Neutral Current Calculator with Third Harmonics (Neutral Sizing)

Santaji Gadepatil
B.E. (Electronics & Telecommunication) · Founder & Editor
Connect on LinkedIn
Share
Published
Last updated
Read time
3 min
Neutral Current Calculator with Third Harmonics (Neutral Sizing): formula and free online calculator

In a balanced three-phase circuit the fundamental currents cancel in the neutral, but third harmonics are in phase and add — so a neutral feeding LED lighting, computers or drives can carry more current than the phases. This neutral current calculator finds the neutral current from the third-harmonic content and applies the IEC 60364-5-52 Annex E reduction factors, as explained in neutral conductor sizing with harmonics and power system harmonics.

calculated
calculated
calculated
calculated
calculated
15–33%: size on phase current, factor 0.86
calculated
Type in any field to change it. Press × on a value to calculate that field instead.

How to use the neutral current calculator

Enter the phase RMS current and the third-harmonic current as a percentage of the fundamental (the value a power-quality analyser shows in its harmonic spectrum). The calculator splits the phase current into its fundamental and third-harmonic parts, gives the neutral current, re-expresses the harmonic as a percentage of the phase RMS current (the basis IEC 60364-5-52 uses) and returns the design current for choosing a four-core or five-core cable.

Neutral current formulas

I₁ = I ÷ √(1 + h₃²)  ·  I₃ = h₃ × I₁  ·  IN = 3 × I₃

This assumes balanced phases and that the third harmonic is the only significant triplen harmonic. Other odd harmonics raise the phase RMS slightly but cancel in the neutral.

Worked example

Phase current 100 A with a third harmonic of 30% of the fundamental:

  • Fundamental I₁ = 100 ÷ √(1 + 0.3²) = 95.78 A, third harmonic I₃ = 28.73 A
  • Neutral current IN = 3 × 28.73 = 86.2 A (0.862 × phase current)
  • As a share of the phase RMS current the harmonic is 28.7%, which falls in the 15–33% band
  • Size the cable on the phase current with a factor of 0.86: design current = 100 ÷ 0.86 = 116.3 A

Neutral current and design current for 100 A phase current

3rd harmonic (% of fundamental) % of phase current Neutral current IN ÷ I Sized on Design current
10% 10.0% 29.9 A 0.30 phase 100.0 A
20% 19.6% 58.8 A 0.59 phase 116.3 A
30% 28.7% 86.2 A 0.86 phase 116.3 A
40% 37.1% 111.4 A 1.11 neutral 129.6 A
50% 44.7% 134.2 A 1.34 neutral 156.0 A
60% 51.4% 154.3 A 1.54 neutral 154.3 A
80% 62.5% 187.4 A 1.87 neutral 187.4 A

Practical notes

  • Do not use a reduced neutral on circuits feeding LED drivers, IT equipment, UPS or single-phase VFDs; many designers use a full-size or double-size neutral for such loads.
  • The IEC factors apply to four- and five-core cables where the neutral is inside the same cable and adds heat; for single-core cables, check the neutral on its own current.
  • Measure the harmonic spectrum at full load — percentages measured at light load often look high while the actual amps are small.
  • Harmonic filters or 3rd-harmonic blocking transformers (zig-zag, delta windings) reduce the neutral current at the source.

Frequently asked questions

Why does the neutral carry third-harmonic current?

The 50 Hz currents of the three phases are 120° apart and cancel in the neutral. Third-harmonic currents of the three phases are all in phase (3 × 120° = 360°), so they add, and the neutral carries three times the third-harmonic current of one phase.

Can the neutral current be higher than the phase current?

Yes. With pure third harmonics the neutral current exceeds the phase current once the third harmonic is about 33% of the phase RMS current (about 35% of the fundamental). Circuits feeding many single-phase rectifier loads commonly reach 1.4–1.7 × phase current.

What are the IEC 60364-5-52 reduction factors for harmonics?

For four- and five-core cables, Annex E gives 1.0 (size on phase current) up to 15% third harmonic, 0.86 (phase current) for 15–33%, 0.86 (neutral current) for 33–45%, and 1.0 (neutral current) above 45%, where the harmonic is a percentage of the phase current.

Do other harmonics add in the neutral?

Only triplen harmonics (3rd, 9th, 15th …) add. The 5th, 7th, 11th and 13th cancel in a balanced system, like the fundamental. Load unbalance adds a further fundamental-frequency neutral current.

Free widget

Put this calculator on your website

Copy one snippet. It resizes itself and works on any site or blog.

<iframe src="https://zentacalculator.com/embed/electrical/neutral-current-harmonics/" title="Neutral Current Calculator with Third Harmonics (Neutral Sizing)" width="100%" height="640" style="border:1px solid #e2e5ee;border-radius:12px;max-width:720px" loading="lazy"></iframe>
<p style="font-size:13px"><a href="https://zentacalculator.com/electrical/neutral-current-harmonics/">Neutral Current Calculator with Third Harmonics (Neutral Sizing)</a> by <a href="https://zentacalculator.com/">Zenta Calculator</a></p>
<script>addEventListener('message',function(e){if(e.origin==='https://zentacalculator.com'&&e.data&&e.data.zentaHeight){document.querySelectorAll('iframe[src="https://zentacalculator.com/embed/electrical/neutral-current-harmonics/"]').forEach(function(f){if(f.contentWindow===e.source)f.style.height=e.data.zentaHeight+'px'})}})</script>
Why Zenta Calculator

From formula to answer in seconds

One clear path from the numbers you have to a result you can use, for students, engineers and everyday users.

  1. 01

    Enter what you know

    Type any values you have, in the units you use. Leave the unknown blank and the calculator solves for it.

  2. 02

    See the formula and steps

    Every result shows the equation, a worked example and a chart, so you understand the answer and not just the number.

  3. 03

    Get answers you can trust

    Formulas follow published standards and textbooks, and every worked example is checked before a page goes live.