Apparent, real and reactive power on one screen, for single and three-phase supplies in the UK, Europe, India and North America — with the power factor as a required input rather than a quiet assumption.
Calculator
Power factor:
The power factor is required, not defaulted. Tables that assume 0.8 are quoting a generator-set convention, not a property of your load — a resistive heater is 1.0 and a lightly loaded motor can be below 0.5.
100.000 kVA at a power factor of 0.8
80.000 kW
60.000 kVAr reactive · 144.3 A per line · three phase
The three powers, and the current they imply
One load, described three ways
Quantity
Value
What it is
Apparent power
100.000 kVA
Voltage times current. What the cable, breaker and generator have to carry.
Real power
80.000 kW
What does work and what the meter bills. Apparent power times the power factor.
Reactive power
60.000 kVAr
Stored and returned each cycle. Does no work, and still occupies the cable.
Phase angle
36.87°
Between current and voltage. Its cosine is the power factor.
Line current
144.34 A
S ÷ (√3 × line-to-line voltage). The √3 is where three-phase arithmetic goes wrong.
The three powers form a right triangle: apparent squared equals real squared plus reactive squared. That is why a poor power factor costs current rather than energy — the real power is unchanged, but the cable carries the hypotenuse. At 400 V between lines, the voltage to neutral is 230.9 V — the same √3, seen from the voltage side.
Sizing a supply for a motor
Shaft output, from the nameplate7.500 kWwhat the motor delivers
Electrical input8.333 kWoutput ÷ efficiency
Apparent power drawn10.417 kVAinput ÷ power factor
Line current15.04 Awhat the cable must carry
A motor nameplate states output shaft power, not input. The supply has to deliver that divided by the efficiency, and then divided again by the power factor — two divisions, and skipping either under-sizes the cable. Here a 7.5 kW motor needs 10.42 kVA of supply, which is 39% more than the nameplate number suggests.
Which rating runs out first
Usable real power into this load800.0 Wthe kVA rating binds
Crossover power factor0.900below it the VA rating binds, above it the W rating does
A generator or UPS carries two nameplate numbers and the smaller one wins. Sizing on the kVA figure alone is how a unit gets overloaded by equipment it appeared to have room for: at a load power factor of 0.8, this one delivers 800.0 W of real power whatever its label says. A genset sold as 100 kVA is sold as 80 kW for the same reason — the manufacturer had to assume a power factor, and picked 0.8.
Correcting the power factor
Reactive power to cancel33.71 kVArcapacitor bank sizing figure
Apparent power afterwards84.21 kVAdown from 100.00 kVA, same real power
Correction does not reduce the energy used — the real power is unchanged. It reduces the current, which is what frees capacity in cables, transformers and generators, and what removes a power-factor penalty from a commercial tariff. Note that the last few hundredths cost the most: going from 0.95 to 0.99 needs more correction than the arithmetic suggests, because the tangent of the angle rises steeply as the angle approaches zero.
Supplies, and where the √3 lives
Common low-voltage supplies, ordered by line voltage
Supply
Line to line
Line to neutral
Phases
Region
120 V single phase
120 V
120 V
Single
United States & Canada
208 V three phase
208 V
120 V
Three
United States & Canada
230 V single phase
230 V
230 V
Single
UK, Europe & India
240 V split phase
240 V
120 V
Single
United States & Canada
400 V three phase
400 V
230 V
Three
UK, Europe & India
480 V three phase
480 V
277 V
Three
United States & Canada
Read the first two number columns together on the three-phase rows: 400 and 230, 208 and 120, 480 and 277. Each pair is a factor of √3 apart, and that is the same 1.732 that appears in the current formula. The 240 V North American row is the exception worth knowing — it is two 120 V legs in antiphase rather than a phase pair, so there is no √3 in it at all.
What this converter covers
Enter kVA, kW or line current and get all three powers, the phase angle and the current — plus motor sizing, generator ratings and correction.
kVA to kW and back through the power factor, in either direction
Line current for single-phase, split-phase and three-phase supplies
Sizing a supply from a motor nameplate, through efficiency and power factor
Which of a generator or UPS’s two ratings binds
Capacitor sizing for power factor correction
Power factor required √3, not 3 Two ratings, one binds kVA · kW · kVAr · amps
Free, no signup — exact by definition, not an estimate.
Updated 8 September 2026
At a glance
Formula shown
S = k × V × I with k = 1 single phase and √3 three phase · P = S × pf · S² = P² + Q²
Scenario support
100 kVA at 0.8 is 80 kW · 400 V three phase at 100 A is 69.3 kVA, not 40
Educational estimate
Planning support from the values you enter — not professional advice.
Two quantities, one product
Multiply the voltage by the current and you get volt-amperes. That is apparent power: everything the cable, the breaker and the generator have to carry.
