used for electrical wiring due to its high cost (approximately 50-100 times more expensive than copper), lower tensile strength compared to copper, and tendency to tarnish when exposed to sulfur compounds in the air. Silver is used in specialized applications like high-end audio cables, RF connectors, and aerospace components where maximum conductivity justifies the cost.