Cable Cross-Section Sizing

Area from current, length, allowable voltage drop, and material

Calculation
Quick Introduction

Voltage drop is often a key criterion in cable sizing. Too small a cross-section increases voltage drop, losses, and thermal stress.

This calculator sizes the required conductor area from current, length, material, and allowable voltage drop. It can also verify the voltage drop for an existing area.

  • Material dependence via resistivity ρ
  • Different factor for single-phase vs three-phase
  • Practical recommendation to next standard cable size
Formulas (MathJax)
\[\Delta U = \frac{k\,I\,L\,\rho}{A}\]
\[A = \frac{k\,I\,L\,\rho}{\Delta U}\]
\[\Delta U_{allow} = U\cdot\frac{\Delta U_{\%}}{100}\]
\[k=2\;(1\sim),\quad k=\sqrt{3}\;(3\sim)\]
Symbol Legend
  • \(A\): conductor area [mm²]
  • \(I\): current [A]
  • \(L\): one-way cable length [m]
  • \(\rho\): resistivity [Ω·mm²/m]
  • \(\Delta U\): voltage drop [V]
  • \(U\): nominal voltage [V]
  • \(k\): system factor (1~ or 3~)


Examples
Example 1 (three-phase): \(U=400\,V\), \(I=32\,A\), \(L=45\,m\), \(\Delta U=3\%\), copper ⇒ required area about \(8.2\,mm^2\), recommended \(10\,mm^2\).
Example 2 (verification): for \(A=10\,mm^2\), same data gives \(\Delta U\approx9.0\,V\) or \(2.26\%\).
Detailed Description & Summary

Voltage-drop-based cable sizing is a practical pre-dimensioning method for feeders, branch circuits, and machine connections. Final design should additionally consider installation method, ambient temperature, grouping, protection requirements, and local standards.

The resistivity values used are approximate 20°C values. At higher operating temperatures, conductor resistance increases, and actual voltage drop will be higher.

Summary
  • Sizes A from I, L, material and allowable voltage drop
  • Checks voltage drop for an existing cable area
  • Provides direct recommendation to next standard cross-section

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