Wire Resistance Calculator

Calculate electrical wire resistance using Ohm's Law and material properties.

Input wire dimensions, material resistivity, and current to calculate resistance, power dissipation, and voltage drop across the wire.

Examples

Click on any example to load it into the calculator.

Copper Wire - Standard Household

Copper Wire - Standard Household

Typical copper wire used in household electrical wiring with 2.5mm diameter.

Length: 50 m

Diameter: 2.5 mm

Resistivity: 1.68e-8 Ω·m

Current: 15 A

Temperature: 20 °C

Aluminum Wire - Power Transmission

Aluminum Wire - Power Transmission

Aluminum wire commonly used in power transmission lines with larger diameter.

Length: 1000 m

Diameter: 15 mm

Resistivity: 2.82e-8 Ω·m

Current: 100 A

Temperature: 25 °C

Gold Wire - Electronics

Gold Wire - Electronics

Gold wire used in high-precision electronic applications and bonding.

Length: 0.1 m

Diameter: 0.025 mm

Resistivity: 2.44e-8 Ω·m

Current: 0.001 A

Temperature: 20 °C

Silver Wire - High Conductivity

Silver Wire - High Conductivity

Silver wire offering the highest conductivity for specialized applications.

Length: 10 m

Diameter: 1 mm

Resistivity: 1.59e-8 Ω·m

Current: 5 A

Temperature: 20 °C

Other Titles
Understanding Wire Resistance Calculator: A Comprehensive Guide
Master the fundamentals of electrical resistance in wires and learn how to calculate resistance, power loss, and voltage drop for any electrical application. This guide covers everything from basic Ohm's Law to advanced temperature effects.

What is Wire Resistance?

  • Fundamental Concepts
  • Ohm's Law
  • Material Properties
Wire resistance is a fundamental concept in electrical engineering that describes how much a wire opposes the flow of electrical current. It's measured in ohms (Ω) and depends on the wire's material properties, dimensions, and temperature. Understanding wire resistance is crucial for designing efficient electrical systems, preventing power loss, and ensuring safe operation of electrical circuits.
The Physics Behind Resistance
When electrons flow through a wire, they collide with the atoms in the material, creating resistance. The more collisions, the higher the resistance. This is why longer wires have more resistance (more atoms to collide with) and thicker wires have less resistance (more pathways for electrons to flow). The material itself also plays a crucial role - some materials like silver and copper have very low resistance, while others like nichrome have high resistance.
Ohm's Law and Resistance
Ohm's Law states that voltage (V) equals current (I) times resistance (R): V = I × R. This fundamental relationship means that when current flows through a wire with resistance, a voltage drop occurs across the wire. This voltage drop represents energy lost as heat, which is why wires can get warm when carrying current. The power dissipated in the wire is given by P = I²R, showing that power loss increases with both current and resistance.
Material Resistivity
Resistivity (ρ) is an intrinsic property of materials that measures how strongly they oppose electrical current. It's measured in ohm-meters (Ω·m) and varies dramatically between materials. Silver has the lowest resistivity at 1.59×10⁻⁸ Ω·m, followed by copper at 1.68×10⁻⁸ Ω·m. Aluminum has higher resistivity at 2.82×10⁻⁸ Ω·m, while materials like nichrome can have resistivity as high as 1.10×10⁻⁶ Ω·m.

Common Material Resistivities (at 20°C):

  • Silver: 1.59×10⁻⁸ Ω·m (highest conductivity)
  • Copper: 1.68×10⁻⁸ Ω·m (most common conductor)
  • Gold: 2.44×10⁻⁸ Ω·m (corrosion resistant)
  • Aluminum: 2.82×10⁻⁸ Ω·m (lightweight alternative)
  • Tungsten: 5.60×10⁻⁸ Ω·m (high melting point)
  • Iron: 9.71×10⁻⁸ Ω·m (magnetic properties)

Step-by-Step Guide to Using the Calculator

  • Gathering Data
  • Inputting Values
  • Interpreting Results
Using the wire resistance calculator is straightforward, but accuracy depends on precise measurements and correct material properties. Follow these steps to get reliable results for your electrical calculations.
1. Measure Wire Dimensions Accurately
Use a caliper or micrometer to measure the wire diameter precisely. Even small measurement errors can significantly affect resistance calculations since resistance is inversely proportional to the cross-sectional area (which depends on diameter squared). For wire length, measure the actual path the current will take, including any bends or routing.
2. Select the Correct Material Resistivity
Choose the resistivity value that matches your wire material. If you're unsure, copper is the most common choice for electrical wiring. Be aware that resistivity values can vary slightly between different grades and purities of the same material. For critical applications, consult manufacturer specifications.
3. Consider Temperature Effects
Most materials have a positive temperature coefficient, meaning resistance increases with temperature. For copper, resistance increases by about 0.4% per degree Celsius above 20°C. If your wire operates at elevated temperatures, include this in your calculation for more accurate results.
4. Analyze the Results
The calculator provides resistance, cross-sectional area, power loss, and voltage drop. Check if the voltage drop is acceptable for your application (typically less than 3% for power distribution). Power loss shows how much energy is wasted as heat, which affects efficiency and may require cooling considerations.

