--- title: "kW to kVA Calculator" description: "Convert kW to kVA using power factor, and size the transformer, generator or UPS that has to supply it. Formula, worked example and a kVA chart." standard: "S = P / PF" source: "https://energycalchq.com/tools/kw-to-kva" --- You know the load in kW. The transformer, the generator and the UPS are all sold in kVA. This is the conversion between what the load does and what the source has to be rated for — and it is where sizing decisions get made. ## The formula ``` S = P / PF ``` Where `P` is real power in kW, `PF` is power factor, and `S` is apparent power in kVA. Dividing by a number below 1 always makes the answer bigger. That is the point: the source has to be rated for the *current* it supplies, and reactive current flows whether or not it does work. ## A worked example A factory with a 45 kW connected load running at 0.86 power factor: ``` S = 45 / 0.86 = 52.3 kVA ``` So the supply has to be good for 52.3 kVA, even though only 45 kW does anything useful. The extra 7.3 kVA is the magnetising current the motors need to establish their fields — necessary, but not work. ## How much the power factor costs you Take a fixed 100 kW load and watch what the source has to be rated for: | Load PF | kVA required | Extra capacity over 100 kW | | --- | --- | --- | | 1.0 | 100 kVA | — | | 0.95 | 105 kVA | 5 % | | 0.9 | 111 kVA | 11 % | | 0.85 | 118 kVA | 18 % | | 0.8 | 125 kVA | 25 % | | 0.75 | 133 kVA | 33 % | | 0.7 | 143 kVA | 43 % | | 0.6 | 167 kVA | 67 % | | 0.5 | 200 kVA | 100 % | At 0.7 power factor you are buying, installing and paying maximum demand charges on a transformer 43 % larger than the work you are doing requires. At 0.5 you are buying twice the transformer. This is the entire commercial case for power factor correction. Capacitors are cheap compared with a transformer one frame size larger, a cable one size larger, and a monthly maximum demand charge levied in kVA — which most Indian industrial tariffs are. The [kVAr converter](/tools/power-conversion) sizes the correction; [APFC panel step sizing](/blog/apfc-panel-step-sizing) covers building the panel that switches it. ## kW to kVA chart | kW | PF 0.7 | PF 0.8 | PF 0.85 | PF 0.9 | PF 0.95 | | --- | --- | --- | --- | --- | --- | | 5 | 7.1 | 6.3 | 5.9 | 5.6 | 5.3 | | 10 | 14.3 | 12.5 | 11.8 | 11.1 | 10.5 | | 15 | 21.4 | 18.8 | 17.6 | 16.7 | 15.8 | | 20 | 28.6 | 25.0 | 23.5 | 22.2 | 21.1 | | 30 | 42.9 | 37.5 | 35.3 | 33.3 | 31.6 | | 45 | 64.3 | 56.3 | 52.9 | 50.0 | 47.4 | | 50 | 71.4 | 62.5 | 58.8 | 55.6 | 52.6 | | 75 | 107 | 93.8 | 88.2 | 83.3 | 78.9 | | 100 | 143 | 125 | 118 | 111 | 105 | | 125 | 179 | 156 | 147 | 139 | 132 | | 150 | 214 | 188 | 176 | 167 | 158 | | 200 | 286 | 250 | 235 | 222 | 211 | | 250 | 357 | 313 | 294 | 278 | 263 | | 300 | 429 | 375 | 353 | 333 | 316 | | 400 | 571 | 500 | 471 | 444 | 421 | | 500 | 714 | 625 | 588 | 556 | 526 | ## From kVA to a standard rating The calculated kVA is a minimum, not a purchase order. Three things happen between the two. **Round up to a standard rating.** Transformers come in 25, 63, 100, 160, 250, 315, 400, 500, 630, 1000, 1600 kVA. Our 52.3 kVA lands on a 63 kVA unit. **Add headroom for growth.** A transformer sized exactly to today's load has no room for the extension nobody has mentioned yet. 20 % is a common allowance, which would push the same example toward 63 kVA comfortably, or 100 kVA if expansion is genuinely expected. **Apply diversity going the other way.