Wire Resistance Calculator
Calculate DC wire resistance from conductor material, length, cross-sectional area, or AWG size, including one-way conductor and two-conductor cable loop resistance. It is intended for DC and low-frequency conductor resistance estimates, not code-compliant ampacity or high-frequency AC resistance.
Engineering tool
Wire Resistance Calculator
Calculate DC conductor resistance from material resistivity, conductor length, cross-sectional area, or AWG size while keeping one-way and loop length conventions explicit.
Preset material values are reused from the shared AWG reference data.
Single-conductor modes use the entered conductor length directly.
Use effective conductive area. Do not use cable outside diameter or insulation diameter.
Result console
- Wire Resistance
- 68.96mΩ
- Resistance per Meter
- 6.896mΩ/m
- Resistance per Kilometer
- 6.896Ω/km
- Total Conductor Length
- 10m
- Material
- Copper
- Resistivity
- 1.724e-8Ω·m
- Conductor Area
- 2.5mm²
- Conductance
- 14.5012S
DC conductor resistance only. This calculator does not determine safe ampacity, fuse size, short-circuit current, PCB trace resistance, motor winding resistance, transformer winding resistance, or high-frequency AC resistance.
Formula reference
Wire resistance formulas
The calculator uses SI units internally. Display units are converted only after the calculation, so rounded AWG area is not used as an intermediate value.
R = rho L / ARloop = rho(2Lone-way) / AL = RA / rhoA = rho L / RmaxR/L = rho / AVariable definitions
- R
- conductor resistance, ohms
- rho
- electrical resistivity, ohm-meter
- L
- total conductor length used in the resistance model
- Lone-way
- one-way source-to-load cable run
- A
- conductive cross-sectional area
Wire Resistance Formula Audit
| Core Formula | R = rho L / A. |
|---|---|
| Inverse Length Formula | L = RA / rho. |
| Inverse Area Formula | A = rho L / R. |
| Resistance per Unit Length Formula | R/L = rho / A. |
| Loop Resistance Formula | Rloop = rho(2Lone-way)/A for two equal conductors. |
| One-Way Length Convention | One-way cable length is source-to-load physical run length. |
| Total Conductor Length Convention | Total conductor length is the length actually used in R = rho L/A. |
| Resistivity Unit Convention | Internal resistivity unit is ohm-meter. |
| Area Unit Convention | Internal area unit is square meter. |
| Length Unit Convention | Internal length unit is meter. |
| Resistance Unit Convention | Internal resistance unit is ohm. |
| Material Data Source | `data/reference/awg.ts` material presets. |
| Material Reference Temperature | Copper and aluminum presets are approximate values near 20°C. |
| AWG Dataset Reuse | `awgRecords` from `data/reference/awg.ts`. |
| AWG Precision Policy | Calculations use raw shared dataset values, not display-rounded area. |
| AWG Selection Direction | Required-area mode selects an AWG record with area greater than or equal to the required area. |
| Temperature Boundary | No automatic rho(T) correction; WIR-011 owns temperature-dependent wire resistance. |
| DC / AC Boundary | DC and low-frequency resistive model only; high-frequency AC resistance may be higher. |
| Stranded Wire Boundary | Use effective conductive cross-sectional area, not cable outside diameter. |
| Ampacity Boundary | No ampacity or code-compliant current rating is calculated. |
| PCB Boundary | No PCB trace resistance or IPC trace sizing. |
| Motor Boundary | No motor winding resistance or motor-specific copper loss. |
| Transformer Boundary | No transformer winding wire sizing. |
| Conductance | Conductance may be shown as G = 1/R when R is positive. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| Area input | rho=1.724e-8, L=10m, A=2.5mm² | R=0.06896Ω |
| Milliohm display | 0.06896Ω | 68.96mΩ |
| Resistance per meter | rho/A | 0.006896Ω/m |
| mΩ per meter | 0.006896Ω/m | 6.896mΩ/m |
| Ω per kilometer | 0.006896Ω/m × 1000 | 6.896Ω/km |
| Two-wire loop | one-way 10m, two equal conductors | Rloop=0.13792Ω |
| Loop length | one-way 10m | total conductor length=20m |
| Length solve | R=.06896Ω, A=2.5mm² | L=10m |
| Loop length solve | Rloop=.13792Ω, A=2.5mm² | one-way length=10m |
| Required area | rho=1.724e-8, L=10m, Rmax=.1Ω | A=1.724mm² |
| Length doubles | same rho and A | R doubles |
| Area doubles | same rho and L | R halves |
| Resistivity doubles | same L and A | R doubles |
| Zero length | L=0 | R=0 |
| Area conversion | 1mm² | 1e-6m² |
| Area conversion | 1cm² | 1e-4m² |
| Area conversion | 1in² | 0.00064516m² |
| Length conversion | 1km | 1000m |
| Length conversion | 1ft | 0.3048m |
| Length conversion | 1in | 0.0254m |
| Resistance conversion | 1mΩ | 0.001Ω |
| Resistance conversion | 1µΩ | 1e-6Ω |
| Resistivity conversion | 1Ω·mm²/m | 1e-6Ωm |
| Resistivity conversion | 1µΩ·cm | 1e-8Ωm |
| Copper example | 1.724e-8Ωm | 0.01724Ω·mm²/m |
| Copper example | 1.724e-8Ωm | 1.724µΩ·cm |
| Inverse check | R=ρL/A | L=RA/ρ |
| Inverse check | R=ρL/A | A=ρL/R |
| Loop identity | single conductor ×2 | equal two-conductor loop resistance |
| AWG raw area | AWG area from shared dataset | matches direct-area calculation |
| Area monotonicity | larger area | lower resistance |
| Area monotonicity | smaller area | higher resistance |
| Material monotonicity | higher rho | higher resistance |
| R/L identity | rho/A | independent of length |
| Negative length | L<0 | rejected |
| Zero area | A=0 | rejected |
| Zero resistivity | rho=0 | rejected |
| Negative Rmax | Rmax<0 | rejected |
| NaN | invalid number | rejected |
| Infinity | non-finite value | rejected |
Engineering Notes
- DC conductor resistance follows R=rho L/A.
