Three-phase power
Real, apparent, and reactive power from line voltage, current, and power factor — the kW you pay for, the kVA the system carries, and the kVAR a poor power factor drags along.
Three-phase & single-phase power · real, apparent & reactive · PF correction
kW = √3 · V · I · PF / 1000
What this gives you
Three-phase power comes in three forms, and this splits a balanced load into all of them from just the line voltage, the line current, and the power factor. Apparent power (kVA) is what the conductors, transformer, and utility actually have to carry: kVA = √3 × V × I ÷ 1000. Real power (kW) is the working power that turns shafts and makes heat, and it is what the utility kilowatt-hour meter bills: kW = kVA × PF. Reactive power (kVAR) is the magnetizing power that sloshes back and forth without ever doing work: kVAR = √(kVA² − kW²). Together the three form the power triangle, and the power factor is simply its cosine — the fraction of the carried kVA that shows up as useful kW.
Why the three numbers differ
If the power factor were a perfect 1.0, the three values would collapse into one and kVA would equal kW. Real motors, transformers, and ballasts never reach that — they draw magnetizing current that lags the voltage, so a slice of every amp you carry produces reactive kVAR instead of working kW. That is why a 480 V feeder at 20 A carries 16.6 kVA but delivers only about 14 kW: the missing 8.8 kVAR is real current in your wires and your transformer, heating them and eating capacity, while doing nothing on the shaft. Size conductors and transformers on the kVA, bill and heat-balance on the kW, and reach for capacitors when the kVAR gets large relative to the kW.
Field note — a poor power factor costs you twice
Low power factor is expensive on both sides of the meter. It inflates the line current for a given amount of real work, so your conductors and transformer run hotter and closer to their limit for no extra output — a plant at 0.75 PF carries about 13 percent more current than the same load at 0.85. And most utilities add a demand or reactive-power surcharge once your facility PF drops below roughly 0.90 to 0.95. If a feeder is running warm but the connected kW looks modest, check the power factor before you assume the wire is undersized; the fix is often a capacitor bank, not a re-pull.
Single-phase or three-phase
Set the Phase selector to match the supply. The only thing that changes is the √3 line-to-line factor: a balanced three-phase load carries kVA = √3 × V × I ÷ 1000, while a single-phase load is simply kVA = V × I ÷ 1000. Everything downstream is identical — kW = kVA × PF and kVAR = √(kVA² − kW²) hold either way — so the power triangle, the angle, and the correction math all behave the same; only the apparent-power scale shifts. A 240 V single-phase load at 20 A and 0.9 PF, for instance, is 240 × 20 ÷ 1000 = 4.80 kVA carrying 4.32 kW.
Power-factor correction
Capacitors supply reactive power locally so the utility does not have to push it down the feeder. To lift the power factor from its present value to a target PFt, the capacitor bank must furnish Qc = kW × (tan(cos⁻¹ PF) − tan(cos⁻¹ PFt)). The real power kW never changes — correction only trims the reactive leg of the triangle, shrinking kVAR and, with it, the kVA the system carries. On the diagram the green arrow marks the kVAR the capacitor removes and the dashed green hypotenuse is the smaller apparent power that remains. Enter the target you want to reach in the Target PF field; a target outside 0–1 simply blanks the capacitor result.
Worked example
A 480 V three-phase feeder pulling 20 A at 0.85 power factor: apparent power is √3 × 480 × 20 ÷ 1000 = 16.63 kVA, real power is 16.63 × 0.85 = 14.13 kW, and reactive power is √(16.63² − 14.13²) = 8.76 kVAR. To correct that load to 0.95 PF you need 14.13 × (tan(cos⁻¹ 0.85) − tan(cos⁻¹ 0.95)) = 4.11 kVAR of capacitors. That drops the reactive leg from 8.76 to 4.64 kVAR, pulls the apparent power down to about 14.9 kVA, and lowers the line current from 20 A to roughly 17.9 A — freeing feeder and transformer capacity for no extra real work.