Calculate wire resistance in ohms from AWG gauge or diameter, length and material, with ohms per foot and per meter, voltage drop and maximum run length.
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Wire Resistance Formula
The wire resistance calculation is based on the relationship between resistance, resistivity, wire length, and cross-sectional area.
The same equation can be rearranged to solve for any missing value:
- R = resistance of the wire, in ohms (Ω)
- rho = resistivity of the wire material, in ohm-meters (Ω·m)
- L = wire length, in meters (m)
- A = cross-sectional area of the wire, in square meters (m²)
Choose resistance/voltage drop or maximum one-way length, then select material, AWG, bare conductor diameter or metal area, current path and conductor temperature. Enter one-way length once; an out-and-back pair applies twice that length. Current is optional for resistance and required positive for maximum length. Optional supply voltage adds drop percentage. Only validated saved inputs are recomputed; editing marks the result stale and Reset clears this calculator’s saved values.
Typical Resistivity Values for Common Wire Materials
Resistivity depends on purity, alloy and temperature. These are approximate values at20°C. The copper preset uses1.724×10⁻8Ω·m; the worked examples retain a custom1.68×10⁻8Ω·m value. Linear correction ρ(T)=ρ20[1+α(T−20°C)] is approximate near20°C. The illustrative nichrome preset is not a universal alloy or high-temperature fit; use manufacturer data for the actual grade. The model holds geometry fixed and omits AC effects, contact resistance and heating feedback; voltage-drop results do not establish ampacity or code compliance.
| Material | Resistivity, Ω·m | Notes |
|---|---|---|
| Silver | 1.59 × 10-8 | Very low resistance |
| Copper | 1.724 × 10-8 | Common electrical conductor |
| Gold | 2.44 × 10-8 | Corrosion resistant |
| Aluminum | 2.82 × 10-8 | Lightweight conductor |
| Tungsten | 5.60 × 10-8 | Higher resistance than copper |
| Nichrome | 1.10 × 10-6 | Used for heating elements |
Unit Conversions Used in Wire Resistance Calculations
| Quantity | Conversion |
|---|---|
| Resistivity | 1 Ω·cm = 0.01 Ω·m |
| Length | 1 ft = 0.3048 m |
| Length | 1 in = 0.0254 m |
| Area | 1 cm² = 0.0001 m² |
| Area | 1 in² = 0.00064516 m² |
| Resistance | 1 kΩ = 1,000 Ω |
Example Calculations
Example 1: Calculate wire resistance
For this custom-material example at20°C, use resistivity1.68×10-8Ω·m and coefficient0.00393 per°C, one conductor of length10m, and metal area0.01cm² (=1mm²). Select Custom material and resistance mode. The copper preset uses a different approximate reference value.
Convert area first:
Then calculate resistance:
The wire resistance is 0.168 Ω.
Example 2: Calculate wire length
For maximum one-way length, select Custom material with resistivity1.68×10-8Ω·m and coefficient0.00393 per°C at20°C, area0.01cm² (=1mm²), one conductor, current1A and allowed drop2V. These limits correspond to2Ω maximum conductor resistance.
Convert area first:
Then calculate length:
The wire length is about 119.05 m.
FAQ
Why does a longer wire have more resistance?
A longer wire gives electrons more material to pass through. This increases resistance. In the formula R = rho*L/A, resistance is directly proportional to length. If you double the wire length and keep the same material and area, the resistance doubles.
Why does a thicker wire have less resistance?
A thicker wire has a larger cross-sectional area. This gives current more space to flow. In the formula R = rho*L/A, resistance is inversely proportional to area. If the area doubles and the material and length stay the same, the resistance is cut in half.
Should you use one-way length or round-trip length?
This calculator always takes one-way length. Choose Single conductor for that conductor alone or Out-and-back pair for two equal conductors; the pair option doubles the current-path length internally. Do not also enter the round-trip length. Maximum length is likewise reported as one-way length at the assumed constant current.
