The kVA calculator above moves between the three numbers that describe an alternating-current load — apparent power in kilovolt-amperes, real power in kilowatts, and the current flowing in the line — for single-phase, three-phase and DC systems. Most people arrive from one of two directions: a transformer or generator nameplate in kVA, needing the current it can deliver; or a load in kilowatts, needing the kVA of equipment to feed it. This page does both, and shows the reactive component that explains why the two differ.
Arb Digital builds free calculators that each own one job, and the boundary here is worth stating plainly. The site's electrical power calculator starts from circuit quantities — volts, amps, ohms and power factor — and derives the power figures from them. This page runs in the opposite direction: the power rating is the input, and the line current is the answer. If you want the power triangle explained and corrected rather than converted, the power factor calculator sizes the capacitor to close the gap. If you are choosing a standby generator from a list of appliances rather than from a kVA figure, the generator size calculator is the one that adds motor starting surge.
What This kVA Calculator Does
Apparent power is the plain product of voltage and current, regardless of whether the two waveforms are in step. It is measured in volt-amperes because calling it watts would imply it all does work, and in any circuit with inductance it does not. Real power is the portion that converts into heat, light or rotation: apparent power scaled by the power factor. Reactive power is what is left — energy that moves into a magnetic or electric field and back out every cycle, doing nothing useful but occupying capacity in every conductor it passes through.
The three quantities form a right triangle: apparent power is the hypotenuse, real power the adjacent side, reactive power the opposite side, and the cosine of the angle between hypotenuse and adjacent is the power factor. That geometry is the whole of the arithmetic here. Given any one side and the power factor the other two follow, and given apparent power and voltage the current follows too.
The system selector changes one thing: how apparent power, voltage and current relate. In DC or single-phase AC, apparent power is simply volts times amps. In a balanced three-phase circuit quoted at line-to-line voltage it is the square root of three times volts times amps, because line voltage and per-phase current are not measured across the same pair of conductors. Getting that 1.732 wrong in either direction is the most common error here, and a large one.
How to Use It
- Pick the system first. Three-phase is the default because that is where kVA ratings are most often quoted. Switching to DC forces the power factor to 1, because there is no phase angle to speak of.
- Choose your starting point. Whichever of kVA, amps or kW you actually know becomes the input; the other two fields stop being read and become answers instead.
- Enter the correct voltage. For three-phase this is the line-to-line value. Entering the line-to-neutral value here understates the apparent power by a factor of 1.732.
- Set a realistic power factor. If you do not know it, an equipment nameplate usually prints it. Guessing 1 on a motor load will understate the kVA and the current by roughly a fifth.
- Read the spare-capacity figure as a planning number. It is your own margin percentage applied to the result, so that a transformer or generator is not sized to run permanently at its own limit.
The Formula: How kVA, kW and Amps Relate
For a single-phase AC circuit, apparent power in volt-amperes is S = V × I, using RMS values of voltage and current. For a balanced three-phase circuit with the line-to-line voltage, S = √3 × VLL × Iline. Rearranged for the current, which is what most people come here for, that is I = S ÷ (√3 × VLL).
Real power follows from the power factor. OpenStax University Physics Volume 2, section 15.4 on power in an AC circuit, gives the average power as P = IrmsVrmscos φ and names cos φ the power factor, describing it as the amount by which the delivered power falls short of the theoretical maximum because voltage and current are out of phase. Reactive power is then Q = √(S² − P²), which is the same as S sin φ.
The units themselves are all the same dimension — volts times amperes — and are distinguished by convention rather than by physics, so that a reader can tell at a glance which of the three quantities is meant. NIST's Office of Weights and Measures page on SI units lists the ampere among the seven base units from which the derived electrical units are constructed.
Work the default values as a check. A three-phase 400 V system with a 50 kVA rating at a power factor of 0.8. The line current is 50,000 ÷ (1.7320508 × 400) = 50,000 ÷ 692.82 = 72.17 A. Real power is 50 × 0.8 = 40 kW. Reactive power is √(50² − 40²) = √900 = 30 kVAR. With 25% spare capacity the equipment rating comes out at 62.5 kVA.
Why Transformers and Generators Are Rated in kVA and Not kW
A transformer's limits are thermal, and the heat comes from current in the windings and flux in the core. Neither cares whether current is in phase with voltage. A 500 kVA transformer overheats at 500 kVA whether that is 500 kW of resistive heaters at unity power factor or 350 kW of motors at 0.7, so a kilowatt rating would be meaningless.
Generators are a different case, and it catches people out. The alternator is current-limited, so it is rated in kVA; the engine driving it is torque-limited, so it is rated in kW. Manufacturers publish both, usually a kVA figure at an assumed power factor of 0.8 with a kW figure eighty per cent of it. Feed such a set a unity-power-factor load and you still cannot exceed the engine kW, even with alternator capacity to spare; feed it 0.5 and the alternator hits its current limit long before the engine is working hard.
Motors are rated a third way again: by mechanical output power at the shaft, in kilowatts or horsepower. That is neither the electrical real power drawn nor the apparent power, because motor efficiency sits between them. A 15 kW motor at 90% efficiency draws about 16.7 kW electrically, and at a power factor of 0.85 that is about 19.6 kVA. Three different numbers for one machine. The motor torque calculator relates that shaft figure to speed and torque.
