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Cable sizing and voltage drop

A cable’s voltage drop (ΔU = 2ρLI/S) or the cross-section to plan, copper or aluminium, cold or under load, with the recommended commercial size.

Parameters

One way only; the factor 2 counts the round trip.
Usual reference values: 3% for lighting, 5% for other uses.

Result

Recommended cross-section

6 mm²

Calculation
S = 2·ρ·L·I / ΔUmax = 2 × 0.020 628 × 5 m × 10 A / 0.36 V = 5.7299 mm²
Relative drop
2.865 %
Voltage drop
0.34379 V
Voltage at the end of the cable
11.656 V
Power lost in the cable
3.4379 W
required 5.7299 mm²bought 6 mm²4.7138 % more copper than needed
Note

Use 6 mm²: the drop falls to 2.865 %.

Calculation, assumptions and sources

OverviewThe voltage drop of a given cable, or the cross-section to plan to stay under an allowed drop, at 230 V as well as 12 V, with the next standard commercial size above.

The voltage drop of a given cable, or the cross-section to plan to stay under an allowed drop, at 230 V as well as 12 V, with the next standard commercial size above. Copper or aluminium conductor, at 20 °C or at 70 °C, the operating temperature under load, where copper’s resistance is 20% higher than when cold.

Method & formulasΔU = 2 × ρ × L × I / S
ΔU = 2 × ρ × L × I / SS = 2 × ρ × L × I / ΔUmaxρ(70 °C) = ρ(20 °C) × (1 + α × 50)P lost = ΔU × I

The factor 2 counts the current’s round trip: the entered length is the cable’s, one way. The resistivity comes from the metal (0.01724 Ω·mm²/m for annealed copper at 20 °C) and its temperature, through the coefficient α.

Voltage drop
the volts lost in the cable’s resistance; the appliance receives the source voltage minus this drop.
Resistivity ρ
the resistance of a conductor one metre long and one square millimetre across. Aluminium is 1.64 times copper.
Standard cross-section
the commercial sizes: 1.5, 2.5, 4, 6, 10, 16 mm²… The first one above the need is chosen.
Allowed drop
the design threshold: 3% for lighting, 5% for other uses, the usual reference values in installation standards.
Validity domainThe calculation holds for direct current and single-phase resistive loads (cos φ = 1).

The calculation holds for direct current and single-phase resistive loads (cos φ = 1). In AC with cos φ < 1 or three-phase, the formula changes (factor √3, cable reactance). Only the voltage drop is checked: the allowable heating, tied to the protection rating, can demand a larger size. For an installation under a standard, the standard prevails.

Voltage drop at 12 VThe absolute drop depends only on the cable and the current; its relative weight depends on the voltage.

The absolute drop depends only on the cable and the current; its relative weight depends on the voltage. 0.7 V lost is 0.3% at 230 V and 5.8% at 12 V. At equal power, 12 V also demands nineteen times the current, hence nineteen times the drop. Solar setups, campervans and boats need large cross-sections; for a long cable, raising the voltage is often the first remedy.

Reading the resultThe power lost, drop times current, heats the cable.

The power lost, drop times current, heats the cable. 12 V electronics often cut out around 11 V.