Three-Phase Neutral Current Calculator (Unbalanced Loads)

What this tool does

In a balanced three-phase system the three currents cancel and the neutral carries nothing; whatever is left over after cancelling is the neutral current. For loads with the same power factor on every phase the three currents sit 120° apart and the neutral current is √(I₁² + I₂² + I₃² − I₁I₂ − I₂I₃ − I₃I₁) — notably it can never exceed the largest phase current. Electronic loads such as switch-mode power supplies break this rule: their third harmonics add up in the neutral instead of cancelling, so the neutral can carry more than any phase.

Formula

I_N = √(I₁² + I₂² + I₃² − I₁I₂ − I₂I₃ − I₃I₁) (120° apart, same power factor on all three)

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.