Wire Resistance Calculator gives fast ohm results from conductor material, wire size, length, and temperature, helping compare cable resistance for electrical design checks faster.
From Resistivity to Ohms: The Formula Behind This Calculator
Three things determine how much a piece of wire resists current: what it’s made of, how long it runs, and how much room the current has to move through. Multiply the first by the second, divide by the third, and you get resistance at a 20°C reference point:
$$R_0 = \rho \frac{L}{A}$$
ρ (rho) is resistivity, a fixed property of the material measured in ohm-meters — copper, aluminum, silver, and each other option in the material list carries its own constant. L is conductor length. A is cross-sectional area, whether you type that in directly or let the calculator derive it from an AWG gauge number.
Temperature moves that baseline. The calculator applies a linear correction on top of R₀:
$$R(T) = R_0 \left[1 + \alpha (T – 20)\right]$$
α (alpha) is the material’s temperature coefficient of resistance, and T is the operating temperature in Celsius. For most metals α is a small positive number, so a hotter wire measures higher resistance than the same wire at the 20°C reference. A couple of materials in the list run the other way — more on that below.
When you pick a gauge instead of typing an area, the tool converts using the standard AWG geometric relationship:
$$A_n = 0.012668 \times 92^{\frac{36-n}{19.5}} \text{ mm}^2$$
where n is the AWG number. Area scales by a fixed ratio for every step in gauge, which is why 10 AWG isn’t twice as thick as 12 AWG — the two are about 1.6 times apart, following the same 92-based progression the American Wire Gauge standard has used since the 1850s.
12 AWG Copper at 100 Feet: Walking Through the Numbers
Take 100 feet of 12 AWG solid copper wire, the kind you’d find feeding a branch circuit, running through an enclosed space that hits 60°C in summer — a realistic worst case for an attic run or a conduit in direct sun.
First, the gauge converts to area. Plugging n = 12 into the AWG formula gives about 3.31 mm², or 3.311 × 10⁻⁶ m². Length converts from feet to meters: 100 ft × 0.3048 = 30.48 m. Copper’s resistivity is 1.68 × 10⁻⁸ Ω·m. Multiply length by resistivity, divide by area, and R₀ comes out to roughly 0.155 Ω at the 20°C reference point.
Now apply the temperature correction. Copper’s α is 0.00393, and the wire is running 40°C above the reference (60 − 20). That gives a multiplier of 1 + (0.00393 × 40) = 1.157, so the final resistance is about 0.179 Ω — a 15.7% jump over the cool-wire baseline just from heat.
| Step | Value |
|---|---|
| Cross-sectional area (12 AWG) | 3.31 mm² (3.311 × 10⁻⁶ m²) |
| Length (100 ft converted) | 30.48 m |
| Copper resistivity (ρ) | 1.68 × 10⁻⁸ Ω·m |
| Resistance at 20°C reference (R₀) | 0.155 Ω |
| Temperature coefficient (α) | 0.00393 per °C |
| Operating temperature | 60°C |
| Final resistance R(60°C) | 0.179 Ω |
| Change from 20°C baseline | +15.72% |
| Resistance per meter | 5.87 mΩ/m |
Is 0.18 Ω High or Low? Comparing Against Standard Wire Tables
Manufacturer and standards-body wire tables commonly list 12 AWG copper at close to 1.6 Ω per 1,000 feet at 20°C. Run the math on 100 feet at that rate and you land near 0.155 Ω — matching the calculator’s R₀ almost exactly, which is a useful sanity check whenever you’re unsure if a result looks reasonable.
There’s a wrinkle worth flagging. Those published tables typically use annealed copper’s resistivity, 1.724 × 10⁻⁸ Ω·m — the IACS commercial-wire standard. This calculator’s default “Copper” selection instead uses the theoretical pure-metal value, 1.68 × 10⁻⁸ Ω·m.
The gap between the two is about 2.6%, small but real, so if your number needs to match a manufacturer’s spec sheet closely, switch the material dropdown to “Copper (Annealed)” rather than leaving it on the default.
Unlike voltage drop or ampacity, there’s no pass-or-fail line here. A higher resistance reading isn’t automatically a problem — it just means more energy turns into heat and more voltage gets lost across that run for a given current. Whether that matters depends on the load and the distance, which is a separate calculation from resistance by itself.
Gauge, Material, and Temperature: Which Actually Moves the Needle
Cross-section swings the result hardest, because area sits in the denominator and scales geometrically with gauge. Drop three AWG sizes and area roughly doubles; resistance roughly halves. Length matters too, but it’s a straight linear multiplier — doubling the run doubles resistance, no exponential curve involved.
