Cable Voltage Drop and Resistance Calculator

Work out the resistance of a copper or aluminium cable, the voltage drop and the power lost, and the longest run or smallest cable for your limit.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

The resistance of a conductor is its resistivity times its length divided by its cross-section area. Copper is about 1.72 times ten to the minus eight ohm metres at 20 degrees, and aluminium about 2.82. Resistance rises about 0.4 percent for each degree of temperature rise.

The voltage drop for a three-phase circuit is root three times the current times the resistance of one conductor times the power factor. For a single-phase or direct current circuit the current goes out and back, so the factor is two. Divide by the supply voltage for the drop as a percentage.

Formulas used

  • R = \dfrac{\rho L}{A}
  • \Delta V = \sqrt{3}\,I R \cos\varphi
  • P = 3 I^2 R

Worked example

With the default numbers in the calculator above:

  1. Resistivity at the conductor temperature: 1.72 ×10⁻⁸ Ω·m
  2. Resistance of one conductor: 0.0538 Ω
  3. Voltage drop: 2.68 V
  4. Voltage drop as a share of the supply: 0.65 %
  5. Power lost as heat in the cable: 165.12 W
  6. Longest run for the drop limit: 386.95 m
  7. Smallest cable area for the drop limit at this length: 2.07 mm²

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Is voltage drop the only thing to check?

No. The cable also needs the right current rating for how it is installed, and it must trip the protective device in a fault. Check all three.

Why does the temperature matter?

Resistance rises as the conductor heats up, so a hot cable drops more voltage than a cold one.

Does this include reactance?

No, only resistance. For large cables and long runs the reactance adds to the drop. Use the cable maker's figures for the final answer.

Related calculators

Further reading: Standard electrical engineering texts (resistivity and voltage drop). Cable selection must be done by a licensed person to the wiring rules.

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