A wire resistance calculator answers one narrow question: how many ohms does this specific piece of conductor have? Not how thick it needs to be, not how much voltage you will lose along it — just the resistance of a length of metal with a known cross-section, at a known temperature. That is the quantity everything else is built on, and it is worth being able to compute directly.
Arb Digital publishes a free tools library with several electrical tools that sit close to this one, and the boundaries are worth stating up front. The conductivity to resistivity calculator works on the material property: it converts σ to ρ and back, in whatever units you are given, and corrects the property for temperature. This page starts where that one ends — it takes a material and turns a physical piece of wire into ohms, including the AWG geometry and the out-and-back loop. The voltage drop calculator takes the resistance as given and answers how many volts and what percentage you lose at a stated current. The wire size calculator runs the question backwards and returns the smallest conductor that passes both the ampacity and the drop check. Four adjacent tools, four different outputs.
What This Wire Resistance Calculator Does
It evaluates R = ρL ÷ A with a temperature correction, and it does the fiddly parts for you.
You can describe the conductor by cross-sectional area in square millimetres, by diameter, or by AWG gauge. The AWG path uses the geometric definition of the gauge series rather than a stored table, so it works for any gauge number including the fractional and negative ones, and it will not silently disagree with a rounded published value.
The output is the resistance of a single conductor of the length you enter, the resistance per metre, the loop resistance for a circuit where current goes out along one conductor and returns along another of the same size, and the I²R heat dissipated in that loop at the current you specify. The bars alongside show the same conductor at 20 °C, at your stated temperature, at 70 °C and at 90 °C, because temperature is the input people most often forget.
How to Use It
- Pick the material. Annealed copper is the default because it is what almost all building and appliance wiring is. Aluminium is roughly 1.6 times more resistive for the same cross-section. Nichrome is there because heating elements are the case where high resistivity is the point.
- Choose how to describe the size. Area is the most reliable, diameter is what a micrometer gives you, and AWG is what the reel says. They are all the same conductor described three ways.
- Enter the length of one conductor. Not the round trip — the loop figure is shown separately so the distinction stays visible.
- Set the operating temperature honestly. A conductor sitting in a hot loft, bundled with others, at its rated current, is not at 20 °C.
- Read the loop figure for any real circuit. Current has to come back, and unless the return path is a busbar or an earth, it comes back through a conductor with the same resistance.
The Formula: How Wire Resistance Is Calculated
The base equation. R = ρ × L ÷ A, where ρ is resistivity in ohm-metres, L is length in metres and A is cross-sectional area in square metres. Resistance rises with length and falls with area, both exactly linearly. Because area goes as the square of diameter, doubling the diameter quarters the resistance.
Area from diameter. A = π × d² ÷ 4. For stranded conductors this is the conductor area, not the overall bundle area including the gaps between strands, which is why a stranded cable is physically fatter than a solid one of the same rating.
Diameter from AWG. The gauge series is geometric by definition: d = 0.127 mm × 92((36 − n) ÷ 39). Gauge 36 is exactly 0.005 inches and gauge 0000 is exactly 0.46 inches, with 39 equal ratio steps between them. Every other gauge follows from that, which is why each drop of three gauges roughly doubles the area.
Temperature correction. RT = R20 × (1 + α × (T − 20)), where α is the temperature coefficient of resistance for the material. The table of resistivity and temperature coefficient maintained by the Department of Physics and Astronomy at Georgia State University is the source of the nominal values in the material selector. Units throughout follow the SI units definitions published by NIST.
Worked example, matching the values this page loads with. Copper at ρ = 1.68 × 10⁻⁸ Ω·m, area 2.5 mm² = 2.5 × 10⁻⁶ m², length 30 m, at 20 °C. R = 1.68 × 10⁻⁸ × 30 ÷ 2.5 × 10⁻⁶ = 0.2016 Ω, which is 0.00672 Ω per metre. The loop is twice that, 0.4032 Ω. At 16 A the loop dissipates I²R = 256 × 0.4032 = 103.2 watts, spread along 60 metres of conductor. Raise the temperature to 70 °C and the correction factor is 1 + 0.00393 × 50 = 1.1965, so the single-conductor resistance becomes 0.2412 Ω — very nearly 20% more.
Why the Loop Resistance Is the Number That Matters
Almost every practical use of a wire resistance figure is a loop problem, and quoting the single-conductor value is the most common way an otherwise correct calculation ends up half the size it should be.
Current in a two-wire circuit travels out along one conductor and back along another. Both have resistance, both drop voltage, and both dissipate heat. If your load is 30 metres away, the current sees 60 metres of copper. That is why the calculator shows both numbers and labels them, and why the loop figure is the one to use for voltage drop, for fault-loop impedance and for heat.
There are genuine exceptions. A DC circuit returning through a large chassis or a busbar has an asymmetric loop. A three-phase balanced load has no neutral current in the ideal case, so the "return" is through the other phases and the loop factor is not simply two. Both of those are handled properly in the voltage drop calculator, which asks how many phases you have before it computes anything.
Temperature Is Not a Rounding Error
Copper's temperature coefficient is about 0.00393 per degree Celsius, which sounds small and is not.
A cable run measured with a meter in a cool workshop is being measured at perhaps 18 °C. The same cable, carrying its rated current, bundled with other cables, in a warm ceiling void, can easily sit at 70 °C. That is a 50-degree rise and a 20% increase in resistance — which means 20% more voltage drop and 20% more heat than the cold measurement suggested, at exactly the moment the circuit is working hardest.
