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Electrical Resistance Calculator

Calculate electrical resistance from voltage and current using Ohm's Law, or from resistivity, conductor length, and cross-sectional area — compare both methods when all inputs are available.

Circuit Details

V
A
Ω·m
m
mm²

Live Results

Ohm's Law Resistance

12.00Ω

Resistivity-Based Resistance

0.02Ω

Voltage

120V

Current

10A

Resistivity

1.72e-8Ω·m

Length

10.00m

Conductor Area

10.00mm²

High resistance detected. Verify conductor size and material.

Resistance calculations follow standard electrical formulas. Always verify final design with conductor specifications and local electrical code.

How to Use This Electrical Resistance Calculator

  1. Enter voltage and current for Ohm's Law. Input the system voltage in volts and the load or circuit current in amperes. When both values are provided, the calculator computes resistance using R = V ÷ I — the classic Ohm's Law relationship used for loads, heaters, and simple circuit elements.
  2. Enter material resistivity. Input the conductor resistivity in ohm-meters (Ω·m). Copper at room temperature is approximately 1.72 × 10⁻⁸ Ω·m; aluminum is about 2.82 × 10⁻⁸ Ω·m. Resistivity characterizes how strongly a material opposes current flow.
  3. Enter conductor length. Specify the one-way conductor length in meters. Longer conductors accumulate more resistance because electrons encounter more scattering over the path. This value is used with resistivity and cross-sectional area in the resistivity formula.
  4. Enter conductor cross-sectional area. Input the conductor area in square millimeters (mm²). Larger cross-sections reduce resistance by providing more paths for current. Convert from AWG or circular mils using wire tables if needed — the Wire Gauge Calculator can help size conductors for ampacity and voltage drop.
  5. Review dual-mode results and warnings. When both Ohm's Law inputs and resistivity inputs are complete, the calculator shows both resistance values side by side. Warnings flag unusually high resistance (> 10 Ω) or suspiciously low resistivity values. Compare results against conductor specifications and local electrical code before finalizing design.

Formulas & Example

This calculator supports two standard resistance formulas. Ohm's Law uses observed voltage and current; the resistivity formula uses material and dimensional properties of the conductor.

Ohm's Law:
  R = V ÷ I

Resistivity Formula:
  Area (m²) = Area (mm²) ÷ 1,000,000
  R = (ρ × Length) ÷ Area (m²)

Where:
  R = Resistance (Ω)
  V = Voltage (V)
  I = Current (A)
  ρ = Resistivity (Ω·m)
  Length = Conductor length (m)

Worked Example

Ohm's Law with a 120 V circuit drawing 10 A:

Voltage = 120 V
Current = 10 A

R = 120 ÷ 10 = 12 Ω

Result: 12 Ω resistance

The same load could also be analyzed with the resistivity formula if conductor dimensions are known. Pair this tool with the Wire Gauge, Voltage Drop, Motor FLA, Transformer Sizing, and Breaker Size calculators for a complete electrical design workflow.

Frequently Asked Questions

What is electrical resistance?▾
Electrical resistance (R) is the opposition a material or circuit element presents to the flow of electric current, measured in ohms (Ω). It determines how much voltage is required to push a given current through a conductor or load. Higher resistance means less current for the same applied voltage. Resistance depends on material properties, conductor dimensions, and temperature.
What is the difference between Ohm's Law and the resistivity formula?▾
Ohm's Law (R = V ÷ I) calculates resistance from measured or known voltage and current — ideal when you can observe circuit behavior directly. The resistivity formula (R = ρ × L ÷ A) calculates resistance from material properties and physical dimensions before a circuit is built. Ohm's Law answers 'what is the resistance of this operating circuit?' while the resistivity formula answers 'what resistance will this conductor have?'
What affects electrical resistance?▾
Resistance increases with conductor length, decreases with larger cross-sectional area, and varies with material resistivity. Temperature raises resistance in most metals — copper and aluminum conductors are rated at 20 °C or 75 °C depending on the table. Connection quality, skin effect at high frequencies, and parallel paths also influence effective resistance in real installations.
How does conductor area impact resistance?▾
Resistance is inversely proportional to cross-sectional area — doubling the area halves the resistance. This is why larger AWG numbers (smaller wires) have higher resistance and more voltage drop. A 10 mm² copper conductor has one-tenth the resistance of a 1 mm² conductor of the same length. When sizing feeders and branch circuits, area must satisfy both ampacity requirements and acceptable voltage drop.
What are typical resistivity values for common conductors?▾
At 20 °C, approximate resistivity values are: copper 1.72 × 10⁻⁸ Ω·m, aluminum 2.82 × 10⁻⁸ Ω·m, iron 1.0 × 10⁻⁷ Ω·m, and nichrome 1.10 × 10⁻⁶ Ω·m. Silver has the lowest resistivity among common metals at 1.59 × 10⁻⁸ Ω·m. Always confirm values against the conductor manufacturer's data sheet and the temperature at which your application operates.

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