The neutral gets bigger, not smaller
Take the defaults: 20 A of fundamental on each of the three phases, perfectly balanced, with 60 percent third harmonic, 30 percent fifth, 15 percent seventh, 8 percent ninth, 5 percent eleventh and 4 percent thirteenth. That is an unremarkable profile for a panel full of switch-mode power supplies without power factor correction.
Each phase conductor carries 24.4 A true RMS — the 20 A fundamental with all the harmonics stacked on it in quadrature. The neutral carries 36.3 A. Half again as much as any phase, on a balanced panel, with the fundamental contribution to the neutral being exactly zero.
The whole 36.3 A comes from the third and ninth harmonics. Three times 12 A of third harmonic is 36 A, three times 1.6 A of ninth is 4.8, and those two combine to 36.3. The fifth, seventh, eleventh and thirteenth contribute nothing at all when the phases are balanced.
Why three times, and not zero
The fundamental currents on A, B and C are 120 degrees apart, which is why three equal ones cancel exactly on the neutral. Triple the frequency and you triple every angle: 120 becomes 360, and 240 becomes 720. Both of those are a whole number of full turns, so all three third harmonics arrive in step. They do not cancel, they add — arithmetically, not as phasors.
Every third order does this. The ninth, the fifteenth, the twenty-first. That family is what electricians mean by triplens. The fifth and seventh are still 120 degrees apart, just in the other rotational order for the fifth, so they cancel on the neutral the same way the fundamental does.
Where the crossover sits, and why the page computes it
With nothing but a third harmonic present, the neutral overtakes the phase conductor at 35.4 percent third harmonic — that comes from solving three times h against the square root of one plus h squared, which lands at one over the square root of eight. But nothing on a real panel has only a third harmonic.
Fifth and seventh raise the phase RMS without adding anything to the neutral, which pushes the crossover higher. Ninth adds to the neutral and pulls it lower. Phase imbalance moves it again. At the defaults the crossover works out at 36.5 percent rather than 35.4, and the entered 60 percent is well past it. That is why the page solves for it with the rest of the form in place rather than printing a rule.
The conductor nobody watches
Every phase conductor in a panel has an overcurrent device in series with it. The neutral does not. A phase that gets overloaded eventually trips something and somebody investigates; a neutral carrying 36 A when it was sized on the assumption it would carry the imbalance between three balanced phases just runs warm. It does that for years, and what eventually fails is a termination that has been through a few thousand thermal cycles.
This is why the arithmetic is worth doing rather than assumed, and it is also why the page prints a number and refuses to print a verdict. What a conductor can carry, and how that figure is adjusted for harmonic content, comes from the ampacity table in the code edition your jurisdiction has adopted and from somebody licensed looking at the actual installation.
What would make this wrong
Two things. It applies the same harmonic percentages to all three phases, scaled by each phase fundamental, which is close to right when the three phases carry similar equipment and less right when they do not. And it assumes the harmonic phase angles line up across the three phases, which is what makes triplens add; in reality different equipment produces third harmonic at slightly different angles and some cancellation occurs, so the real neutral current tends to sit a little below this figure rather than above it.
A true RMS clamp meter on the actual neutral conductor settles the whole question in about ten seconds and beats any calculation on this page. Use the arithmetic to know whether it is worth going to look.
Questions people ask
Why is my neutral current higher than my phase current?
Third harmonic. At three times the frequency all three phases arrive in step rather than 120 degrees apart, so instead of cancelling on the neutral they add arithmetically — three times the per-phase third harmonic current. At the defaults, 60 percent third harmonic on 20 A phases puts 36 A on the neutral while each phase carries 24.4 A.
What are triplen harmonics?
Every third order: the third, ninth, fifteenth and so on. They are the ones whose phase shift between A, B and C works out to a whole number of full turns, so they arrive in step on all three phases and add on the neutral instead of cancelling. The fifth, seventh, eleventh and thirteenth are still 120 degrees apart and cancel on the neutral when the phases are balanced.
At what third harmonic level does the neutral overtake a phase?
With nothing but a third harmonic present it is 35.4 percent, which is one over the square root of eight. With other harmonics present it moves, because fifth and seventh raise the phase RMS without touching the neutral while ninth adds to the neutral. The page solves for it with the rest of your form in place — at the defaults it lands at 36.5 percent.
Is the neutral protected by a breaker?
In an ordinary four-wire installation, no. Every phase conductor has an overcurrent device in series with it and the neutral does not, so a neutral carrying more than it was sized for simply runs hot without tripping anything. That is why the arithmetic is worth doing on a panel of electronics, and it is also the reason a shared neutral shows up as a degraded termination years later rather than as an event.
How do I measure the harmonic content?
A power quality meter or a clamp meter that reports individual harmonic orders, on the panel with the loads running normally. Failing that, the equipment data sheet sometimes publishes current distortion figures. The defaults on this form are placeholders for switch-mode supplies without power factor correction and are not a claim about what your panel is doing.