This is also why the effect is self-reinforcing. More resistance means more I²R heat, which raises the temperature further, which raises the resistance again. In a well-designed circuit that loop converges harmlessly. In an undersized or poorly ventilated one it is the mechanism behind thermal problems, which is precisely why insulation temperature ratings and derating factors exist in wiring regulations.
Not every material behaves this way. Nichrome's coefficient is roughly a tenth of copper's, which is exactly why it is used for heating elements: you want an element whose resistance barely moves as it glows, so the power stays predictable.
Where the Simple Formula Stops Being Accurate
R = ρL ÷ A is a DC equation about a uniform solid conductor, and several real effects sit outside it.
Skin effect. At alternating current, the current density concentrates toward the outside of the conductor, so the effective area is less than the geometric area and the AC resistance is higher than the DC value. At 50 or 60 Hz this is negligible for small conductors and becomes significant for large ones — which is why very large power conductors are often several smaller ones in parallel rather than one huge one.
Proximity effect. Nearby conductors carrying current distort each other's current distribution, raising resistance further. Tightly bundled cables are the usual case.
Stranding. A stranded conductor's strands spiral, so each strand is slightly longer than the cable, adding a percent or two. Published cable resistances account for this; a calculation from nominal area does not.
Terminations. A crimp, a screw terminal or a connector adds contact resistance that is often comparable to metres of the cable itself, and unlike the conductor it degrades with age, corrosion and thermal cycling. Many faults diagnosed as "high resistance cable" are a single bad termination.
Alloy and temper. The resistivity figures here are nominal values for the pure annealed metal. Hard-drawn copper, tinned copper and copper-clad aluminium all differ, and the difference can be several per cent.
Reading a Resistance Figure in Context
Whether a resistance is acceptable depends entirely on what the wire is for, and the same 0.2 ohms is either invisible or fatal to the design.
In a 230 V lighting circuit drawing 1 A, 0.4 ohms of loop resistance drops 0.4 V — about 0.17%, entirely irrelevant. In a 12 V automotive circuit driving a 20 A load, the same 0.4 ohms drops 8 V, leaving 4 V at the load and dissipating 160 watts in the wiring. Low-voltage, high-current circuits are where conductor resistance decides whether a design works at all, which is the reason car and solar installations use conductor sizes that look absurd next to their mains equivalents.
For signal circuits the concern flips again: resistance matters less than what it does to a divider with the load impedance, or to a sensor's excitation, or to a four-wire measurement's ability to cancel it. If you are working on small electronics, the resistor combination calculator and the LED resistor calculator handle the discrete-component side of the same arithmetic.
Arb Digital builds fast, dependency-free calculators and interactive tools that load instantly, rank in search and keep visitors reading.
Browse the Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using single-conductor resistance for a two-wire circuit — current returns, so the loop is twice the length and twice the resistance.
- Calculating at 20 °C for a conductor that runs hot — copper gains about 20% resistance between 20 °C and 70 °C, and the hot figure is the one that matters under load.
- Confusing diameter with area — area goes as the square of diameter, so a wire 40% thicker has half the resistance, not 40% less.
- Assuming AWG steps are linear — the series is geometric, and three gauge numbers roughly double or halve the area.
- Ignoring terminations — one poor crimp can add more resistance than the entire cable run, and it is the part that degrades over time.
Related Free Tools From Arb Digital
Use the conductivity to resistivity calculator when the question is about the material property rather than a specific piece of wire, the voltage drop calculator to turn resistance into volts and a percentage at a given current, and the wire size calculator to run the problem backwards and find the smallest conductor that passes. The resistor combination calculator, the LED resistor calculator and the resistor power rating calculator cover discrete components. Everything else is in the free online tools hub.
Frequently Asked Questions
That tool works on the material property: it converts conductivity to resistivity and back and corrects the property for temperature. This one takes a material and a physical conductor — a length, a cross-section or an AWG gauge — and returns the ohms that piece of wire actually has, including the out-and-back loop for a real circuit.
Voltage drop takes the conductor resistance and a current and tells you how many volts and what percentage you lose along the run. This page produces the resistance itself. If your question ends in volts or a percentage, use the voltage drop tool; if it ends in ohms, use this one.
For nearly every real circuit, the loop. Current travels out along one conductor and back along another, so a load 30 metres away sees 60 metres of copper. The single-conductor figure is only correct when the return path is something else, such as a chassis, a busbar or the other phases of a balanced three-phase load.
For copper, about 0.39 per cent per degree Celsius. Going from a 20 °C bench measurement to a 70 °C loaded conductor in a warm void raises resistance by roughly 20 per cent, which raises voltage drop and heat by the same proportion at exactly the moment the circuit is most loaded.
From the geometric definition of the gauge series rather than a stored table: diameter equals 0.127 mm times 92 raised to the power of (36 minus n) divided by 39. Gauge 36 is exactly 0.005 inches and gauge 0000 is exactly 0.46 inches, with 39 equal ratio steps between, so three gauge numbers roughly double or halve the area.
Common causes are terminations, stranding and temperature. Contact resistance at a crimp or screw terminal can exceed the whole cable; stranded conductors spiral so each strand is longer than the cable; and the conductor may simply be warmer than the temperature you entered. Alloy and temper account for a few per cent more.
It computes the DC resistance. At mains frequency that is close enough for small conductors, but skin effect concentrates current toward the outside of large conductors and proximity effect adds more in tight bundles, so the AC resistance of a large cable is higher than the value here.
This tool applies a published physical relationship to inputs you supply, for education and preliminary work. It is not an electrical design, and conductor sizing, protection and installation must follow the wiring regulations in force where you are and be carried out by a qualified electrician.