What actually does work is real power, measured in watts, and it is smaller — sometimes much smaller. The ratio between them is the power factor, and it is the only thing that connects the two.
Both quantities are volts times amps dimensionally, which is exactly why they get confused. The units are kept apart on purpose: kVA, kW and kVAr all reduce to the same dimensions and name three different things, so nothing about the dimensions can settle which one a number is.
A load draws current out of phase with the voltage when it stores energy and hands it back each cycle — motors and transformers do this in their magnetic fields. That returned energy does no work, but it still travelled down the cable, and it still has to be carried.
So the answer to “how many kW is 100 kVA” is that the question is incomplete. It is 100 kW into a resistive heater, 80 kW at the power factor generator makers assume, and under 50 kW into a lightly loaded motor. This page asks for the power factor and returns nothing without it.
Where the √3 comes from
The costliest arithmetic error on this page is a 3 where a √3 belongs, and it is available from two directions.
Three-phase apparent power is √3 × V × I, with V measured between two lines. The three phases each carry current, but they peak at different moments — 120 degrees apart — so they do not simply add.
The same √3, seen from the voltage and from the current
Supply
Line to line
Line to neutral
Ratio
UK, EU, India
400 V
230 V
1.732
US commercial
208 V
120 V
1.732
US industrial
480 V
277 V
1.732
Read those pairs and the √3 stops being a formula to memorise. It is already printed on every three-phase supply in the world: 400 and 230 are the same pair of numbers as 208 and 120.
That also names the second error. The V in the three-phase formula is the line-to-line voltage. Feeding 230 into it on a 400 V supply produces the same 1.732 mistake arrived at from the voltage side rather than the phase count.
One genuine exception is worth knowing. A North American 240 V domestic supply is not three-phase — it is two 120 V legs in antiphase, so it is single-phase arithmetic with no √3 anywhere in it, despite having two live conductors.
Why a genset is 100 kVA and 80 kW
Generators, transformers and UPS units are rated in kVA rather than kW, and the reason is honest: the manufacturer does not know what you are going to plug in.
What limits a generator is heat, and heat comes from current. Current is apparent power divided by voltage, whatever the power factor happens to be. So the rating that actually describes the machine is the kVA one.
The kW figure on the same nameplate is that kVA rating multiplied by an assumed power factor, and for diesel gensets the assumption is 0.8 — which is where a 100 kVA / 80 kW label comes from. Nothing measured 80. It is 100 × 0.8.
A UPS has the same pair, usually with a different assumption. Older units used 0.6 to 0.8; modern ones are often 0.9 or 1.0. Whichever it is, the smaller of the two ratings binds. A 1000 VA / 900 W unit feeding a load at power factor 0.7 delivers 700 W, not 900, because the VA rating ran out first. Feeding a load at 1.0 it delivers 900 W, because now the W rating is the limit.
The crossover sits at the ratio of the two ratings. Below it the VA limit binds, above it the W limit does, and the calculator marks where the change happens for whatever pair you enter.
The nameplate is output
A motor rated 7.5 kW does not draw 7.5 kW. It delivers 7.5 kW at the shaft, and getting from there back to the supply takes two divisions that are easy to skip.
First divide by the efficiency, because the motor dissipates some of its input as heat. At 90% efficiency, 7.5 kW of shaft power needs 8.33 kW of electrical input.
Then divide by the power factor, because the supply has to carry apparent power. At 0.85, that 8.33 kW of real power is 9.8 kVA — which on a 400 V three-phase supply is a little over 14 A per line.
The gap between the nameplate figure and the supply requirement is therefore around 30%, and it compounds: skipping both divisions under-sizes the cable by roughly a third. Wiring codes handle this by sizing motor circuits from full-load current tables rather than from the power rating, which is the same point expressed as a rule.
Horsepower ratings work identically and are also output figures. One mechanical horsepower is 745.7 W, so a 10 hp motor delivers 7.46 kW at the shaft and the same two divisions apply after that.
What correction actually buys
Power factor correction is widely described as saving energy, and for most installations that is not what it does.
A capacitor bank supplies the reactive power the load was drawing from the supply, so the reactive component stops travelling down the cable. The real power is unchanged — the machines do exactly the same work and the kWh meter reads exactly the same.
What changes is current, and the consequences of current:
Cables, transformers and switchgear are freed up, because they were carrying the hypotenuse of the power triangle rather than one of its sides. A site at 0.7 that corrects to 0.95 sheds about a quarter of its current for the same output, which can be the difference between needing a supply upgrade and not.
And on commercial tariffs it removes a penalty. Many suppliers bill reactive energy separately or apply a charge below a threshold power factor, typically around 0.9 — which is the actual financial case, and it is a billing case rather than an energy one.
