Neutral current of an unbalanced load
The neutral current of an unbalanced three-phase load.
Reads AS/NZS 3000:2018. Tables checked 2 Oct 2026.
Try a job 4
Each job fills in example values. Replace them with your values.
- Find the neutral current of a shop boardThe neutral current of a board with 45, 30 and 25 A on its phases.
- Neutral current with heaters and a motorHeaters on one phase and a motor on another: the neutral with two power factors.
- Neutral current of a farm on one phaseMost of the load on one phase: how close the neutral comes to that phase.
- Check the neutral of a mostly three-phase loadThe out-of-balance current a reduced neutral must still carry.
Inputs
Worked example with the default inputs. The live calculator replaces it when the page loads.
- Line voltage
- 400 V
- Phase A current
- 32 A
- Phase B current
- 20 A
- Phase C current
- 10 A
- Phase A power factor
- 1
- Phase B power factor
- 1
- Phase C power factor
- 1
Neutral current
19.08A
- Neutral as a share of the largest phase
- 59.6%
- Largest phase current
- 32A
- Real power, three phases
- 14.32kW
This result is a design aid. Verify it against the current standard.
Calculation steps
- Phase A current, at 0° from phase A volts32A
- Phase B current, at -120° from phase A volts20A
- Phase C current, at 120° from phase A volts10A
- Formula: one power factor, so
I_N = √(Ia² + Ib² + Ic² − Ia·Ib − Ib·Ic − Ic·Ia)
19.08 A - Neutral currentResult19.08A
AS/NZS 3000:2018 Cl 3.5.2(b)(ii)
- Neutral current angle from phase A-27
- Neutral as a share of the largest phase59.6%
- Real power, three phases14.32kW
About this calculator
How this is calculated
In a star load each phase current returns through the neutral. The three phase voltages are 120° apart, so the three currents are too. When the currents are equal and at one power factor, they cancel and the neutral carries nothing. When they are not equal, the neutral carries what is left over.
The tool works that left-over current as a phasor sum. It sets phase A at 0°, phase B at −120° and phase C at +120°. It then turns each current back by its own power factor angle, because a lagging load draws its current after its voltage. The three currents are added as vectors, and the size of the sum is the neutral current. The tool also gives the angle of the sum from the phase A voltage.
When all three power factors are the same, the angles cancel out of the sum. The tool then shows the short formula: the square root of the sum of the three squares, less the three products of pairs.
The neutral can carry more than the largest phase. That happens when the power factors differ a lot, so two currents line up. The tool warns when it does.
The answer is the current at the supply frequency only. Third harmonic currents from electronic loads add in the neutral, not cancel. The harmonics tool works those.
| Step | Table or clause | What it decides |
|---|---|---|
| Phasor of each phase | The phase angle less the power factor angle | Where each current points |
| Neutral current | The phasor sum of the three | The current the neutral carries |
| One power factor | I_N = √(Ia² + Ib² + Ic² − Ia·Ib − Ib·Ic − Ic·Ia) | The short form of the sum |
| Neutral size | Cl 3.5.2(b)(ii) | A neutral at least the size of the largest active |
| A smaller neutral | Cl 3.5.2 Exception 3 | Allowed for a mostly multiphase load that still carries the out-of-balance current |
| Harmonics | Cl 3.5.2(b)(i) | Third harmonic currents add to the out-of-balance current |
Worked examples
- A shop board with 45, 30 and 25 A on its phases has 18.03 A in the neutral, 40.1 % of the largest phase.
- A farm supply with 40 A on one phase and 5 A on the others has 35 A in the neutral, 87.5 % of the largest phase. Nearly all of the load comes back on it.
- Heaters on phase A and a motor on phase B at 0.8 power factor give 19.69 A in the neutral, 65.6 % of the largest phase.
- A mostly three-phase load of 60, 55 and 50 A at 0.85 power factor leaves 8.66 A in the neutral, 14.4 % of the largest phase.
Limits
The tool takes three phase currents and their power factors, all lagging. It does not take a leading load, such as a capacitor bank, or a load connected between two phases.
It gives the current, not the conductor size. Take the larger of the neutral current and the largest phase current to the cable size tool.
See also: Three phase power, Max demand by phase and Cable size.
Questions
Each answer describes what this tool calculates. The result is a design aid. Verify against the current standard.
How do you work out the neutral current of a three-phase load?
Add the three phase currents as phasors, 120° apart, each turned by its power factor angle. The size of the sum is the neutral current. With one power factor on all phases it is √(Ia² + Ib² + Ic² − Ia·Ib − Ib·Ic − Ic·Ia).
Why is the neutral current not the difference between the phases?
The phase currents are 120° apart, so they do not add or subtract in a straight line. 32 A, 20 A and 10 A give 19.08 A in the neutral, not 22 A or 12 A.
Can the neutral carry more than a phase?
Yes. With very different power factors the phasors can line up, and the neutral can carry more than the largest phase. Third harmonic currents from electronic loads also add in the neutral. The tool warns when the sum passes the largest phase.
How big must the neutral of a three-phase circuit be?
AS/NZS 3000 Cl 3.5.2(b)(ii) asks for a neutral at least as large as the largest active. Exception 3 allows a smaller one where most of the load is multiphase and the neutral still carries the out-of-balance current with its harmonics.
Does a balanced load need a neutral?
Three equal currents at one power factor cancel, so the neutral carries no current at the fundamental. A star load with single-phase items still needs it, as the balance changes when a load switches off.
Clauses and tables this tool reads
- AS/NZS 3000:2018 Cl 3.5.2(b)Neutral of a multiphase circuit
- AS/NZS 3000:2018 Cl 3.5.2Neutral conductor of a circuit
Every clause and table, with how each was verified
Tables last checked on 2 Oct 2026.
Related tools
- Cable size calculatorFind the smallest cable size that passes each check.AS/NZS 3008.1.2AS/NZS 3008.1.1AS/NZS 3000
- Voltage unbalance of a supplyVoltage or current unbalance from three line readings.
- Harmonics, neutral current and K-factorTHD, neutral current and K-factor from a spectrum.AS/NZS 3008.1AS/NZS 3000
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