kW to kVA Calculator

kW and kVA count two different things

kilowatts measure real power, the part that turns a shaft, heats an element or lights a room. kilovolt-amperes measure apparent power, the full product of voltage and current that the wires, breaker and transformer must carry. The gap between the two is reactive power, and the ratio that connects them is the power factor.

Equipment nameplates rarely agree on which number they quote. A motor lists kW on its shaft rating. A generator, a transformer and a UPS list kVA, because their size is set by current, and current follows apparent power. Converting from the kW you know to the kVA you must buy is therefore the first step of any equipment selection, and it is one division long.

The formula: divide kW by the power factor

The conversion is one step and one direction. Apparent power is always the larger number, so the power factor goes in the denominator:

kVA = kW / power factor

Run the other way, kW = kVA x power factor. The power factor is a pure ratio with no units, and it is the same number in single phase and three phase. What changes with phase is only the current behind the kVA, which the next section covers. The U.S. Energy Information Administration defines power factor as the ratio of real power in kilowatts to apparent power in kilovolt-amperes, which is exactly this division read in reverse.

Read the table as a sizing warning. A 500 kW load at a 0.8 power factor needs 625 kVA of capacity, a quarter more than the kW figure suggests. Buying hardware on the kW number alone leaves the transformer or generator running 25 percent over its rating.

Worked example: a 100 kW load at 0.8 power factor on 480 volts

Take a shop with 100 kW of motors running at a 0.8 power factor on a 480 volt three-phase supply. The apparent power is 100 / 0.8 = 125 kVA. The line current that the panel and the feeder must carry is 125,000 / (1.7320508 x 480) = 150.35 amps per line.

The same 100 kW at unity power factor would draw only 120.28 amps, because 100,000 / (1.7320508 x 480) = 120.28. The 30 extra amps per line are reactive current: they do no work, but they heat the conductors, trip breakers and fill the transformer just the same.

The kvar step uses the 3-4-5 triangle of power: at a 0.8 power factor the reactive share is 0.6 of the apparent power, so 125 kVA carries 75 kvar. Add 25 kW and 75 kvar as vectors and the result is back to 125 kVA.

Worked example: a 30 kW air compressor at 0.85 power factor

A 30 kW rotary screw compressor on a 480 volt three-phase panel is a common sizing question. At a nameplate power factor of 0.85 the apparent power is 30 / 0.85 = 35.29 kVA, and the line current is 35,294 / (1.7320508 x 480) = 42.45 amps.

That number alone does not finish the job. Compressors start loaded, and a motor starting from rest draws several times its running current for a second or two. Generators in particular need margin for that inrush, which is why the next step adds headroom before picking a model.

The same arithmetic on a single-phase 240 volt feed would give 35,294 / 240 = 147.06 amps, more than three times the three-phase current at the same kVA. That is the practical reason large compressors order a three-phase service.

From kVA to amps: finishing the sizing job

Once the kVA number exists, current follows from the voltage and the phase count. Single phase divides by the voltage. Three phase divides by 1.7320508 times the line-to-line voltage, or 3 times the line-to-neutral voltage.

The single-phase column explains why panel schedules grow so fast in small shops. The same 45 kVA that needs a 54 amp three-phase feeder needs a 187.5 amp single-phase feeder, and conductor price scales with amps.

Sizing a generator, transformer or UPS from a kW load

Three habits keep the conversion honest. First, convert every load to kVA at its own power factor before adding, because kVA values add like vectors only when the power factors match. Second, add headroom for motor starting, typically 25 percent on the largest motor. Third, round up to a standard nameplate size instead of down.

Standard dry-type transformer sizes run 15, 30, 45, 75, 112.5, 150, 225, 300, 500 and 750 kVA. Generator sets come in their own ladder, often 20, 30, 45, 100, 130, 200 and 300 kW of output, which at a 0.8 power factor corresponds to 25, 37.5, 56.3, 125, 162.5, 250 and 375 kVA of rating.

What power factor to use when the nameplate is silent

When a datasheet lists only watts, pick the power factor from the type of load. Resistive loads sit at 1.0. Induction motors land near 0.85 at full load and drift toward 0.7 when they run lightly loaded. Electronics with power factor correction sit at 0.9 or better, while uncorrected small supplies can lag to 0.6.

The U.S. Energy Information Administration's glossary defines power factor and apparent power in exactly these terms, and the SI prefix page at NIST explains why 1 kVA is 1,000 VA. Both are worth a bookmark when a vendor's units do not match your load schedule.

Common mistakes when converting kW to kVA

Multiplying instead of dividing is the most common error, and it hides well because both answers look plausible. kVA is the larger number, so if your result came out smaller than the kW you started with, the division went the wrong way. A related slip is applying the power factor twice, once in the conversion and again in the current formula.

Using one power factor for a mixed panel is the second error. Sum the kW and the kvar separately, then rebuild the kVA, rather than averaging power factors. The third error is forgetting that the conversion says nothing about current until voltage and phase are known: 125 kVA is 150 amps at 480 volts three phase but 521 amps at 240 volts single phase.

The reverse direction, starting from a kVA nameplate and asking how much real power comes out, is its own tool: the kVA to kW calculator multiplies by the power factor instead of dividing. Once current is known, the voltage drop calculator checks the feeder, and the power factor calculator sizes the capacitor bank that brings a lagging load back toward unity.

Sources: the EIA glossary definition of power factor, the EIA glossary definition of apparent power, and the NIST page on SI units and prefixes for the kilo prefix.