Three phase power calculator
Three phase power calculator
kW, kVA and kVAR on a balanced three-phase load from line voltage and line current.
How this is calculated
For a balanced load, S = √3 x V_line x I_line and P = S x cos φ. The √3 is there because line voltage is √3 times phase voltage on a star connection while line current equals phase current, and the two factors cancel to √3 across the three phases.
- The √3 form holds for a balanced load on either star or delta. On an unbalanced load each phase carries its own current and the honest answer is the sum of three single-phase calculations, not this one.
- Per-phase power is the total divided by three, which is what a single-phase protective device on one limb of the load sees.
The three-phase power formula has a √3 in it that nobody enjoys explaining. It comes from line voltage being √3 times the phase voltage while the line current is the same as the phase current, and it holds for star and delta alike on a balanced load.
Where the √3 comes from
On a star connection each phase sees the line voltage divided by √3 across it, and the full line current through it. Three phases of (V/√3) × I × cos φ add up to √3 × V × I × cos φ. On a delta the voltage is the line voltage and the current is the line current divided by √3 — the same three-phase total by the other route.
That is why the formula does not need to know how the machine is connected. What it does need is balance: three unequal currents are three separate single-phase calculations, and their sum is not what this page computes.
Worked through
A balanced load at 415 V line-to-line drawing 18 line amperes at a power factor of 0.88. Apparent power is √3 × 415 × 18 = 12,938 VA, so 11,386 W of real work and 6,145 VAR of circulating power.
Each phase carries a third of the real power — 3.795 kW — and the phase angle between voltage and current is 28.36°. Those two lines are what a per-phase protective device and a power-factor capacitor bank are each chosen against.
Questions readers ask
Which voltage do I enter?
The line-to-line figure — 415 V at a board, 440 V on some machines, 11 kV on a feeder. Entering the phase-to-neutral 240 V with the √3 in the formula double-counts the conversion and gives an answer √3 too small.
Is the current the line or the phase current?
Line — what a clamp meter on any one of the three conductors reads. On a delta machine that is √3 times the current actually flowing in each winding, which is why a winding rating and a line rating differ.
What if the three phases are not equal?
Then there is no single three-phase power factor and the √3 formula is not exact. Measure each line current, compute three single-phase powers and add them; a four-wire system also has a neutral current that the balanced formula cannot see.
Do I need the power factor to size a cable?
Yes, because a cable is chosen on current and the current is set by the apparent power. The kW figure alone tells you what the load does, not what the conductor carries — which is the whole reason a kVA rating and a kW rating are different numbers.
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