Material choice is the next biggest lever. Aluminum’s resistivity, 2.65 × 10⁻⁸ Ω·m, runs about 58% higher than copper’s 1.68 × 10⁻⁸ Ω·m, which is exactly why aluminum conductors get sized a gauge or two heavier than copper for equivalent current. Silver, at 1.59 × 10⁻⁸ Ω·m, edges out even copper as the least resistive option in the list, though its cost keeps it out of ordinary wiring.
Temperature behaves the way you’d expect for ordinary metals — resistance climbs as things heat up — but two entries in the material list break that pattern. Carbon (α = −0.0005) and silicon (α = −0.075) both carry negative temperature coefficients, meaning their resistance drops as they warm.
Leave the material dropdown on silicon while modeling a heating element and you’ll see resistance fall as temperature rises, which is correct semiconductor physics but not what most people mean when they ask about “wire” resistance.
A few conditions in the code are worth knowing about even if you never trigger them. If a negative-α material and a large enough temperature swing push the corrected resistance below zero, the calculator floors the result at 0 Ω instead of returning a non-physical negative number.
The reverse-lookup that reports “closest AWG” for a custom area only displays for values that resolve to roughly −10 through 50 gauge; anything outside that range — think a bus bar or a hair-thin trace — just shows “Custom Profile” instead of a meaningless gauge number.
Unit selection is a quieter source of error than any of the physics. The resistivity field alone accepts three different units — ohm-meters, microohm-centimeters, and ohm-centimeters — and the profile field accepts twelve, spanning square millimeters, circular mils, and raw diameter in six different length units. Picking cm² when you meant mm² inflates the area by a factor of 100 and understates resistance by the same margin, with no warning beyond a number that looks wrong.
The material list also includes near-perfect insulators — glass at 1.0 × 10¹⁰ Ω·m, PTFE (Teflon) at 1.0 × 10²³ Ω·m — sitting eighteen to thirty-one orders of magnitude above copper. They’re in there to illustrate scale, not because anyone is calculating the “resistance” of a glass wire.
Common Questions About Wire Resistance
What’s the difference between resistance and resistivity?
Resistivity is a fixed property of a material — copper’s doesn’t change whether you’re looking at a hair-thin trace or a thick bus bar. Resistance is what you get once that material is shaped into an actual conductor, since it factors in length and cross-sectional area on top of the material constant.
Does wire length or wire gauge affect resistance more?
Gauge usually moves faster, since area scales geometrically with AWG number while length is only a linear multiplier. Doubling a run’s length doubles its resistance; dropping three gauge sizes can produce roughly the same effect in the opposite direction.
Why is aluminum wire more resistive than copper?
Aluminum’s resistivity, 2.65 × 10⁻⁸ Ω·m, sits about 58% above copper’s 1.68 × 10⁻⁸ Ω·m because aluminum’s outer electrons are more loosely bound and scatter more easily as current passes through. That difference is why aluminum branch wiring is typically run one or two gauges heavier than copper for the same job.
Does wire resistance really change with temperature?
For ordinary metals, yes — resistance rises in a roughly straight line as temperature climbs, governed by the material’s α value. A copper conductor running hot inside a wall or conduit will measure noticeably higher resistance than the same wire sitting at a cool 20°C.
How do I convert an AWG number to a cross-sectional area?
Area scales by a factor of 92 raised to a fractional power based on distance from a reference gauge — the same relationship this calculator uses internally. In practice you don’t need to do it by hand: 12 AWG works out to about 3.31 mm², and 10 AWG to about 5.26 mm².
What counts as a “normal” resistance for a length of copper wire?
It depends entirely on gauge and length, but 12 AWG copper is commonly tabulated at roughly 1.6 Ω per 1,000 feet at 20°C. Thinner gauges or longer runs push that number up quickly, since resistance climbs linearly with length and drops off just as fast with more cross-sectional area.
Why do some materials get less resistive as they heat up?
In ordinary metals, heat causes more electron collisions, which raises resistance. Semiconductors like silicon and carbon work the other way — added heat frees up more charge carriers than it disrupts, so their resistance falls as temperature rises. That’s why both carry a negative α value in this calculator’s material list.
Does higher wire resistance mean higher voltage drop?
For a given current, yes — voltage drop equals current multiplied by resistance, so a higher-resistance run loses more voltage over its length. Resistance alone doesn’t say whether that drop is actually a problem, though; that depends on the current involved and how far the load sits from the source.
What This Calculator Doesn’t Model
This tool computes theoretical DC resistance from bulk resistivity, geometry, and a linear temperature model. It doesn’t account for skin effect or proximity effect at AC frequencies, the resistance difference between solid and stranded conductors of the same gauge, connector or termination resistance, or the manufacturing tolerances that make real wire drift slightly from published resistivity constants. Treat the output as a physics-based estimate to sanity-check against, not a replacement for a manufacturer’s datasheet or a direct measurement.