Voltage Drop Calculation: Formula and Worked Examples
Current flowing through a cable's resistance and reactance drops some voltage before it reaches the load. Here is the formula, a full worked example, and what to do when a cable fails the check.
The formula
For an LV cable of length L (km, one way) carrying current I (A):
- Three phase: ΔV = √3 × I × L × (R·cos φ + X·sin φ)
- Single phase: ΔV = 2 × I × L × (R·cos φ + X·sin φ)
- Percentage: ΔV% = ΔV ÷ V × 100, using the line voltage for three phase
R and X are the cable's resistance and reactance in Ω/km. cos φ is the load power factor and sin φ = √(1 − cos²φ). The X term is why a low power factor makes drop worse on large cables: at big conductor sizes the reactance, not the resistance, starts to dominate.
Where R comes from
Conductor resistance is resistivity divided by cross-section: R = ρ ÷ A. The calculator on this site uses an operating-temperature resistivity of 22.5 Ω·mm²/km for copper and 36 Ω·mm²/km for aluminium. Operating temperature matters because resistance rises with heat; a cable at full load is hotter than the 20 °C value in a catalogue. For a final design, use the manufacturer's published R and X for the actual cable and installation.
Worked example
Assumptions (illustrative, not a project): 415 V three-phase feeder, 150 A load, 80 m one-way, 70 mm² copper, cos φ = 0.85, reactance 0.08 Ω/km (an indicative figure for LV multicore cable), one cable.
- R = 22.5 ÷ 70 = 0.3214 Ω/km
- sin φ = √(1 − 0.85²) = 0.5268
- R·cos φ + X·sin φ = 0.3214 × 0.85 + 0.08 × 0.5268 = 0.2732 + 0.0421 = 0.3154 Ω/km
- L = 0.08 km
- ΔV = 1.732 × 150 × 0.08 × 0.3154 = 6.55 V
- ΔV% = 6.55 ÷ 415 × 100 = 1.58%
Whether 1.58% is acceptable depends on the limit set for the feeder in your specification and on what the upstream cables already use up. You can check it against any limit in the voltage drop calculator.
If the cable fails the limit
- Step up the conductor size (the usual first fix).
- Run two cables in parallel, which halves the current per cable.
- Shorten the route or move the source closer to the load.
- Raise the system voltage if the equipment allows.
- Improve the power factor, which lowers the current for the same real power.
Voltage drop is one of three checks
A cable that passes voltage drop can still be too small for its current once derating for ambient temperature, grouping and installation method is applied, or too small to survive a fault until the breaker clears. Always check all three, as covered in cable sizing basics; the conductor sizing calculator runs ampacity, voltage drop and short-circuit withstand together. This article is part of the data center design guide.
Written by the Vision Matrix Institute editorial team. Worked examples use stated, illustrative assumptions; check them against your project data, the applicable standards and manufacturer datasheets before use.
Frequently Asked Questions
What is the voltage drop formula for a three-phase cable?
ΔV = √3 × I × L × (R·cos φ + X·sin φ), where I is the load current in amperes, L is the one-way cable length in km, R and X are the cable's resistance and reactance in ohms per km, and φ is the load power-factor angle. Divide by the line voltage and multiply by 100 for the percentage.
What is the acceptable voltage drop?
It depends on the applicable code, the project specification and the load. Many specifications set a total limit from the source to the furthest load and split it between feeders and final circuits, but the number must come from your project's governing documents, not from a rule of thumb.
How do I reduce voltage drop?
Increase the conductor size, run cables in parallel, shorten the route, use a higher system voltage, or improve the power factor. Increasing size is the usual first step; the others change the design more.
Is voltage drop the only thing that decides cable size?
No. Cable size is also limited by current-carrying capacity under installation conditions and by short-circuit withstand. Voltage drop often decides the size on long runs, while ampacity decides it on short, heavily loaded ones.
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