Cable sizing and voltage drop
ΔU = 2 × ρ × L × I / S
The voltage drop along a cable, both directions of the problem: how much a given cable loses, or what cross-section to plan to stay under an allowed drop, with the standard commercial size recommended above the exact calculation. The conductor is a choice (copper, aluminium) and so is its temperature: at 70 °C, the operating temperature under load, copper resists 20% more than cold, through the metal’s physical coefficient. The central note explains why 12 V does not forgive length when 230 V ignores it.
0.82511 V (6.8759 %)
- Calculation
- ΔU = 2·ρ·L·I / S = 2 × 0.020628 × 5 m × 10 A / 2.5 mm² = 0.82511 V
- Relative drop
- 6.8759 %
The drop reaches 6.8759 %: beyond the usual 5%. Increase the cross-section, shorten the cable or raise the voltage.
The 3% (lighting) and 5% (other uses) thresholds are the landmarks of installation standards: beyond them, appliances receive a degraded voltage and the cable heats for nothing. This calculation checks the voltage drop; the cable’s allowable heating (the breaker rating) is a second, independent constraint that can demand more.
The absolute drop does not depend on the circuit voltage, but its relative weight does: 0.7 V lost is invisible at 230 V (0.3%) and ruinous at 12 V (5.7%). That is why solar setups, campervans and boats demand cross-sections that look oversized: 12 V does not forgive length.
The entered length is the cable’s, one way: the factor 2 in the formula counts the current’s round trip, line and return. Five metres of cable, ten metres of copper crossed.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasΔU = 2 × ρ × L × I / S
ΔU = 2 × ρ × L × I / S
S = 2 × ρ × L × I / ΔU_max
ρ(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: nothing is a flat rate, everything recomputes.
- Voltage drop
- · the volts lost in the cable’s own resistance: the appliance at the end receives the source voltage minus this drop.
- Resistivity ρ
- · the resistance of a conductor one metre long and one square millimetre across: the metal’s electrical identity card. Aluminium is 1.64 times copper.
- Standard cross-section
- · the commercial sizes: 1.5, 2.5, 4, 6, 10, 16 mm²… You buy the first one above the need, never the exact calculation.
- Allowed drop
- · the design threshold: 3% for lighting, 5% for other uses, the usual landmarks of installation standards.
Validity domainThe calculation holds for direct current and single-phase resistive loads (cos φ = 1): the case of usual low-voltage installations.
The calculation holds for direct current and single-phase resistive loads (cos φ = 1): the case of usual low-voltage installations. In AC with cos φ < 1 or three-phase, the formula changes (factor √3, cable reactance). This calculation checks the voltage drop only: the cable’s allowable heating, tied to the protection rating, is a separate constraint that can demand a larger size. For an installation under a standard, the standard prevails.
Why 12 V does not forgiveThe absolute drop depends only on the cable and the current: 0.
The absolute drop depends only on the cable and the current: 0.7 V lost is 0.7 V, at 12 V as at 230 V. But its relative weight changes everything: 0.3% at 230 V, 5.7% at 12 V, nineteen times more. And at equal power, 12 V also demands nineteen times the current, hence nineteen times the drop: the double handicap explains the spectacular cross-sections of solar setups, campervans and boats, and why the first answer to a long-cable problem is often to raise the voltage.
Reading the resultThe power lost in the cable is the drop times the current: watts turned into pure heat, paid for but never used.
The power lost in the cable is the drop times the current: watts turned into pure heat, paid for but never used. The voltage at the end of the cable is what the appliance actually sees; 12 V electronics often give up around 11 V, which makes the margin narrower than it looks. In sizing mode, the exact cross-section is the mathematical bound and the recommended one is the cable you buy: the latter prevails.