Engineering calculators

Wire Resistance Calculator

Updated Aug 4, 2026 By Jehan Wadia
Rate Formulas
Conductor Material & Resistivity
Resistivity (ρ) = how strongly the material opposes current. Preset values are quoted at 20 °C.
Exact value fed into the calculation.
Wire Length & Cross-Section
One-way conductor length. Converted to metres internally.
Values carry over when you switch modes.
American Wire Gauge — smaller number = thicker wire.
DC Resistance
Total DC resistance of the run (at 20 °C)
Step-by-Step Solution
Same Wire, Different Materials
Multi-Segment Wire Run (Series)
Segments are connected in series — resistances add.
Temperature Adjustment
Base resistivities are referenced at 20 °C (68 °F). Switching the unit converts the value you typed.
Tolerance & Variation Analysis
Manufacturing variation in material resistivity (0–100%).
Measurement / cut-length variation (0–100%).
Both tolerances are combined in the same direction to give a worst-case envelope, not a statistical distribution.
Total Run Results
Total series resistance @ 20 °C
Resistance at operating temperature
Change vs. 20 °C baseline
Total wire length
Worst-case resistance envelope (tolerances applied)
Per-segment breakdown for the current inputs.
Segment Material Length Cross-Section Area R @ 20 °C R @ T
Step-by-Step Solution
Resistance by Segment
Filter the Reference Table
Standard American Wire Gauge (AWG) solid copper conductor properties — diameter, cross-sectional area, DC resistance at 20 °C computed with ρCu = 1.72 × 10-8 Ω·m, and typical current-carrying capability.
AWG Gauge Typical Applications Diameter (in) Diameter (mm) Area (circular mils) Area (mm²) Ω / 1000 ft Ω / 100 ft Ω / 1 ft Ω / m Max Current (A) — Chassis Max Current (A) — Power

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. Our Scientific Notation Calculator can help you convert awkward numbers into this format.

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. If you need to switch between systems first, try the Meters to Feet Calculator or the Mm to Inches Calculator.

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). The Circle Area Calculator is useful if you are working the area out by hand.

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. To choose a gauge for a given load, pair this with the Wire Size Calculator.

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. For resistors wired side by side instead, use the Parallel Resistor Calculator.

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. The Celsius to Fahrenheit Calculator helps if your spec sheet uses the other scale.

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. See the Percent Error Calculator if you want to compare a measured value against the calculated one.

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. If you know any two of voltage, current, and resistance, the Ohms Law Calculator will find the third.

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. If you are pricing out a copper run, the Copper Weight Calculator estimates how much metal you are buying.

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. Before you pull those conductors, check the Conduit Fill Calculator to make sure they fit the raceway.

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. Heat also stretches the metal itself — see the Thermal Expansion Calculator for that side of the story.

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. Use the Power Calculator to size the loss in watts, the Amp Calculator to find the current, and the Electricity Cost Calculator to put a dollar figure on the wasted energy.

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.
  • Working on a circuit board instead of a cable? The Trace Width Calculator applies the same idea to copper traces, and the LED Resistor Calculator sizes a series resistor for small loads.

Formulas used

DC resistance of a conductor
R = \frac{\rho L}{A}
Cross-sectional area from diameter
A = \frac{\pi}{4} d^2
Resistance in terms of diameter
R = \frac{4 \rho L}{\pi d^2}
Equivalent round diameter from area
d = \sqrt{\frac{4A}{\pi}}
AWG wire diameter
d = 0.005 \times 92^{\frac{36-n}{39}}\ \text{in}
Temperature-corrected resistance
R(T) = R_{20}\left[1 + \alpha (T - 20)\right]
Total series resistance of multiple segments
R_{total} = \sum_{i=1}^{n} R_i(T)
Worst-case tolerance envelope
R_{min,max} = R(T)\left(1 \pm \frac{t_\rho}{100}\right)\left(1 \pm \frac{t_L}{100}\right)

Frequently asked questions

How much wire resistance is too much?

There is no single limit. Judge it by voltage drop instead. Multiply the resistance by your current, then double it for the trip out and back. Most electricians keep the drop under about 3% of the supply voltage for a branch circuit.

Example: 0.5 Ω of round-trip resistance at 15 A drops 7.5 V. On a 120 V circuit that is over 6%, so you need thicker wire.

Why does my answer show in mΩ or µΩ instead of ohms?

The unit menu is set to Auto, so the tool picks the size that reads best. Short or thick wires often have less than one ohm, so the answer shows in milliohms (mΩ) or microohms (µΩ).

1 Ω = 1,000 mΩ = 1,000,000 µΩ. You can lock the unit to Ω with the Display Resistance In menu.

