Resistance from resistivity, length and thickness
A wire’s resistance grows in proportion to its length and shrinks in proportion to its cross-sectional area. The material sets the constant ρ (resistivity): copper is 1.68×10−8 Ω·m, aluminum about 1.6× higher. Double the length and you double R; double the diameter and R drops to a quarter, since area goes with diameter squared.
Copper resistance by AWG gauge
AWG numbering runs backwards — a bigger number is a thinner wire with more resistance. The gauge number is not the area in mm².
| AWG | Area (mm²) | Ω per 1000 ft | Ω per km |
|---|---|---|---|
| 4 | 21.15 | 0.248 | 0.815 |
| 8 | 8.37 | 0.628 | 2.06 |
| 10 | 5.26 | 0.999 | 3.28 |
| 12 | 3.31 | 1.588 | 5.21 |
| 14 | 2.08 | 2.525 | 8.28 |
| 18 | 0.823 | 6.385 | 20.9 |
| 24 | 0.205 | 25.67 | 84.2 |
Every 3 gauges roughly doubles the resistance per foot: AWG 14 is about twice AWG 11, and AWG 24 is about eight times AWG 15.
Two things that bite in real circuits
- Count the return path. A 50 m run is 100 m of wire, out and back. Voltage drop uses the full loop length, so a wire that looks fine at 50 m may drop twice what you expect.
- Temperature raises resistance. Copper climbs about 0.4% per °C, so R(80°C) is roughly 24% above R(20°C). Heater wire (nichrome) is chosen for high, stable resistivity, not low.
- AWG is not mm². AWG 12 is 3.3 mm², not 12. Convert before doing any metric sizing.
Common questions
What is the formula for wire resistance?
R equals rho times length divided by cross-sectional area (R = rho L / A). Rho is the material resistivity, so a longer wire has more resistance and a thicker wire has less. Copper resistivity is about 1.68 times 10 to the minus 8 ohm-meters at 20 degrees Celsius.
Does a higher AWG number mean more or less resistance?
More. AWG runs backwards: a higher gauge number is a thinner wire with a smaller area, so its resistance per foot is higher. AWG 24 has far more resistance per foot than AWG 4.
How much does resistance change with temperature?
For copper, resistance rises about 0.4% per degree Celsius. Going from 20 to 80 degrees raises a copper wire resistance by roughly 24%, which matters for wires that run hot.