One thing to watch when setting a target: the last few hundredths are the expensive ones. Going from 0.8 to 0.9 and from 0.9 to 0.99 are not comparable jobs, because the reactive power scales with the tangent of the phase angle and that curve steepens sharply as the angle closes. Most installations stop just above whatever the tariff threshold is, and that is a considered choice rather than a compromise.
Related calculators
Other electrical and energy tools:
Watts to AmpsWatts, amps and volts at UK, EU, India and US supplies — single or three phase, with volt-amps beside the watts.
PowerWatts, kilowatts, horsepower and BTU per hour — with mechanical and metric horsepower listed apart, since they differ by 1.4% under one word.
Battery CapacitymAh to watt-hours at any cell voltage, the airline 100 Wh limit, and how many charges a power bank really gives.
EnergyJoules, kilojoules, calories, food Calories, kWh, BTU and therms — with the two calories listed apart, since one is a thousand of the other.
Wire GaugeAWG and SWG to mm, mm² and circular mils, with resistance and voltage drop — and the 14–21% gap the equivalence charts hide.
Gas m³ to kWhMeter readings to billed energy for UK, EU, US and Indian networks — with the calorific value as an input, because no factor connects volume to energy on its own.
The first two settle the definitions and the voltages; the third is where the output-against-input point becomes a wiring rule; and the SI Brochure is the reason the watt, the volt-ampere and the var are kept as three names for one dimension.
IEEE Std 1459 — Definitions for the Measurement of Electric Power QuantitiesIEEE Standards Association · verified 2026-09-08 · The formal definitions of apparent, active and reactive power and of power factor, including the fact that they are distinct quantities related through the phase angle rather than by any fixed factor
IEC 60038 — IEC standard voltagesInternational Electrotechnical Commission · verified 2026-09-08 · The standard low-voltage supplies used on this page — 230/400 V across the UK, Europe and India and 120/208 V and 277/480 V in North America — and the line-to-line against line-to-neutral relationship between each pair
NFPA 70 — National Electrical CodeNational Fire Protection Association · verified 2026-09-08 · That motor branch-circuit conductors and protection are sized from full-load current tables rather than from a nameplate output rating, which is the practical form of the point this page makes about input against output power
SI Brochure, 9th editionBureau International des Poids et Mesures · verified 2026-09-08 · That the watt, the volt-ampere and the var share the same dimensions while naming different quantities, which is why the units are kept distinct and why no dimensional argument can bridge them
Conversion note
This is unit arithmetic, not an electrical design. Real installations are sized under a wiring code — the NEC in North America, BS 7671 in the UK, the relevant national implementation of IEC 60364 elsewhere — and those codes add derating for ambient temperature, grouping, installation method, cable length and voltage drop, plus separate rules for motor starting current, which can be six times the running figure and is what actually sizes the protective device. Power factor here is treated as a single number; real loads vary it with load level, and non-linear loads such as drives and rectifiers add harmonic distortion, which lowers the true power factor further in a way the displacement power factor used here does not capture. Efficiency and power factor figures for a specific machine come from its nameplate and test certificate, not from typical values. Generator and UPS ratings also depend on ambient temperature, altitude and duty cycle. Have any installation designed and verified by a qualified electrician or engineer working to the code in force where the work is done.
Published the kVA to kW Converter: apparent, real and reactive power plus the phase angle and the line current, entered from whichever of kVA, kW or amps is known.
Requires the power factor and returns nothing without it, because kVA and kW are different quantities that happen to share a dimension -- tables that quietly assume 0.8 are quoting a generator-set convention rather than a property of anyone's load.
Carries six standard low-voltage supplies covering the UK, Europe, India and North America, each with BOTH its line-to-line and line-to-neutral voltage, so the square root of three is visible as a pair of published numbers rather than as a constant to memorise.
Names the two directions the same error arrives from: using the single-phase formula on a three-phase supply, and feeding the line-to-neutral voltage into the three-phase one. Both are wrong by 1.732.
Flags the North American 240 V supply as the genuine exception -- two 120 V legs in antiphase, so single-phase arithmetic with no square root of three anywhere in it despite two live conductors.
Sizes a supply from a motor nameplate through both divisions that get skipped: output shaft power divided by efficiency, and then by power factor, which together add about 30 per cent to the figure on the plate.
Shows which of a generator's or UPS's two nameplate ratings binds at a given load power factor, and computes the crossover between them, since sizing on the kVA figure alone is how a unit gets overloaded.
Sizes power factor correction and states plainly what it buys: the real power and the kWh meter are unchanged, and what falls is current -- which frees capacity and removes a tariff penalty rather than saving energy.
Verified by 69 automated cases, asserting that a power factor of zero, above one, or missing is refused; that the three-phase factor is the square root of three rather than a rounded 1.732; that the power triangle closes at six different power factors; and that the binding rating flips at exactly the ratio of the two nameplate numbers.
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