Three-Phase Voltage Drop: Formula, Example and Design Limits
Voltage drop is one of the fastest ways to detect an undersized or overly long feeder, but the quality of the result depends on the model you use. A simple resistance-only equation is useful for early design work; long feeders and high-current AC circuits may require full resistance and reactance data.
1. Three-phase voltage drop formula
This is a practical AC form when conductor resistance R and reactance X are known per unit length. In a resistance-dominant approximation, R can be obtained from resistivity ρ and conductor section S.
The √3 factor comes from the geometry of a balanced three-phase system and the relationship between phase and line quantities.
2. Worked example
Consider a 400 V three-phase feeder carrying 32 A over a 40 m one-way length using 6 mm² copper. With a simplified resistivity of 0.0175 Ω·mm²/m and power factor 0.90:
That corresponds to roughly 1.46% of 400 V. The exact value changes with conductor temperature and the X component of cable impedance.
3. Limits of the simplified method
Resistance increases as the conductor heats. Reactance also matters more for large conductors, long feeders and lower power factor. For final design, use cable-manufacturer R/X data or the impedance method required by your engineering standard.
4. Recommended workflow
- Calculate design current.
- Select a preliminary conductor from ampacity requirements.
- Check voltage drop.
- Check short-circuit withstand and protection.
- Apply installation, ambient and grouping factors.
- Verify the final cable against the project standard and manufacturer data.
Technical reference
Continue with conductor selection
Use the IEC cable sizing calculator to combine the voltage-drop check with installation conditions, ampacity and short-circuit thermal withstand, or choose the NEC cable sizing calculator for the North American workflow.