Ohmic Conductor Resistance Calculator | Electronics Engineering

Quick Answer

The Ohmic Conductor Resistance Calculator computes the DC resistance (Ω) of a uniform ohmic conductor from its material resistivity, length, and cross-sectional area using the standard resistivity formula R = ρ × L / A.

Calculator

Result Interpretation

The result shows the DC resistance in ohms (Ω) of the conductor, computed from the entered resistivity, length, and cross-sectional area. This value represents the opposition to steady-state (DC) current flow through a uniform conductor at a constant temperature.

Worked Example

Copper wire at 20 °C (100 m, 50 mm²)

Given:

resistivity = 0.0172 Ω·mm²/m (annealed copper at 20 °C)
length = 100 m
cross_section_area = 50 mm²

Expected Result:

resistance = 0.0172 × 100 / 50 = 0.0344 Ω

The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from verified test cases.

Formula / Method

R = ρ × L / A

Where:
• R = DC Resistance (Ω)
• ρ = Resistivity (Ω·mm²/m) — material property at a given temperature
• L = Conductor Length (m)
• A = Cross-Sectional Area (mm²)

Unit consistency:
[Ω·mm²/m] × [m] / [mm²] = [Ω]  ✓

Common resistivity values at 20 °C:
• Annealed copper: 0.01724 Ω·mm²/m (100% IACS)
• Aluminum (1350-H19): 0.02826 Ω·mm²/m (61.2% IACS)
• Gold: 0.0244 Ω·mm²/m
• Silver: 0.0159 Ω·mm²/m
• Tungsten: 0.0528 Ω·mm²/m

Reference: ASTM B193 — Standard Test Method for Electrical Resistivity of Electrical Conductor Materials.

DC Resistance (Ω) of a uniform ohmic conductor.

Variables

Symbol	Label	Role	Description
resistivity	Resistivity	INPUT	Material resistivity in Ω·mm²/m
length	Length	INPUT	Conductor length in metres
cross_section_area	Cross-Sectional Area	INPUT	Cross-sectional area in mm²
resistance	Resistance	OUTPUT	DC resistance in ohms (Ω)

Calculation Steps

Enter the material resistivity in Ω·mm²/m (e.g. 0.0172 for copper at 20 °C).
Enter the conductor length in metres.
Enter the cross-sectional area in mm².
Read the DC resistance (Ω) from the results.

Notes / Limitations

ASSUMPTIONUniform cross-section along the entire conductor length.
ASSUMPTIONConstant temperature — resistivity is temperature-dependent; the entered value must correspond to the operating temperature.
ASSUMPTIONOhmic (linear) conductor — voltage and current are proportional (V = I × R).
ASSUMPTIONDC or low-frequency AC where skin effect is negligible.
LIMITATIONDoes not account for temperature coefficient of resistivity (α). For temperature-corrected values, use R(T) = R₀ × [1 + α × (T − T₀)].
LIMITATIONDoes not model AC effects (skin effect, proximity effect) at high frequencies.
LIMITATIONAssumes homogeneous material — does not handle composite or multi-layer conductors.

Frequently Asked Questions

What does this calculator calculate?

The Ohmic Conductor Resistance Calculator estimates the DC resistance (Ω) of a uniform conductor based on its material resistivity, length, and cross-sectional area.

What units should I use for the inputs?

Enter resistivity in Ω·mm²/m, length in metres (m), and cross-sectional area in mm². Common resistivity values: copper 0.0172, aluminum 0.0283, gold 0.0244 Ω·mm²/m at 20 °C.

How is this formula derived?

The formula R = ρ × L / A comes from the definition of electrical resistivity. Resistivity (ρ) is defined as the resistance of a unit cube of material. For a conductor of length L and uniform cross-section A, the total resistance is proportional to L and inversely proportional to A.

When is this calculation useful?

This calculation is fundamental in electrical wiring design, PCB trace resistance estimation, cable sizing, power distribution engineering, and any application where conductor resistance affects voltage drop, power loss, or thermal performance.

What is the reference standard?

The resistivity formula and measurement methodology are defined in ASTM B193 (Standard Test Method for Electrical Resistivity of Electrical Conductor Materials). Resistivity values are typically referenced at 20 °C per IEC 60028 / ASTM standards.

Technical Details

Assumption: Uniform cross-section along the entire conductor length.
Assumption: Constant temperature — resistivity is temperature-dependent.
Assumption: Ohmic (linear) conductor — V = I × R holds.
Assumption: DC or low-frequency AC where skin effect is negligible.
Limitation: Does not account for temperature coefficient of resistivity.
Limitation: Does not model AC effects (skin effect, proximity effect).
Limitation: Assumes homogeneous material.

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