The Current Is the Number That Actually Sizes Things
Apparent power is a convenient intermediate, but almost nothing in an installation is chosen by kVA directly. Conductors, protective devices, contactors, isolators and terminals are all rated in amperes. That is why current is the headline number here rather than a secondary figure.
It is also why poor power factor costs money twice. Reactive current produces no output but still heats every cable it passes through, and conductor loss goes as the square of current — so a load at 0.7 power factor draws about 43% more current than the same real power at unity and dissipates roughly twice the cable heat. The voltage drop calculator shows the other half of that penalty, the volts lost along the run.
Conductor selection and protective device selection are governed by the wiring rules that apply where the installation is, and those rules bring in ambient temperature, grouping, installation method, insulation type and continuous-load factors that no general-purpose calculator can know. This page publishes no ampacity table and no allowable current for any cable size. It gives you the design current, and the design current is the first line of a process that a qualified person completes. The site's breaker size calculator and wire size calculator follow the same rule.
Where the Three-Phase Assumption Breaks Down
The √3 relationship assumes a balanced three-phase load: equal current in all three lines, equal power factor in each. Real installations drift from that whenever single-phase loads sit between one line and neutral. That is usually good enough for first-pass sizing, but two situations deserve care.
The first is a badly unbalanced board, where one phase carries far more than the others. Total kVA is unchanged, but the hottest conductor is the one that matters and it carries more than the balanced figure suggests. Working from total kVA hides that, so measure current per phase rather than inferring it.
The second is a load rich in harmonics — variable-speed drives, LED lighting, switch-mode supplies and IT equipment — which draws current in short non-sinusoidal pulses. The displacement power factor used here, the cosine of the phase angle, no longer captures the whole story, because true power factor also includes a distortion term. A real installation's apparent power can therefore exceed what this page predicts, and in a four-wire system the neutral can carry more current than any line. If your load is predominantly electronic, treat this kVA as a floor.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering line-to-neutral voltage for a three-phase system — the formula expects the line-to-line figure, and using 230 V where 400 V belongs understates the apparent power by a factor of 1.732.
- Treating kVA and kW as interchangeable — they are equal only at unity power factor, and equipment nameplates deliberately use whichever one reflects that machine's real limit.
- Assuming a generator's kVA rating is available at any power factor — the engine's kW limit and the alternator's kVA limit bind at different points, and the published pair assumes one specific power factor.
- Using a motor's shaft rating as its electrical draw — the nameplate kilowatts are mechanical output, so the electrical input is higher by the efficiency and higher again in kVA by the power factor.
- Sizing a cable straight from this current figure — design current is the start of conductor selection, not the end of it; ambient temperature, grouping and installation method all still apply.
Related Free Tools From Arb Digital
Derive power from circuit quantities with the electrical power calculator or the Ohm's law calculator, and correct a poor power factor with the power factor calculator. Size backup supply from an appliance list using the generator size calculator. For the installation side, see the breaker size calculator, the wire size calculator and the voltage drop calculator. Everything is indexed on the free online tools hub.
Frequently Asked Questions
Divide the apparent power in volt-amperes by the square root of three times the line-to-line voltage. For 50 kVA at 400 V that is 50,000 divided by 692.82, which gives 72.17 amps per line. Power factor does not enter this conversion at all.
kVA is apparent power, the plain product of volts and amps, and it is what conductors and transformers have to carry. kW is real power, the part that does useful work. They are related by the power factor, and they are equal only when the power factor is 1.
Because it sets the ratio between the two power figures. Converting kVA to amps does not need it, but converting kVA to kW or kW to kVA does. Assuming unity power factor on a motor load will understate the required kVA by around twenty per cent.
Both, and for different reasons. The alternator is current-limited so it is rated in kVA; the engine is torque-limited so it is rated in kW. Manufacturers usually publish the pair at an assumed power factor of 0.8, and neither limit can be exceeded regardless of the other.
Yes. Single-phase drops the square-root-of-three factor so apparent power is simply volts times amps. DC does the same and fixes the power factor at 1, because there is no phase angle between voltage and current in a direct-current circuit.
No. This is the design current, which is the first input to conductor selection rather than the result of it. Ambient temperature, grouping, installation method, insulation type and the applicable wiring rules all change the answer, and that selection belongs to a qualified electrician.
It is the energy that moves into a magnetic or electric field and back each cycle without doing work. It does no useful job but still occupies capacity in cables and transformers, and it is the reason apparent power exceeds real power whenever the power factor is below one.
No. It uses displacement power factor, the cosine of the phase angle between two sinusoids. Loads such as variable-speed drives and switch-mode supplies add a distortion component, so on an electronics-heavy installation the real apparent power will exceed what this page predicts.
This tool is provided for educational and estimating use. It performs an idealised balanced-load calculation and is not a design tool for an electrical installation. It deliberately publishes no ampacity, cable-size or protective-device table. Work on mains electricity, and the selection of conductors, transformers and protective devices, must be designed and carried out by a qualified electrician working to the wiring regulations that apply in your jurisdiction.