Do I enter one-way length or the total wire in the circuit?

Enter the one-way length, meaning the distance from the source to the load. The tool gives the resistance of that single conductor.

If you want the resistance of the full loop (hot plus neutral), double the length or double the answer.

What is a circular mil (cmil) and a kcmil?

A circular mil is the area of a circle that is 0.001 inch across. It is a US way to state wire area without using fractions of an inch.

1 kcmil = 1,000 cmil. Big power cables are sold this way, like 250 kcmil. You will also see kcmil written as MCM. Both mean the same thing.

How do I get resistance per foot or per 1000 feet?

The Standard Calculator shows it for you. Look at the Resistance per unit length tile after you press Calculate. It lists ohms per meter and ohms per 1000 feet.

You can also set the length to 1000 and the unit to ft, and read the answer straight off.

What does the worst-case envelope mean in the Advanced tab?

It is the highest and lowest resistance you could get if both tolerances go the wrong way at the same time.

The tool multiplies the resistance by (1 − ρ tolerance)(1 − length tolerance) for the low value, and by (1 + ρ tolerance)(1 + length tolerance) for the high value. It is a safety range, not an average.

Can I mix copper and aluminum in one run?

Yes. Use the Advanced Calculator and give each segment its own material. Add up to 12 segments. The tool adds their resistances because they are in series.

Note: joining copper and aluminum in real wiring needs approved connectors, or the joint can corrode and overheat.

Does wire insulation change the resistance?

No. Only the metal carries the current, so resistance depends on the metal, the length, and the metal's area. Insulation does not add or remove ohms.

Insulation does matter for heat. A hotter wire has higher resistance, and the insulation type sets how hot the wire is allowed to run.

What temperature should I use in the Advanced tab?

Use the temperature the wire will actually reach while working, not the room temperature. For a loaded circuit in a warm wall or conduit, 60–75 °C is common. For a cool bench project, 20–30 °C is fine.

Leave it at 20 °C to see the plain textbook value.

Why is my answer a little different from a wire chart?

Charts use slightly different numbers. This tool uses ρ = 1.72 × 10⁻⁸ Ω·m for copper at 20 °C. Some tables use 1.68 × 10⁻⁸, and others list values for stranded wire or for 75 °C.

The gap is usually 1–5%, which does not change your wire choice.

Can I use this for a nichrome heating element?

Yes. Pick Nichrome from the material list, then enter the wire length and gauge. Nichrome has about 64 times more resistivity than copper, so it makes heat on purpose.

Once you know the resistance, use Ohm's law to find the current and the watts it will produce.

Does this work for wires in parallel?

Not directly. The Advanced tab adds segments in series, so the ohms add up.

For two same-size wires side by side, find the resistance of one wire here, then divide by 2. For three, divide by 3.

What does conductance in siemens (S) mean?

Conductance is the opposite of resistance. G = 1 ÷ R. A high number means current flows easily.

A wire with 0.5 Ω has 2 S of conductance. It is handy when you compare wires side by side, but resistance is what most wiring math uses.

Why does the calculator show other materials in a bar chart?

The chart uses your exact length and area, then swaps in each metal. It shows how much the material alone changes the ohms.

Your chosen metal is the dark bar. This makes it easy to see, for example, that aluminum needs a thicker size to match copper.

Why does the tool say to check my inputs?

Length, diameter, area, and resistivity must all be greater than zero. A blank box, a zero, or a negative number stops the math.

The bad field turns red with a short message. Fix it and the answer appears again right away.

How does 3 AWG steps really halve the resistance?

Each AWG step changes the diameter by a fixed ratio. Three steps thicker gives about double the area, and double the area means half the resistance.

Try it: AWG 14 has about 2.08 mm² and AWG 11 has about 4.17 mm². The resistance per meter drops by about half.

Can I type resistivity in scientific notation?

Yes. Pick Custom as the material and type it like 1.72e-8. That means 1.72 × 10⁻⁸.

You can also switch the unit to Ω·cm, µΩ·cm, Ω·mm²/m, or Ω·cmil/ft, so you can copy a value straight from a datasheet.

Is stranded wire the same as solid wire in this tool?

The math treats the wire as one solid conductor. Real stranded wire has about 2–5% more resistance because the strands spiral and are a bit longer than the cable.

For a safer number on stranded cable, add a few percent, or use the resistivity tolerance box in the Advanced tab.

Which AWG size do most homes use?

AWG 14 for 15 A lighting and outlet circuits, AWG 12 for 20 A circuits, and AWG 10 for 30 A loads like a dryer. Large ranges and service feeders use AWG 6 through 4/0.

The Wire Reference Table lists the job for each gauge along with its ohms and safe current.