Power Factor Calculator

How to use the power factor calculator

Enter the real power in watts and the apparent power in volt-amps and the tool returns the power factor, a number between 0 and 1, along with the reactive power in VAR. Power factor is simply the ratio of the two: the watts that do actual work divided by the volt-amps the supply has to deliver to get that work done. A device rated 800 W that draws 1,000 VA has a power factor of 0.80, which means four-fifths of what the circuit carries turns into useful output and the remaining fifth is current flowing back and forth without producing anything. Keep both inputs in the same units, because entering watts alongside kilovolt-amps produces an answer that is wrong by a factor of a thousand.

The two numbers come off the equipment in different ways, and knowing which is which prevents most bad results. Real power in watts is the figure on an energy label or read from a wattmeter, and it accounts for the phase relationship between voltage and current internally. Apparent power in volt-amps is what you get from an ordinary clamp meter and a voltmeter: measured amps multiplied by measured volts, with no phase correction at all. The gap between them is the reactive power, and the smaller that gap, the closer the power factor sits to 1.0. You would reach for this tool to put a number on a motor, a whole distribution panel, or a piece of equipment whose nameplate quotes VA when you wanted watts.

Power factor matters most on a commercial or industrial account, where the utility can charge for it. Large inductive loads such as motors, transformers and magnetic ballasts draw a magnetising current that swings out and back each cycle without doing work, and that current still has to be carried by every conductor and every transformer between the generator and the plant floor. Utilities therefore meter power factor on larger accounts and apply a penalty when it falls too low. Thresholds and methods vary by tariff, but industry references describe utilities commonly starting to penalise somewhere in the 0.85 to 0.95 range, usually either by billing on kVA demand rather than kW demand or by multiplying the demand charge by a ratio of target power factor to actual.

For a home this is mostly background knowledge rather than a bill you can lower. Residential meters bill real kilowatt-hours, so a poor power factor on a household appliance does not normally cost you anything directly the way it does a factory. It is still worth understanding in two situations: reading a motor nameplate, and sizing a generator or a UPS. Both of those are rated in volt-amps rather than watts precisely because they have to supply the apparent power, not just the real power, so a 1,000 VA UPS will not carry a 1,000 W load with a poor power factor. Read the result as a snapshot of how hard the supply is working relative to what it achieves, and leave correction equipment on a real installation to a licensed electrician.

The formula

On an alternating-current circuit, voltage and current are not necessarily in step. Where they are, every instant of current is doing work and the watts equal the volt-amps. Where an inductive load pushes the current out of phase with the voltage, part of each cycle sees energy flowing into the load and part sees it flowing back out again, so the supply carries current that never becomes useful output. Power factor is the fraction that does.

The three quantities form a right triangle, which is where the square root comes from. Real power in watts is one leg, reactive power in VAR is the other, and apparent power in volt-amps is the hypotenuse. That geometry means reactive power is always recoverable from the other two, and it also means power factor equals the cosine of the phase angle between voltage and current, which is why it is often written as cos phi.

power factor = real power (W) ÷ apparent power (VA)
reactive power (VAR) = √(VA² − W²)
apparent power (VA) = real power (W) ÷ power factor
800 ÷ 1,000 = 0.80;  √(1,000² − 800²) = 600 VAR

Worked example with the defaults: 800 W divided by 1,000 VA gives a power factor of 0.80. The reactive power is the square root of 1,000,000 minus 640,000, which is the square root of 360,000, or 600 VAR. So of the 1,000 volt-amps the supply delivers, 800 do real work and 600 swing back and forth each cycle achieving nothing. Those three numbers form a right triangle with legs of 800 and 600 and a hypotenuse of 1,000, the familiar 3-4-5 proportions scaled by 200.

Run the arithmetic backwards to see what a poor power factor costs in supply capacity. Holding real power at 1,000 W, a power factor of 1.00 needs 1,000 VA and no reactive power. At 0.80 the supply must carry 1,250 VA and 750 VAR. At 0.50, which a lightly loaded motor or an idling transformer can reach, it must carry 2,000 VA and 1,732 VAR, so twice the current for the same useful output. Every conductor, breaker, transformer and generator in the path has to be rated for that larger figure, which is why apparent power is what equipment ratings are written in.

That extra current is exactly what utilities charge for on larger accounts. Practice varies by tariff, but references describe penalties commonly starting somewhere between 0.85 and 0.95, applied either by billing on kVA demand instead of kW demand or by scaling the demand charge by the ratio of a target power factor to the measured one. Residential meters bill real kilowatt-hours, so households rarely see it. Correction on a real installation means adding capacitors sized to the reactive load, which is engineering work for a licensed electrician, not something to derive from a single reading on this page.

Frequently asked questions