Acceptable Voltage Drop Guidelines:

  • Power Distribution: < 3% of source voltage
  • Lighting Circuits: < 3% of source voltage
  • Motor Circuits: < 5% of source voltage
  • Control Circuits: < 10% of source voltage
  • Signal Circuits: < 1% of source voltage

Real-World Applications and Design Considerations

  • Power Distribution
  • Electronics Design
  • Safety Considerations
Wire resistance calculations are essential in countless real-world applications, from household wiring to high-power industrial systems. Understanding these principles helps engineers design efficient, safe, and cost-effective electrical systems.
Electrical Power Distribution
In power distribution systems, minimizing resistance is crucial to reduce energy losses. High-voltage transmission lines use large-diameter conductors to minimize resistance over long distances. The calculator helps engineers determine the optimal wire size for a given current and distance, balancing cost with efficiency. For example, a 1000-meter transmission line carrying 100A might use 15mm diameter aluminum wire to keep voltage drop below acceptable limits.
Electronic Circuit Design
In electronic circuits, wire resistance can affect signal integrity and power delivery. High-frequency signals are particularly sensitive to resistance, which can cause signal degradation. The calculator helps designers choose appropriate wire gauges for power supply lines and signal paths. For sensitive analog circuits, even small voltage drops can cause measurement errors.
Safety and Code Compliance
Electrical codes specify maximum allowable voltage drops and current densities to ensure safety. Wires that are too small for their current can overheat, creating fire hazards. The calculator helps verify compliance with these requirements. For example, a 15A circuit using 14-gauge copper wire should have less than 3% voltage drop over typical household distances.

Common Misconceptions and Advanced Topics

  • AC vs DC Resistance
  • Skin Effect
  • Temperature Compensation
Several misconceptions exist about wire resistance, and understanding advanced topics can help optimize electrical system design.
AC vs DC Resistance
At low frequencies, AC and DC resistance are essentially the same. However, at high frequencies, AC resistance becomes higher due to the skin effect - current tends to flow near the surface of the conductor rather than through its entire cross-section. This effect becomes significant at frequencies above about 1 kHz and increases with frequency. For high-frequency applications, consider using stranded wire or special high-frequency conductors.
Wire Gauge Standards
Wire gauge systems (AWG in the US, metric in Europe) provide standardized sizes, but the actual diameter and resistance can vary between manufacturers. Always verify the actual dimensions and resistivity of your specific wire. The calculator works with actual measurements, so you can use it regardless of the gauge system.
Temperature Effects and Compensation
Temperature significantly affects resistance. For precise applications, consider temperature compensation or use materials with low temperature coefficients. Some applications use resistance temperature detectors (RTDs) that rely on the predictable change in resistance with temperature for accurate temperature measurement.

Temperature Coefficient Examples:

  • Copper: +0.00393 per °C (resistance increases with temperature)
  • Aluminum: +0.00403 per °C
  • Tungsten: +0.00450 per °C
  • Nichrome: +0.00040 per °C (very stable)
  • Constantan: +0.00002 per °C (extremely stable)

Mathematical Derivation and Examples

  • Resistance Formula
  • Power Calculations
  • Practical Examples
The fundamental resistance formula R = ρL/A comes from experimental observations and theoretical physics. Understanding this derivation helps appreciate the relationships between material properties, geometry, and electrical behavior.
Derivation of the Resistance Formula
The resistance formula can be derived from Ohm's Law and the concept of current density. Current density J = I/A, where I is current and A is cross-sectional area. The electric field E = V/L, where V is voltage and L is length. From Ohm's Law in differential form: J = σE, where σ is conductivity (inverse of resistivity). Combining these equations gives V = (L/σA)I, so R = L/σA = ρL/A, where ρ = 1/σ is resistivity.
Cross-Sectional Area Calculations
For circular wires, the cross-sectional area A = πr² = π(d/2)² = πd²/4, where d is diameter. This is why resistance is inversely proportional to diameter squared - doubling the diameter reduces resistance by a factor of four. For non-circular conductors, use the actual cross-sectional area.
Power Dissipation and Efficiency
Power dissipated in a wire is P = I²R = V²/R, where V is the voltage drop across the wire. This power is converted to heat, which can cause temperature rise. For high-power applications, this heating must be considered in thermal design. Efficiency is reduced by the ratio of power lost to total power delivered.

Calculation Examples:

  • 100m of 2.5mm copper wire: R = (1.68×10⁻⁸ × 100) / (π × 0.0025²/4) = 0.34 Ω
  • Power loss at 15A: P = 15² × 0.34 = 76.5 W
  • Voltage drop: V = 15 × 0.34 = 5.1 V (3.4% of 150V)
  • Temperature rise: ΔT = P / (m × c) where m is mass and c is specific heat