Resistance Formula
Compute conductor resistance R and conductance G=1/R from resistivity ρ, length L and area A (wire/PCB design).
Inputs
Formula
R = ρ L / A; G = 1/R
Fundamentals
A conductor's resistance is set by its material and geometry — the basis of sizing and heating.
$R=\rho L/A$, $\rho$ resistivity, $L$ length, $A$ area. Resistivity rises with temperature, so longer/thinner wire has more resistance.
History
The resistance-geometry-material relation was set by Ohm and Kirchhoff as a basic law of experimental electricity.
Engineering applications
Used to design wires, heaters, shunts and grounding resistances.
Glossary
| Resistivity $\rho$ | Material property (Ω·m). |
| Length $L$ | Longer conductor = more resistance. |
| Area $A$ | Larger cross-section = less resistance. |
How to use
- Fill in Resistivity ρ, Length L, Area A in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Resistance R, Conductance G in the results area.
Formula notesResistance R = ρ·L/A (ρ resistivity, L length, A area); temp R = R₀(1+α·ΔT).
Formula · Worked Example · Knowledge
Formula
Conductor resistance $R=\rho L/A$, conductance $G=1/R$; convert area to m² ($A_{m^2}=A_{mm^2}\times10^{-6}$).
Worked Example
ρ=1.68e-8, L=100 m, A=2.5 mm² → R≈0.672 Ω, G≈1.49 S.
Key Points
- Copper ρ≈1.68e-8, aluminium ≈2.82e-8 Ω·m.
- Larger area → lower resistance.
- Resistivity rises with temperature (positive TCR).
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Resistivity ρ (Ω·m) | rho | Ω·m | 1.68e-08 |
| Length L (m) | L | m | 100 |
| Area A (mm²) | A | mm² | 2.5 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Resistance R | R | Ω |
| Conductance G | G | S |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: R = ρ L / A; G = 1/R
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases