Wire Resistance Calculator

How to use the wire resistance calculator

What this calculator does

This calculator estimates the direct-current resistance and conductance of a uniform wire from the material's resistivity, the wire length, and its cross-sectional size. It applies the standard relationship R = ρL / A, where resistance rises with resistivity and length but falls as cross-sectional area increases. The result is a geometry-and-material estimate at 20 °C; it is not a cable ampacity rating, a voltage-drop design check, or a substitute for a manufacturer's specification for stranded, plated, heated, or connector-terminated conductors.

When to use it

Use it to compare copper and aluminum conductors of the same size, estimate the resistance of a laboratory wire sample, check whether a proposed sensor lead is likely to add meaningful series resistance, or convert a known wire diameter into cross-sectional area before a circuit calculation. For installation decisions, combine the resistance estimate with current, voltage drop, thermal limits, and applicable electrical codes.

How to calculate

1. The calculator opens with a complete demonstration: copper at 20 °C, a 10 m length, and a 1.63 mm diameter. The displayed resistance is immediately available, and the Download Excel button already has a validated example workbook ready.
2. Choose Material at 20 °C. A listed material loads its representative resistivity. Choose Custom resistivity when you have a specification or measured value for another conductor.
3. Enter Wire length and select meters, feet, or kilometers. Changing the unit converts the current number instead of changing its physical meaning.
4. Choose Size input method. Use Diameter for a circular wire, or Area when a datasheet already provides the cross-sectional area. Enter the value and choose the matching unit.
5. Read Wire resistance first, then use Conductance, Cross-sectional area, Equivalent diameter, and the formula breakdown to verify the calculation. Download Excel exports the current typed model, not rounded screen text.
6. Reset clears the demonstration and all calculated content. Download Excel is then disabled until a complete valid material, length, and size are entered again.

Input guide

Material at 20 °C is required. Select a named conductor or Custom resistivity. The named values are representative room-temperature values, so a wire alloy, temper, purity, or operating temperature may differ. Selecting a higher-resistivity material increases resistance in direct proportion.

Resistivity at 20 °C is required and must be positive, in ohm-meters (Ω·m). Listed materials lock this field; Custom resistivity makes it editable and accepts forms such as 1.68e-8. Do not enter conductivity here, and do not use a decimal comma. Resistivity is an intrinsic material property; the OpenStax explanation of resistivity and resistance shows why the same material value applies independently of a sample's length or thickness.

Wire length is required, must be greater than zero, and accepts ordinary decimal values such as 10 or 32.8. The adjacent Wire length unit supports meters, feet, and kilometers. Doubling length doubles resistance when every other input stays fixed. A common mistake is entering a round-trip circuit length when only one conductor is intended, or entering one-way length when a two-conductor loop is intended.

Size input method is required. Diameter mode assumes a circular cross-section and calculates A = πd² / 4. Area mode uses the entered area directly. Wire diameter accepts millimeters, meters, or inches; a realistic example is 1.63 mm. Cross-sectional area accepts mm², m², or in²; a matching example is approximately 2.086724 mm². Because area depends on diameter squared, doubling diameter reduces resistance to one quarter, not one half.

Output guide

Wire resistance is the primary estimate in ohms. Zero is not produced for a valid finite wire; a very small value indicates a short, thick, highly conductive wire, while a high value indicates greater opposition to current. Conductance is the exact reciprocal in siemens, so it moves in the opposite direction. NIST identifies the ohm and siemens as the SI units for electric resistance and electric conductance.

Cross-sectional area reports the canonical area in mm² even when diameter or another area unit was entered. Equivalent diameter reports the diameter of a circle with the same area; in Area mode this is a conversion, not a claim that the real conductor is circular. Conductivity is the reciprocal of resistivity in S/m. The summary pills repeat Material, Length, Area, and Resistivity from the same model. The Formula breakdown shows Length in meters, Area in square meters, the Length-to-area ratio, and the reciprocal identity R × G = 1. The Calculation details table repeats the model's symbols, formulas, and current typed values.

Worked example

For the startup example, copper has resistivity 1.68 × 10⁻⁸ Ω·m, length is 10 m, and diameter is 1.63 mm, or 0.00163 m. The area is π × 0.00163² ÷ 4 = 2.0867243803 × 10⁻⁶ m². Substituting into R = ρL/A gives 0.0805089554 Ω, displayed as 0.080509 Ω. Conductance is 1/R = 12.4209784543 S, displayed as 12.420978 S. Those same canonical values populate the initial Excel workbook.