Three-Phase Current Calculator

The formula

For a balanced three-phase load:

I = P / (√3 × V × cos φ × η)

And for single-phase:

I = P / (V × cos φ × η)

V is line-to-line voltage for three-phase (415 V in India) and line-to-neutral for single-phase (230 V). The √3 comes from the 120° displacement between phases — it is the ratio between line and phase voltage in a star-connected system.

Why efficiency belongs in the calculation

A motor nameplate states output power at the shaft. The current flows on the input side. A 45 kW motor at 92 % efficiency draws current corresponding to 48.9 kW, not 45 kW.

Omit it and you understate the current by 8–10 %. On a cable sizing job that is frequently one full size, and it is the reason so many motor circuits run warmer than the design says they should.

If your figure is already the input power — a measured kW reading, or a heater or lighting load — set efficiency to 1.

Typical power factors

An underloaded motor has a notably worse power factor than a fully loaded one, which is why oversizing motors costs money twice: once in the purchase and again on the demand charge.

Starting current

This calculator gives running current. A direct-on-line induction motor draws 6 to 8 times that on start, for a few seconds. That does not change the cable size — cable ratings are thermal and a few seconds is nothing — but it governs the protective device, the contactor rating, and the volt dip seen by everything else on the board.

Star-delta starting cuts inrush to roughly a third, and a soft starter or VFD lower still.

Which current do you actually want?

The same motor has three currents that differ by a factor of seven, and picking the wrong one is the commonest error downstream of this calculator.

• Full load current — what this tool returns. It sets the overload relay and the contactor.
• Design current for the cable — full load current × 1.25 on a continuous-duty motor circuit, before any derating for ambient, grouping or installation method.
• Starting current — six to seven times full load on a direct-on-line start. It never sizes the cable, but it decides the trip curve, the volt drop at the far end of a long run, and whether a generator can carry the start at all.

Efficiency is not power factor

They sit next to each other in the formula and describe unrelated things, which is why one of them usually gets left out.

Efficiency is real loss: the shaft delivers less than the supply provides, and the difference leaves as heat. Omit it and you understate the current by 8–10 % on a typical motor.

Power factor loses nothing. It describes current that flows in and back out again each cycle without doing work — but the cable and the transformer still have to carry it. Omit it and you understate the current by a further 15 %.

For a load that is already stated as input power — a heater, a measured demand figure, a nameplate marked kVA — set efficiency to 1. It is only there to convert shaft output into supply input.

Single phase, and where the √3 goes

On a three-phase supply the three line currents are 120° apart, so they do not simply add. The √3 is what falls out of that geometry, and it is why the same kilowatts draw far less current three-phase than single-phase — roughly 58 % of it.

Use the line-to-line voltage for three-phase (415 V) and the line-to-neutral voltage for single-phase (240 V). Putting 415 V into a single-phase calculation is a quiet way to undersize everything by 42 %.

Prefer a measurement

This calculation estimates what a nameplate would say. Where the machine exists, the nameplate beats it, and a clamp meter on a working load beats both — real plant rarely runs at the rating it was bought at, and a motor at half load draws far less current at a far worse power factor than any formula here assumes.

Unbalance, and why the highest phase decides

The formula assumes a balanced load, and a real board never is. Single- phase loads — lighting circuits, sockets, small heaters — are distributed across the three phases by whoever wired the board, and they switch independently. The calculated current is the average. The cable, the breaker and the transformer all respond to the worst phase.

A board running 10 per cent unbalanced is normal and harmless. At 20 per cent the highest phase is carrying meaningfully more than the calculation says, and any protection set on the computed figure is either nuisance-tripping or is set high enough that it no longer protects the other two phases properly.

Unbalance is worse than an inconvenience where motors are involved. A three-phase motor fed by unbalanced voltages draws a negative-sequence current that produces no useful torque and a great deal of rotor heating — a 2 per cent voltage unbalance can raise winding temperature by around 8 per cent, and NEMA advises derating the motor beyond about 1 per cent. The current unbalance it produces is several times the voltage unbalance, which is why a clamp meter on three phases is the fastest diagnostic there is for a motor that runs hot for no visible reason.

Harmonics, and the neutral that carries more than it should

In a balanced linear system the three phase currents cancel in the neutral and it carries nothing. That is the assumption a great deal of older installation practice was built on, and it is why half-sized neutrals were once normal.

Non-linear loads break it. Switch-mode power supplies, LED drivers and electronic ballasts draw current in pulses near the voltage peak, and the third harmonic they generate is in phase across all three lines rather than 120 degrees apart. Triplen harmonics therefore add arithmetically in the neutral instead of cancelling. On a heavily electronic load the neutral current can reach 1.4 to 1.7 times the phase current.

The consequences are all the more awkward for being invisible to the protection. Nothing trips, because the neutral has no overcurrent device — it simply runs hot, and on an office or data-heavy floor a full-size or oversized neutral stops being optional. Measure with a true-RMS instrument if you want to see it; an averaging clamp meter will under-read a distorted waveform by a wide margin.