- Resistance increases linearly with conductor length.
- Resistance decreases as conductor cross-sectional area increases.
- Electrical resistivity depends on conductor material.
- Material resistivity is specified at a reference temperature.
- Wire resistance changes with temperature, but WIR-001 does not apply temperature correction.
- A two-conductor DC loop has twice the conductor length of the one-way run when both conductors are equal.
- One-way length and total conductor length must not be confused.
- AWG data is reused from the existing ECParts reference dataset.
- Larger AWG numbers generally correspond to smaller conductor sizes.
- Insulation diameter is not conductor diameter.
- Stranded-wire calculations require effective conductive cross-sectional area.
- AC resistance may be higher due to skin and proximity effects.
- Low-resistance assemblies can also include contact and termination resistance.
Common Mistakes
- Using one-way length when loop resistance is required.
- Doubling a length that is already total conductor length.
- Forgetting mm² to m² conversion.
- Using cable outside diameter as conductor diameter.
- Confusing resistivity with resistance.
- Using copper resistivity for aluminum.
- Assuming resistivity is temperature-independent.
- Treating AWG number as conductor diameter directly.
- Assuming larger AWG number means larger wire.
- Using rounded AWG area in internal calculations.
- Using DC resistance as exact high-frequency AC resistance.
- Confusing Ω·m with Ω/m.
Support reference
FAQ
How do I calculate wire resistance?
Use R = rho L / A, where rho is electrical resistivity, L is conductor length, and A is conductor cross-sectional area.
What is the wire resistance formula?
The DC wire resistance formula is R = rho L / A. Resistance increases with length and decreases as conductor area increases.
What is electrical resistivity?
Electrical resistivity is a material property that describes how strongly a conductor resists current flow. It is commonly expressed in ohm-meters.
How does wire length affect resistance?
For the same material and conductor area, resistance is directly proportional to length. Doubling conductor length doubles resistance.
How does wire size affect resistance?
For the same material and length, resistance is inversely proportional to conductor area. Larger conductive area gives lower resistance.
How do I calculate cable loop resistance?
For a two-conductor DC circuit with equal conductors, calculate total conductor length as twice the one-way cable run, then use Rloop = rho(2Lone-way)/A.
What is the difference between one-way length and loop length?
One-way length is the physical source-to-load cable run. Loop length is the total conductive path out and back through two conductors.
Why is a two-wire loop twice the one-way conductor length?
Current leaves through one conductor and returns through another equal conductor, so the total conductor length is two times the one-way run.
How do I calculate resistance from AWG?
Select an AWG size and the calculator uses the shared ECParts AWG dataset for conductor area, then applies R = rho L / A.
Does this calculator convert AWG to mm²?
It displays the AWG area used in the resistance calculation, but the dedicated AWG to mm² Converter remains the primary AWG conversion tool.
Does a larger AWG number have more resistance?
Usually yes. Larger AWG numbers mean smaller conductor diameter and area, which increases resistance for the same material and length.
How do I calculate resistance per meter?
Use R/L = rho/A. The calculator reports resistance per meter and per kilometer for the selected conductor.
How do I calculate resistance per kilometer?
Calculate rho/A in ohms per meter, then multiply by 1000 to get ohms per kilometer.
How do I calculate maximum wire length from resistance?
Rearrange the resistance formula to L = RA/rho. In two-wire loop mode, one-way length is half the total conductor length.
How do I calculate required wire area from a resistance limit?
Use A = rho L / Rmax. If the length is a two-wire one-way run, the calculator uses twice that length for the loop conductor path.
Does copper wire resistance change with temperature?
Yes. Material resistivity is specified at a reference temperature and changes with temperature. WIR-001 does not perform full temperature correction.
What reference temperature is used for resistivity?
The shared copper and aluminum presets identify their resistivity as approximate reference values near 20 °C.
Can I calculate aluminum wire resistance?
Yes. The calculator includes aluminum from the shared AWG material dataset and also supports custom resistivity.
Can I enter custom resistivity?
Yes. Custom resistivity can be entered in ohm-meters, ohm square-millimeters per meter, or micro-ohm centimeters.
What is the difference between resistance and resistivity?
Resistance describes a specific conductor. Resistivity is a material property used with length and area to calculate that conductor resistance.
Can I use cable outside diameter as conductor diameter?
No. Cable outside diameter includes insulation and jacket material. Use effective conductive cross-sectional area.
Does stranded wire have the same resistance as solid wire?
It can be similar if the effective conductive cross-sectional area and material are the same, but do not use outside diameter as conductor area.
Is DC resistance the same as AC resistance?
Not always. At higher frequency, skin effect and proximity effect can make AC resistance higher than DC resistance.
Does this calculator determine safe wire ampacity?
No. Safe ampacity depends on insulation, ambient temperature, bundling, installation method, standards, terminations, and protection devices.
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Related Engineering Resources
Guides and lookup references linked to this tool.
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