** Connected load is not maximum demand — nothing runs everything simultaneously. If your 45 kW is the sum of every nameplate on site, the actual peak is lower, often much lower. See [connected load and maximum demand](/blog/connected-load-maximum-demand-diversity) for the factors. These pull in opposite directions, which is why sizing is judgement rather than arithmetic. The arithmetic just tells you where to start. ## Loading a transformer: what to aim for A transformer is most efficient somewhere near 50 % of its rating, where copper losses (which rise with the square of load) and iron losses (which are constant) balance. | Loading | Verdict | | --- | --- | | Below 30 % | Iron losses dominate; you are paying for magnetising an oversized core all day | | 40 – 70 % | The sweet spot — efficient, with room for growth and for motor starts | | 70 – 85 % | Acceptable, running warm, no room for expansion | | Above 85 % | Winding temperature and life become the concern | | Above 100 % | Insulation life halves for roughly every 6 – 8 °C over rated temperature rise | So a 52.3 kVA load on a 100 kVA transformer is not oversizing — it is 52 % loading, right in the efficient band. ## Sizing a UPS or a generator from kW **UPS.** Same conversion, and then a second one. Convert the equipment's watts to VA at the *UPS's* power factor — which is stated on its nameplate, not on your load's. Then leave headroom: a UPS at 100 % load runs hot, and heat is what kills batteries. See [watts to VA](/tools/watts-to-va). **Generator.** Convert to kVA, then check the starting case separately. A DG set that comfortably carries the running kVA can still stall or dip badly when a large motor starts direct-on-line, because starting kVA is three to five times running kVA. The [DG set sizing calculator](/tools/dg-sizing) works through both. ## Common mistakes **Multiplying instead of dividing.** kW to kVA divides by power factor; kVA to kW multiplies. Getting it backwards on a 0.8 PF load gives 64 kVA for a 80 kW load instead of 100 kVA — a 36 % undersize. **Sizing on connected load with no diversity.** Adds up to a transformer far larger than the site will ever draw. **Ignoring future load.** The cheapest time to install a larger transformer is the first time. **Using the load's power factor for a UPS.** The UPS nameplate power factor is the one that governs its own rating. ## The two ratings a UPS carries, and why they disagree A UPS is advertised with a VA figure and a watt figure, and the ratio between them is the manufacturer's assumed power factor rather than anything about your load. Older units assume 0.6 or 0.7; most current designs assume 0.9, and some are rated at unity. That assumption is a limit, not a conversion. The unit will refuse whichever figure it reaches first. A 3000 VA / 2700 W machine loaded with 2800 W of corrected electronic supplies is over its watt rating while sitting at 93 per cent of its VA rating, and it will alarm and transfer to bypass on a limit the VA number gave no warning of. The practical rule is to check the load against both figures independently and size on whichever is tighter. It is also worth noting that the watt rating is the one that governs runtime, because the battery is delivering real power — two UPS units with identical VA ratings and different watt ratings will not give the same backup time on the same load. ## Generators are rated the same way, and derated differently An alternator is limited by winding current, so its rating is in kVA for exactly the reason a transformer's is. The engine behind it is limited by torque, so its capability is in kW. A generating set carries both, related by a power factor the manufacturer has assumed — almost universally 0.8 lagging. Feed that set a load at 0.95 power factor and the engine becomes the limit before the alternator does: the set can deliver its full kVA only if the load is reactive enough to keep the real power within the engine's capability. A 125 kVA / 100 kW set supplying a 0.95 power factor load can produce about 105 kVA before the engine reaches 100 kW, and the remaining alternator capacity is unusable. That is the opposite of the intuition most people bring to power factor correction, and it catches sites that install capacitors and then run on generator during an outage. Correcting to unity in front of a generating set does not release capacity — it removes the reactive load the set was rated against, and on some machines a leading power factor will destabilise the automatic voltage regulator entirely. Where a plant has both capacitors and a generator, the correction stages should be interlocked to drop out when the set is running.