kVA to kW Calculator

Apparent power and real power are not the same number

Volts times amps gives volt-amperes, and a thousand of them is one kVA. That is apparent power: the total that the wires, the breaker and the transformer have to carry. The kilowatts that turn a motor or heat a room are real power, and in an alternating current circuit the two only match when the load is a pure resistance.

Motors, transformers, compressors and old magnetic ballasts pull current slightly out of step with the voltage. The current sloshes back and forth without doing work, and the utility still has to size for it. That extra is reactive power, measured in kVAR, and the three quantities form a right triangle: 100 kVA at 0.8 power factor is 80 kW and 60 kVAR, because the square root of 100 squared minus 80 squared is 60.

Power factor is real power divided by apparent power, so it runs from 0 to 1 and never above 1. A power factor of 1 means every kVA is doing useful work. A power factor of 0.5 means half of what you paid to install is moving current that produces no output at all.

The single phase formula: kVA x power factor

For a single phase load the conversion is one multiplication:

• kW = kVA x power factor
• kVA = kW / power factor
• power factor = kW / kVA

Two runs with real numbers. A 100 kVA generator nameplate at 0.8 gives 100 x 0.8 = 80 kW. The same generator at 0.95 gives 100 x 0.95 = 95 kW, so the rating on the label and the usable output are two different facts, and the power factor is what connects them.

The reverse direction matters when you size equipment from a load list. A 45 kW load at a power factor of 0.75 needs 45 / 0.75 = 60 kVA of apparent capacity, not 45. Buy a 45 kVA unit for that load and it will be overloaded on current long before it reaches its kW rating. This is the mistake that turns a cheap transformer into an expensive one.

Three phase: where the 1.732 comes from

Three phase power adds a factor of the square root of 3, which is 1.732, because three waveforms 120 degrees apart share the same conductors. With kVA given as the total for all three phases:

A 75 kVA transformer on a 480 V three phase service carries 75,000 / (1.732 x 480) = 90.21 amps per line at full load. If the load runs at a power factor of 0.85, the real power that unit can deliver is 75 x 0.85 = 63.75 kW, and the reactive part is 75 x 0.527 = 39.5 kVAR. The 1.732 belongs in the current calculation only, because the kVA figure already counts all three phases.

Folding the root three in twice is the common error in this conversion. When someone quotes a three phase kVA, all three phases are already counted, and multiplying by 1.732 again inflates the answer by 73 percent.

What a 100 kVA unit delivers at each power factor

The same apparent rating produces less and less real power as the power factor falls. The table holds kVA at 100 and moves only the power factor.

At 0.8, one fifth of the capacity is stranded: you paid for 100 kVA, the breaker and the copper are sized for 100 kVA, and only 80 kW can go to work. The reactive column is the part the meter measures but the load never uses.

This is why a data center will pay extra for a UPS with a unity output rating. Moving from 0.8 to 1.0 on a 100 kVA unit frees 20 kW, which is a quarter more real capacity from the same footprint, the same switchgear and the same cooling.

Working backwards from kW to kVA

Load schedules are written in kW, because that is what the equipment consumes, and every purchase is quoted in kVA. Divide to cross over. A 250 kW load at a power factor of 0.92 needs 250 / 0.92 = 271.74 kVA, and on a 480 V three phase service that is 271,740 / (1.732 x 480) = 326.85 amps per line.

A smaller case shows the same steps. A 15 kVA load at 208 V three phase draws 15,000 / (1.732 x 208) = 41.64 amps. At 480 V the same 15 kVA draws only 18.04 amps, which is why commercial buildings run distribution at the higher voltage and step down at the equipment.

If the load list gives amps and volts instead of kW, go through apparent power first: 1.732 x volts x amps / 1000 gives kVA, then multiply by the power factor for kW. Skipping the power factor gives you the size of the wire you need, not the size of the generator you need.

Typical power factors by load

The power factor is a property of the load, not of the supply, so the honest answer to "what number do I type" comes from the equipment. Some anchors are solid, and the Department of Energy's motor systems guidebook notes that induction motor power factor runs from about 10 percent at no load to 85 percent or more at full load, which is a wider swing than most people expect.

When the exact figure matters, read it off the nameplate or ask the supplier for the test report. When it does not, use 0.8 for a mixed motor load and 1.0 for heat, and label the result as an estimate.

Why demand is billed in kVA

Residential bills are in kilowatt hours, which is energy: kW multiplied by hours. A commercial demand charge is different, and many tariffs measure it in kVA because the utility has to deliver the current whether or not it does work. The California Energy Commission's note on demand components puts it plainly: at a power factor of 0.8 the demand for a given kW rises by 25 percent, and at 0.5 it doubles.

That turns power factor into a line item. Take 250 kW of load at 0.92, which is 271.74 kVA, and correct it to 0.98, which is 255.10 kVA. The gap is 16.64 kVA, and at a demand charge of 12 dollars per kVA that is 199.65 dollars a month for current that never did any work.

Many utilities also add a penalty once the power factor drops below a threshold, and the Department of Energy's motor system guidance notes that a 95 percent threshold is common, so the practical target is 0.95 or better. Capacitors at the motor or the panel fix it, and the kVA to kW conversion on this page is how you measure whether the fix paid off.