Voltage Drop Formulas for Cables
Voltage drop formulas for single-phase and three-phase cables, percentage drop, a worked example using resistance and reactance per km, and a table by current.
The formulas
| Circuit | Voltage drop |
|---|---|
| Three-phase | Vd = √3 × I × L × (R cos φ + X sin φ) |
| Single-phase (out and back) | Vd = 2 × I × L × (R cos φ + X sin φ) |
| DC or resistive load | Vd = k × I × L × R, with k = 2 (two-wire) or √3 (three-phase) |
| Percentage | Vd % = Vd / V × 100 |
I is the load current in amperes, L the one-way route length in kilometres (divide metres by 1000), R and X the cable resistance and reactance in ohms per kilometre from the data sheet, and V the system voltage.
Worked example: 50 A over 100 m at 400 V
The cable data is R = 1.15 Ω/km and X = 0.08 Ω/km at a power factor of 0.85 (φ = 31.79°). These are example values, so use your own data sheet.
- R cos φ + X sin φ = 1.15 × 0.85 + 0.08 × 0.5268 = 1.02 Ω/km
- Three-phase: Vd = √3 × 50 × 0.1 × 1.02 = 8.83 V, which is 2.208% of 400 V
- Single-phase on the same cable: Vd = 2 × 50 × 0.1 × 1.02 = 10.2 V
Drop by current on the same cable (three-phase, 100 m)
| Current | Voltage drop | Percentage of 400 V |
|---|---|---|
| 10 A | 1.766 V | 0.4415 % |
| 20 A | 3.532 V | 0.883 % |
| 50 A | 8.83 V | 2.208 % |
| 100 A | 17.66 V | 4.415 % |
Frequently asked questions
What voltage drop is allowed?
It depends on the standard and the circuit. A limit of 3% to 5% from the origin to the load is common, but follow your own standard.
Why does a long cable need a larger conductor?
Resistance grows with length and falls with cross-section, so a longer run needs more copper to keep the drop within the limit.
Does the reactance matter?
For small cables it is minor. For large cables, roughly 150 mm² and above, it becomes a large share of the drop, so include it.
Should I use the cold or the hot resistance?
Use the value at operating temperature. A copper conductor at 90 °C has about 27% more resistance than at 20 °C.
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