Calculate three-phase neutral current from phase-current magnitudes using standard 120° separation or custom phasor angles, with A, mA, kA, and imbalance results.

Three-phase, four-wire wye system; use RMS currents for one frequency and a common angle reference. Triplen harmonics can add in the neutral. This estimate alone cannot size conductors or establish protection or code compliance; consult a qualified electrical professional.

Neutral Current Formula

The following formula calculates neutral RMS current for a three-phase, four-wire wye system with sinusoidal currents at one frequency and120° separation. Custom current angles use a vector sum. Triplen harmonics can add in the neutral; this estimate alone cannot establish conductor sizing, protection or code compliance.

In = sqrt(A² + B² + C² - A × B - A × C - B × C)
  • Where In is the Neutral Current (amps)
  • A is the phase A current (amps) 
  • B is the phase B current (amps) 
  • C is the phase C current (amps) 

How to Calculate Neutral Current?

The following example problems outline how to calculate Neutral Current.

Example Problem #1

  1. First, determine the phase A current (amps). In this example, the phase A current is 10 amps.
  2. Next, determine the phase B current (amps). For this problem, the phase B current is 23 amps.
  3. Next, determine the phase C current (amps). In this case, the phase C current is 3 amps.
  4. Finally, calculate the Neutral Current using the formula above: 

In = √(A^2+B^2+C^2-A*B-A*C-B*C)

Inserting the values from above and solving yields: 

In = √(10^2+23^2+3^2-10*23-10*3-23*3) = √309 ≈ 17.5784 (amps)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

phase A current (amps) = 5

phase B current (amps) = 41

phase C current (amps) = 2

Entering these given values into the calculator above yields: 

In = √(5^2+41^2+2^2-5*41-5*2-41*2) = √1413 ≈ 37.5899 (amps)