Voltage drop is the voltage lost in the conductors between the source and the load. In a DC circuit it is pure resistance — no reactance, no power factor — which makes it easy to calculate accurately and impossible to hide behind assumptions.
Run your own numbers in the DC Cable Sizing Calculator, which reports drop in volts, drop as a percentage, receiving-end voltage and I²R loss for every candidate cable size.
One-Way Length vs Two-Way Circuit Length
This is the single most common error in DC calculations.
Current leaves the source on the positive conductor and returns on the negative conductor. Both carry the full current, so the resistive path is twice the route length.
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Enter the one-way length. A well-built calculator adds the return path internally. Entering 200 m for a 100 m run doubles the answer.
The Formula
$$\Delta V = I \times 2 R_T L$$
where $R_T$ is the conductor resistance in Ω/km at operating temperature and $L$ is the one-way length in km.
From resistivity:
| Quantity | Copper | Aluminium |
|---|---|---|
| ρ₂₀ reference | 0.01724 Ω·mm²/m | 0.02826 Ω·mm²/m |
| ρ IEC 60364 Annex G normal service | 0.0225 Ω·mm²/m | 0.036 Ω·mm²/m |
| α | 0.00393 /K | 0.00403 /K |
Where the manufacturer publishes a maximum DC resistance at 20 °C, use that value instead of computing one from resistivity.
Temperature-Corrected Resistance
Resistance rises with temperature, and cables do not operate at 20 °C.
| Conductor temperature | Copper R relative to 20 °C |
|---|---|
| 20 °C | 1.000 |
| 40 °C | 1.079 |
| 60 °C | 1.157 |
| 70 °C | 1.197 |
| 90 °C | 1.275 |
A 4 mm² copper conductor is 4.31 Ω/km at 20 °C and 5.16 Ω/km at 70 °C — a 20% larger voltage drop for the same current, from temperature alone.
Percentage Drop and Receiving-End Voltage
The percentage matters more than the volts. Losing 5 V is trivial on a 1170 V string and catastrophic on a 48 V battery circuit.
Power Loss: I²R
$$P_{loss} = I^2 R_{loop}, \qquad R_{loop} = \frac{2 R_T L}{n_{parallel}}$$
For a resistive DC circuit at a given current, loss% equals drop%. Use that as a check on your working.
Worked Example 1 — PV String
12 A, 600 V, 40 m one-way, 4 mm² copper at 70 °C.
- R₇₀ = 5.157 Ω/km
- R_loop = 2 × 5.157 × 0.040 = 0.4126 Ω
- ΔV = 12 × 0.4126 = 4.95 V = 0.83%
- Receiving-end voltage = 595.05 V
- Loss = 12² × 0.4126 = 59.4 W = 0.83%
Comfortably inside a 1% target.
Worked Example 2 — Long String Run
14 A, 1170 V string, 100 m one-way, 4 mm² copper at 70 °C.
- R_loop = 2 × 5.157 × 0.100 = 1.0314 Ω
- ΔV = 14 × 1.0314 = 14.44 V = 1.23%
- Loss = 14² × 1.0314 = 202 W = 1.23%
Still acceptable against a 2% limit. At 6 mm² the drop falls to 0.82% and the loss to 135 W — a genuine 67 W saving per string, every operating hour.
Worked Example 3 — Low-Voltage Battery Circuit
30 A, 48 V, 30 m one-way, 6 mm² copper at 70 °C.
- R_loop = 0.2063 Ω
- ΔV = 6.19 V = 12.9% — far beyond any acceptable limit
At 48 V this run needs roughly 50 mm² to stay under 2%. Low-voltage DC is dominated by voltage drop, never by ampacity. The dedicated 12V/24V/48V DC Cable Size Calculator is built for exactly this case.
What Changes the Drop
| Change | Effect on ΔV |
|---|---|
| Double the length | ×2 |
| Double the current | ×2 |
| Double the cross-section | ÷2 |
| Copper → aluminium, same mm² | ×1.64 |
| 20 °C → 70 °C conductor | ×1.20 |
| Two cables in parallel per polarity | ÷2 |
Acceptable Limits
| Circuit | Common design limit |
|---|---|
| PV string / array DC | 1% |
| Array to inverter | 1–2% |
| Battery to inverter | 2% |
| General DC branch circuit | 3% |
| Absolute outer bound | 5% |
These are design decisions taken in the project design basis, not universal code numbers. Tighter limits cost copper; looser limits cost energy every hour of operation.
Copper or Aluminium?
Aluminium needs roughly 64% more cross-sectional area for the same resistance. On short, high-current runs copper wins on space and termination simplicity. On long array-to-inverter feeders, aluminium at one or two sizes larger is often cheaper for the same electrical performance — provided the terminations are specified correctly.