Three Phase Power Calculator
Conductors carry amps. Amps come from kVA. And the number on the equipment nameplate is usually kW, which is kVA multiplied by a power factor that is rarely close to one. Size a feeder from kW at a power factor of 0.8 and you have understated the current by a quarter — enough to drop a conductor size on a calculation that looked comfortable. This calculator converts in both directions, shows what the kW-only shortcut would have given, and works out what power factor correction actually changes, which is not the energy bill.
- Line current
- 42.5 A Three phase: I = kVA × 1000 ÷ (V × √3). The √3 comes from the 120 degree phase separation, not from there being three wires — three phase delivers √3 times the power of single phase at the same voltage and current, not three times.
- Apparent power
- 35.29 kVA 30.00 kW ÷ a power factor of 0.85. This is the figure the conductors, breakers and transformer have to carry — the current follows kVA, not kW.
- If you sized the wire from kW
- 36.1 A Against the real 42.5 A. Ignoring power factor understates the current by 15%, which on a marginal calculation is a whole conductor size. The load draws the higher figure whatever the nameplate kW says.
- Reactive power
- 18.59 kVAR Power that flows out to the load and back every cycle without doing work, sustaining the magnetic fields in motors and transformers. It does no work and it still occupies conductor capacity, which is the whole reason power factor matters.
- Mechanical output
- 37.00 hp 30.00 kW of electrical input × 92% efficiency. A motor nameplate gives horsepower as shaft output, so the electrical input is always larger — by the efficiency and then again by the power factor.
- Correcting to 0.95 power factor
- 38.0 A (11% less) Adding about 8.7 kVAR of capacitance. The real power stays at 30.00 kW — correction does not save a single kilowatt-hour. What it frees is conductor and transformer capacity, and it removes a power factor penalty where the utility bills one.
- Does correction save money?
- Only on a demand tariff A residential meter bills kilowatt-hours, which correction does not change, so there is nothing to gain. Commercial and industrial tariffs frequently bill kVA demand or apply a power factor penalty, and there the saving is immediate and often large. Check the tariff before buying capacitors.
- Motor loads are worst at light load
- PF falls as load falls An induction motor holds its magnetising current whatever it is driving, so a motor running at a quarter of its rating has a dreadful power factor. Oversized motors are a common and invisible cause of a poor site power factor, and the fix is a correctly sized motor rather than more capacitors.
Where the square root of three comes from
Three phase power is not three times single phase. The three voltages are separated by a hundred and twenty degrees, so the instantaneous contributions do not add arithmetically — the vector sum works out to the square root of three, about 1.732.
So three phase apparent power is line voltage multiplied by line current multiplied by 1.732, and current is apparent power divided by that same product. It is the single most reliable place to make an arithmetic error in a load calculation.
The practical benefit is that the same power moves at a lower current, which means smaller conductors for the same load. It is also why three phase motors are smaller, cheaper and smoother than single phase motors of the same output — the rotating field arrives for free.
For single phase the factor is simply one, and the same formulas apply with it removed.
kW, kVA and the conductor
Real power in kilowatts is what does work: turns the shaft, makes the heat, produces the light. Apparent power in kilovolt-amperes is the product of voltage and current, and it is what the wire, the breaker and the transformer actually see.
The ratio between them is the power factor. A resistive load — a heater, an incandescent lamp — is close to one. An induction motor at full load is typically 0.85, and a lightly loaded one can be far worse. Welders, older fluorescent ballasts and some electronic supplies are lower still.
Current always follows apparent power. A ten kilowatt load at a power factor of 0.8 draws the current of a twelve and a half kVA load, and the conductor has to be sized for that. Working from kW and forgetting the division is a quiet way to undersize a feeder by a full step.
This is also why transformers are rated in kVA rather than kW. The transformer does not know or care what the load does with the current; it only knows how much it has to pass.
What correction does and does not do
Power factor correction adds capacitance to supply the reactive current locally, so it stops travelling back and forth along the supply. The reactive power falls, the apparent power falls, and the current falls with it.
The real power does not change. Not by one kilowatt, not by one kilowatt-hour. A house billed on energy alone gains nothing at all from correction, and the devices sold to homeowners on that premise do not work.
On a commercial or industrial tariff the picture is different. Where the utility bills kVA demand, or applies a penalty below a threshold power factor, correction reduces the bill directly and often pays back quickly. It also frees capacity in an existing transformer and feeder, which can defer a service upgrade.
The other lever is upstream of the capacitors. An induction motor draws its magnetising current regardless of load, so a motor running at a quarter of its rating has a very poor power factor. Right-sizing motors improves site power factor without buying anything, and it saves real energy as well.
What this is based on
- Three phase power relationships — S = √3 × V × I, P = S × PF
- Horsepower conversion — 1 hp = 746 W of shaft output
Electrical conversions. Conductor sizing under the NEC requires the ampacity tables, derating for ambient temperature and conductor count, and the continuous load factor, none of which are applied here. Power factor correction on a system with harmonics or variable frequency drives needs detuned capacitors and an engineering review, because plain capacitors can resonate with the supply.
Frequently asked questions
What is the formula for three phase current?
Current equals kVA times 1000 divided by line voltage times the square root of three. If you have kW instead of kVA, divide by the power factor first — the conductor carries the current that kVA produces, not the current kW suggests.
Why the square root of three?
Because the three phase voltages are separated by 120 degrees, so they combine as vectors rather than arithmetically. Three phase delivers 1.732 times the power of single phase at the same voltage and current, not three times.
What is the difference between kW and kVA?
kW is the power doing work. kVA is voltage times current — what the conductors, breakers and transformer actually carry. Power factor is the ratio between them, and it is why transformers are rated in kVA.
Does power factor correction save energy?
No. It reduces current and apparent power while real power stays identical, so a meter billing kilowatt-hours sees no change. It saves money only where the tariff bills kVA demand or penalises low power factor, which is a commercial and industrial arrangement.
Why is my power factor bad?
Most often lightly loaded induction motors. A motor draws its magnetising current whatever it is driving, so one running at a quarter of its rating has a very poor power factor. Right-sizing the motor fixes the cause rather than the symptom.