Wire Resistance Calculator
Enter a wire length, cross-section or AWG gauge, material, and temperature to get the DC resistance, conductance, voltage drop, and power dissipated in the wire. The calculator uses the standard resistivity formula with a linear temperature correction. Switch between metric and imperial units and use the AWG gauge selector as a shortcut for the diameter. Results update as you type.
Formula
Worked example
A 10 m copper wire (diameter 2.05 mm, AWG 12) at 20 C: area = pi*(1.025e-3)^2 = 3.301e-6 m^2, R = 1.724e-8 * 10 / 3.301e-6 = 0.05222 Ohm. At 5 A, voltage drop = 5 * 0.05222 = 0.261 V, power loss = 25 * 0.05222 = 1.306 W.
The wire resistance formula
The DC resistance of a uniform cylindrical wire depends on three things: the resistivity of the material (rho, in Ohm*metre), the total length (L, in metres), and the cross-sectional area (A, in square metres). The relationship is R = rho * L / A. A longer wire has more resistance; a thicker wire has less. Resistivity is a property of the material and temperature only, not of the shape of the wire. Common conductors have resistivities that span several orders of magnitude: silver is the best conductor at 1.59e-8 Ohm*m, followed by copper at 1.72e-8 Ohm*m, then aluminum at 2.82e-8 Ohm*m. Resistors used in heating elements, such as nichrome, have resistivities hundreds of times higher.
Temperature correction
For most metals, resistance rises with temperature because lattice vibrations scatter electrons more vigorously. The linear correction is R_T = R_20 * [1 + alpha * (T - 20)], where alpha is the temperature coefficient of resistance and 20 C is the standard reference point. Copper has alpha = 0.00393 per C, so a 100 C rise increases its resistance by about 39%. Constantan (an alloy of copper and nickel) has an extremely small alpha near zero, which makes it useful in precision resistors that must stay stable over temperature. This calculator applies the correction whenever you specify a temperature other than 20 C.
AWG gauge and cross-sectional area
American Wire Gauge (AWG) is a standardized system used mainly in North America. Confusingly, a higher AWG number means a thinner wire: AWG 4/0 (the thickest common size) has a diameter of about 11.7 mm, while AWG 40 is barely 0.08 mm. The diameter for any integer AWG n is defined by the formula d = 0.005 * 92^((36-n)/39) inches, so you can always compute the exact cross-section from the gauge. The calculator does this for you when you enable the AWG selector: it converts the chosen gauge to a diameter, computes the cross-sectional area using A = pi * (d/2)^2, and feeds that into the resistance formula.
Voltage drop and power loss
When current flows through a wire with non-zero resistance, two things happen: the voltage at the far end is lower than at the source by V = I * R (Ohm's law), and the wire heats up, dissipating P = I^2 * R watts. Both effects are unwanted in power distribution: excessive voltage drop means the load doesn't receive its rated voltage, and excessive power loss wastes energy and raises temperature. For a round-trip circuit, double the length before calculating because the current travels the same wire twice. A useful rule of thumb for building wiring is to keep the voltage drop across conductors below 3% of the supply voltage.
Copper wire resistance by AWG gauge (at 20 C)
| AWG | Diameter (mm) | Resistance (mOhm/m) |
|---|---|---|
| 4/0 | 11.68 | 0.16 |
| 3/0 | 10.4 | 0.202 |
| 2/0 | 9.27 | 0.253 |
| 1/0 | 8.25 | 0.32 |
| 2 | 6.54 | 0.508 |
| 4 | 5.19 | 0.808 |
| 6 | 4.11 | 1.29 |
| 8 | 3.26 | 2.05 |
| 10 | 2.59 | 3.26 |
| 12 | 2.05 | 5.19 |
| 14 | 1.63 | 8.25 |
| 16 | 1.29 | 13.1 |
| 18 | 1.02 | 20.9 |
| 20 | 0.812 | 33.2 |
| 22 | 0.644 | 52.8 |
| 24 | 0.511 | 84 |
| 26 | 0.405 | 133 |
| 28 | 0.321 | 212 |
| 30 | 0.255 | 338 |
Standard AWG gauge diameters and resistance per metre for annealed copper.
Frequently asked questions
What is the formula for wire resistance?
R = rho * L / A, where rho is the material resistivity in Ohm*metre, L is the wire length in metres, and A is the cross-sectional area in square metres. For a round wire of diameter d, the area is pi*(d/2)^2. To correct for temperature, multiply by [1 + alpha*(T - 20)], where alpha is the temperature coefficient and T is the operating temperature in degrees Celsius.
Why does a higher AWG number mean a thinner wire?
AWG is based on the number of drawing steps needed to produce the wire from a standard rod. More drawing steps make the wire thinner, so a higher AWG number corresponds to a thinner diameter. The scale runs from 4/0 (0000, the thickest common size at about 11.7 mm) to 40 (about 0.08 mm), with resistance per metre increasing sharply as the gauge rises because the cross-sectional area shrinks.
How does temperature affect wire resistance?
Most metals have a positive temperature coefficient, meaning resistance rises with temperature. The effect is linear over typical operating ranges: R_T = R_20 * [1 + alpha * (T - 20)]. Copper has alpha of about 0.00393 per C, so a 50 C rise above 20 C increases resistance by roughly 20%. Nichrome and similar high-resistance alloys are used in heating elements partly because their temperature coefficient is much lower, keeping resistance more stable.
Should I double the wire length for a round-trip circuit?
Yes. In any circuit where the current travels from a source to a load and back through a separate return conductor, each conductor adds resistance. The total loop resistance is twice the one-way wire resistance (assuming both conductors are the same gauge and material). Enter double the one-way length to get the total voltage drop across the complete path.
Which wire material has the lowest resistance?
Silver has the lowest resistivity of any pure element at about 1.59e-8 Ohm*m at 20 C, but copper (1.72e-8 Ohm*m) is used almost universally for electrical wiring because it is far cheaper and nearly as conductive. Aluminum (2.82e-8 Ohm*m) is used in overhead power lines and building wiring where weight matters, even though it requires a larger cross-section to match copper resistance.
What is conductance and how is it related to resistance?
Conductance (G) is simply the reciprocal of resistance: G = 1/R, measured in siemens (S). A wire with 0.05 Ohm resistance has a conductance of 20 S. It expresses how easily current flows rather than how much it is opposed. The unit used to be called the "mho" (ohm spelled backwards) and you may still see that in older references.