What kVA actually measures
kVA is apparent power: everything the supply has to push down the wire. kW is real power: the part that turns into heat, light or motion at the far end. In a purely resistive load, a heater or an old filament lamp, the two are identical. Add anything with a magnetic field or a switching supply, which means essentially every motor, transformer and drive, and some of the current spends its time going back and forth without doing anything useful. The ratio of the useful part to the total is the power factor.
That gap is not academic, because it decides which number you size things from. Cables, breakers, transformers, UPS units and generators all have to carry the whole current, whether or not it does any work when it arrives. So every one of them is rated in kVA. Your load schedule, your energy bill and your engine's fuel burn all track the work actually done, so they are in kW. Two numbers, both correct, describing the same installation, and typically 20 to 25 percent apart.
The formula
three phase: kVA = √3 × V × I ÷ 1000
kW = kVA × power factor
V is the supply voltage, which for three phase means the line to line figure printed on the nameplate (208, 400 or 480 rather than 120, 230 or 277). I is the current in one line conductor. Note that the power factor appears in the kW line and nowhere in the current line: it changes how much work the current does, not how much current there is.
Where the square root of 3 comes from
The 1.732 gets memorised and almost never explained, and because it makes the answer bigger, a lot of people quietly assume it is a safety margin or an efficiency. It is neither. It is geometry.
In a balanced three-phase system the three voltages are 120 degrees apart. Measure between two lines rather than between a line and neutral and you are adding two vectors at 120 degrees, which gives you √3 times the line-to-neutral voltage. So the total apparent power is three conductors each carrying Vphase × I, and substituting Vphase = Vline ÷ √3 turns 3 into 3 ÷ √3, which is √3. That is the whole derivation: the square root of 3 is just 3 divided by the square root of 3.
The practical payoff is that at the same voltage and current, three phase moves 73 percent more power than a single-phase pair does, which is why anything above a few tens of kW is three phase almost everywhere in the world.
Worked example
A 100 kVA three-phase supply at 400 V, power factor 0.80.
The multiplier is √3 × 400 = 692.8.
Current: 100 × 1000 ÷ 692.8 = 144.3 A in each line.
Real power: 100 × 0.80 = 80 kW.
Reactive power: √(100² − 80²) = √3600 = 60 kVAR, exactly.
That last one is a small gift from the arithmetic. At a power factor of 0.8 the power triangle is a 3-4-5 triangle: 60, 80 and 100. It is the same triangle from school geometry, which makes 0.8 an unusually easy power factor to sanity-check in your head.
Why a 100 kVA generator is an 80 kW generator
This is the single most expensive misunderstanding in the subject, and it is nobody's fault: both numbers are printed, both are honest, and quotes rarely say which one they mean.
Generator sets are rated at a power factor of 0.8 lagging by convention, which is what ISO 8528 assumes. So a set advertised as 100 kVA is offered as 80 kW, and a genuinely 100 kW machine is a 125 kVA set. If you add up a load schedule in kW and then shop for a generator with the same number on it, you will buy one 25 percent too small, and you will not find out until the day it is actually needed.
The honest comparison is kW against kW, or kVA against kVA, with your own power factor used to move between them. This calculator prints both figures side by side for exactly that reason. Worth adding: on most real installations it is motor starting, not running load, that decides the size, because a motor can draw six or seven times its running current for a few seconds. Running totals tell you what the machine must sustain; starting surge tells you what it must survive.
The number worth improving rather than just measuring
Power factor is one of the few figures in an electrical installation you can genuinely change. Here is roughly what different loads look like:
| Load | Typical power factor | What that means for a 100 kVA supply |
|---|---|---|
| Heaters, filament lighting | 1.00 | 100 kW of work |
| Modern electronics with correction | 0.95 | 95 kW of work |
| Well-loaded motors | 0.85 | 85 kW of work |
| Generator rating convention | 0.80 | 80 kW of work |
| Lightly loaded motors | 0.50 | 50 kW of work |
Read the right-hand column again: the same 100 kVA supply does anything from 50 kW to 100 kW of useful work depending entirely on what you hang off it. An oversized motor running at a quarter load is the classic case, and it is why "just fit a bigger one to be safe" can quietly halve the capacity of a switchboard.
Capacitors can correct a lagging power factor and free up real capacity without pulling any new cable, which is often much cheaper than upgrading a supply. Many commercial tariffs also charge for poor power factor directly, so the improvement can show up twice. It is worth getting an electrician to measure yours rather than assuming, since the number you actually have is usually better than 0.8 and occasionally a good deal worse.