kVA to kW Calculator (and kW to kVA)
kVA to kW Calculator (and kW to kVA)
Convert apparent power to real power and back at any power factor, and get the full-load current at your voltage — the arithmetic behind every generator, UPS and transformer rating.
kVA ⇄ kW
a 62.5 kVA generator set at its rated 0.8 power factor, 415 V three-phase
Apparent, real and reactive power
- kVA
- apparent power: RMS volts × RMS amps ÷ 1000
- kW
- real power: the part that does work, and what the meter bills
- kVAR
- reactive power: energy that shuttles between source and load
- PF
- power factor = kW ÷ kVA = cos φ for a sinusoidal supply
Worked example
a 62.5 kVA generator set at its rated 0.8 power factor, 415 V three-phase
kW = kVA × PF = 62.5 × 0.8 = 50 kW
kVAR = √(62.5² − 50²) = 37.50 kVAR; φ = arccos 0.8 = 36.9°
Full-load current = 62,500 ÷ (1.732 × 415) = 86.95 A per line
The same set drives a 50 kW load at unity power factor too — but never more than 50 kW, because the engine, not the alternator, runs out first
A 3 kVA UPS with an output power factor of 0.9 supplies 2.7 kW, or 13.0 A at 230 V
Ratings you will meet
| Equipment | Rated in | Convention | Example |
|---|---|---|---|
| Diesel generator set | kVA (and kW) | 0.8 power factor | 1563 kVA = 1250 kW (Cummins DQGAA) |
| UPS | kVA (and W) | output power factor 0.8, 0.9 or 1.0 | 3,000 VA = 2,700 W at 0.9 (APC Smart-UPS SRT) |
| Distribution transformer | kVA | no power factor stated — it is a limit on current | 100 kVA feeds any mix of kW and kVAR |
| Motor | kW or HP (output) | input kVA is higher: divide by efficiency, then by PF | 1 HP = 0.746 kW out; at 80% efficiency and PF 0.8 that is 0.932 kW and 1.17 kVA in |
| Heater, geyser, kettle | W | power factor 1, so W = VA | 2,000 W = 2,000 VA = 8.70 A at 230 V |
Why generators and UPS units are rated in kVA
A generator, a transformer and a UPS are all limited by two different things at once. The windings and the semiconductors are limited by current, and current times voltage is apparent power, measured in volt-amperes. The engine behind a generator, or the battery behind a UPS, is limited by real power in watts. Since the ratio between the two depends on the load’s power factor, which the manufacturer cannot know, the machine is rated in kVA — the honest limit — and a kW figure is quoted alongside it at an assumed power factor.
The convention is 0.8 for generator sets. Cummins’s DQGAA data sheet, for instance, lists 1250 kW (1563 kVA) standby and 1100 kW (1375 kVA) prime, both at 0.8 power factor — 1563 × 0.8 = 1250 kW. So a “62.5 kVA” set is a 50 kW set: it will run a 50 kW resistive load all day, and it will run a 62.5 kVA motor load that happens to draw only 50 kW. What it cannot do is give you 62.5 kW because your load turned out to be resistive; the engine is not there.
UPS units differ. Older units were rated at 0.6–0.8; modern online units are typically 0.9 or 1.0. An APC Smart-UPS SRT 3000VA is 2,700 W — a power factor of 0.9 — so it supplies 2.7 kW, about 13.0 A at 230 V. Sizing a UPS on watts alone, when its output power factor is 0.8, buys you a unit a quarter too small.
Transformers are pure kVA. A 100 kVA distribution transformer has no stated power factor at all: its limit is winding current and core heating. Load it with 100 kVA at 0.5 power factor and it delivers 50 kW while running just as hot as it would at 100 kW.
To improve a poor power factor rather than work around it, see the power factor calculator. For the three-phase relationships behind the √3, the three-phase power calculator; to turn a load in watts into amps directly, the watts to amps calculator.
Frequently asked questions
How do I convert kVA to kW?
Multiply by the power factor: kW = kVA × PF. A 62.5 kVA set at the usual 0.8 rating gives 50 kW.
How do I convert kW to kVA?
Divide by the power factor: kVA = kW ÷ PF. 40 kW at a power factor of 0.9 needs 44.44 kVA of alternator or transformer capacity.
What size generator do I need for a 10 kW load?
At the usual 0.8 rating, at least 10 ÷ 0.8 = 12.5 kVA of alternator, and enough engine for 10 kW plus starting surges. Motors draw several times their running current for a second or two at start; a generator supplier will size for that, not for the steady figure.
Is 1 kVA equal to 1 kW?
Only at unity power factor. For a resistive load — a heater or a filament lamp — the two are equal. For anything with motors or electronics, kW is smaller.
Does a poor power factor cost me money?
On a domestic meter, not directly: the meter counts kWh. It costs you in cable and breaker size, in voltage drop, and on commercial and industrial tariffs where a low power factor attracts a penalty or a kVA-based demand charge.
Related calculators
References
- Cummins generator set data sheet DQGAA (D-3333k, 6/15): 1250 kW (1563 kVA) standby, 1100 kW (1375 kVA) prime, both at 0.8 power factor. APC by Schneider Electric Smart-UPS SRT 3000VA (SRT3000XLI): 3,000 VA / 2,700 W — an output power factor of 0.9.
- Hughes E, Hiley J, Brown K, Smith I M. Electrical and Electronic Technology, 12th ed. Pearson 2016: three-phase star and delta relationships, the power triangle and power-factor improvement.
- ABB, Technical Application Papers No. 8: Power factor correction and harmonic filtering in electrical plants (1SDC007107G0202): Qc = P (tan φ₁ − tan φ₂), and CY = 3 × CΔ for a three-phase bank.