Introduction
Every wire fights the flow of electricity a little. That fight is called resistance, and it is measured in ohms (Ω). This Wire Resistance Calculator tells you how many ohms your wire has. Just pick the metal, type the length, and choose the wire size.
The math is simple: R = ρL / A. Here ρ (rho) is how well the metal blocks current, L is the wire length, and A is the area of the wire's cut end. Thicker wire means less resistance. Longer wire means more.
You can enter wire size three ways: by diameter, by cross-sectional area, or by AWG gauge number. The tool works in metric and imperial units, so meters, feet, millimeters, and inches all work. It shows each step of the math so you can check the answer or learn how it works.
The Advanced Calculator adds more power. You can chain up to 12 wire segments in series, mix different metals, and see how heat changes the total resistance. Hot wire has more resistance than cool wire, and this tool shows you how much. You can also set tolerance ranges to find the worst-case high and low values.
The Wire Reference Table lists 45 AWG copper wire sizes with diameter, area, ohms per 1000 feet, ohms per meter, and safe current limits. It is handy for house wiring, car projects, speaker runs, and voltage drop checks.
How to use our Wire Resistance Calculator
Pick your wire material, type in the wire length, and set the wire thickness. The calculator gives you the DC resistance of the wire in ohms, plus the area, the diameter, the resistance per foot and per meter, and a full step-by-step solution.
Standard Calculator
Conductor Material: Choose the metal your wire is made of, like copper or aluminum. Each metal has its own resistivity, so this changes the answer a lot. Pick "Custom" if your metal is not listed.
Custom Resistivity (ρ): Only shows when you pick Custom. Type the resistivity value and pick its unit, such as Ω·m. You can type it in short form, like 1.72e-8.
Resistivity in Use: This box fills in by itself. It shows the exact resistivity the math is using.
Wire Length: Type how long the wire is and pick the unit (mm, cm, m, km, in, or ft). Use the one-way length of the wire. Longer wire means more resistance.
Cross-Section Input Mode: Choose how you want to describe the wire thickness: by Diameter, by Cross-Sectional Area, or by AWG Gauge. Your numbers carry over when you switch.
Wire Diameter: Type the width of the wire across the middle and pick the unit (mm, in, or mil). Thicker wire means less resistance.
Cross-Sectional Area: Type the area of the cut end of the wire and pick the unit (mm², cm², m², in², cmil, or kcmil).
AWG Gauge: Pick a standard wire size from 4/0 down to 40. A smaller number means a thicker wire. The diameter and area boxes fill in for you.
Display Resistance In: Pick the unit for the answer, like mΩ or Ω. Leave it on Auto and the tool picks the best one.
Advanced Calculator
Segments: Each segment is one piece of wire in the run. Set its material, length, and thickness the same way as above. Click Add Segment for more pieces, up to 12. The pieces are joined in series, so their resistances add up.
Temperature Coefficient (α): Only shows when a segment uses a custom material. Type how much the resistance changes per degree above 20 °C, and pick per °C or per °F.
Operating Temperature: Type how hot the wire will get and pick °C or °F. Hot wire has more resistance than cool wire.
Show Total Length In: Pick the unit used to show the total length of all segments added together.
Resistivity Tolerance: Type the percent that the metal's resistivity may vary, from 0 to 100. This covers small changes from the factory.
Length Tolerance: Type the percent that your wire length may be off, from 0 to 100. This covers cutting and measuring errors. Both tolerances give you a worst-case high and low resistance.
Wire Reference Table
Filter box: Type an AWG size or a job, like "12" or "house wiring", to find that row fast. The table lists diameter, area, ohms per 1000 ft, ohms per meter, and safe current for solid copper wire.
What Is Wire Resistance?
Every wire fights the flow of electricity a little bit. That push-back is called resistance, and we measure it in ohms (Ω). No wire is perfect, so some of the energy you send down a wire turns into heat instead of reaching your light, motor, or speaker.
The Wire Resistance Formula
DC wire resistance comes from three things: the material, the length, and the thickness.
R = ρ × L ÷ A
- R – resistance in ohms (Ω)
- ρ (rho) – resistivity of the metal, in Ω·m. This tells you how much that metal blocks current.
- L – length of the wire in meters. Twice as long means twice the resistance.
- A – cross-sectional area in square meters. Twice the area means half the resistance.
If you know the wire's diameter instead of its area, find the area first with A = π/4 × d². Because area depends on diameter squared, a wire that is twice as wide has four times the area and only one-fourth the resistance.
Why the Metal Matters
Silver is the best conductor, but copper is close and costs far less, so most wiring is copper. Aluminum has about 64% more resistance than copper for the same size, so aluminum wire must be thicker to do the same job. Metals like nichrome have very high resistivity on purpose. They are used in heaters and toasters, where making heat is the goal.
AWG Wire Gauge
In the United States, wire thickness is often given as AWG (American Wire Gauge). The rule feels backwards: a smaller gauge number means a thicker wire. AWG 10 is thicker than AWG 14. Going down 3 gauge steps roughly doubles the area and cuts resistance in half. Common sizes include AWG 14 for 15-amp home circuits, AWG 12 for 20-amp circuits, and AWG 10 for 30-amp circuits like a dryer.
Temperature Changes Resistance
Metals get more resistive when they heat up. The formula is:
RT = R20 × [1 + α(T − 20)]
Here α (alpha) is the temperature coefficient of the metal, and 20 °C is the reference temperature where resistivity values are listed. Copper has α ≈ 0.00393 per °C, so a copper wire running at 65 °C has about 18% more resistance than the same wire at room temperature. That is why engineers check resistance at the hot operating temperature, not just at 20 °C.
Why It Matters
Wire resistance causes voltage drop (V = I × R) and power loss (P = I² × R). On a long run, too much resistance means dim lights, slow motors, weak signals, and wasted energy as heat. Electricians usually keep voltage drop under about 3% for a branch circuit. The fixes are simple: use a thicker wire, shorten the run, or pick a better conductor.
Things to Keep in Mind
- Use the one-way length here. A circuit needs current to go out and come back, so for voltage drop you often double the length.
- This is DC resistance. With AC, the skin effect pushes current toward the outside of the wire and raises resistance, especially in big conductors and at high frequencies. The Impedance Calculator covers the AC picture, including reactance.
- Stranded wire has slightly more resistance than solid wire of the same gauge because the strands twist and are a bit longer.
- Ampacity limits (how much current a wire may safely carry) come from heat and code rules, not from this formula alone. Always follow your local electrical code.