Article — kVA Calculator (Apparent Power, 1-Phase & 3-Phase)
kVA calculator — convert volts and amps to apparent power
kVA stands for kilovolt-ampere, the unit of apparent power. For a single-phase circuit, kVA = V × I ÷ 1000. For a balanced three-phase system, kVA = √3 × V × I ÷ 1000, where V is the line-to-line voltage and I is the line current. The 1.732 multiplier comes from the geometric sum of three currents that are 120 degrees apart in time.
Apparent power is what the utility actually delivers through the wires. Some of that power does work (kW); some bounces back and forth between source and load without doing anything useful (kVAR). The ratio between real and apparent power is the power factor, and it sits at the heart of every kVA calculation.
What is kVA?
kVA is apparent power — the product of root-mean-square voltage and current in a circuit, divided by 1000 to convert volt-amperes to kilovolt-amperes. It captures the total electrical loading on the wires, transformer, and generator, regardless of how efficiently the load converts that energy into useful work.
A 100 kVA transformer can supply up to 100,000 volt-amperes simultaneously. Whether the load uses all of that as real work (a heater bank, power factor 1.0) or wastes some as circulating reactive power (an induction motor, power factor 0.85) does not change the apparent power demand on the transformer windings.
Utilities size every transformer, substation, and generator in kVA — never in kW. The reason is simple: a transformer's windings heat up from current, regardless of phase angle. A 500 kVA transformer can carry 500,000 VA whether the load runs at unity power factor or 0.7.
kVA formula for single-phase and three-phase
The single-phase formula is the simpler case: multiply the line voltage by the line current and divide by 1000. For a US household running at 240 V and drawing 100 A, that is 240 × 100 ÷ 1000 = 24 kVA peak demand.
1-phase kVA = V × I / 10003-phase kVA = √3 × V × I / 1000From kW kVA = kW / cos φTo amps (1Ø) I = kVA × 1000 / VTo amps (3Ø) I = kVA × 1000 / (√3 × V)The three-phase formula uses line-to-line voltage and the per-phase line current. A factory motor branch at 480 V drawing 50 A per phase pulls 1.732 × 480 × 50 ÷ 1000 = 41.6 kVA. Real power depends on the motor's power factor, typically around 0.88 at full load, so the same circuit delivers about 36.6 kW of mechanical work.
kVA vs kW vs kVAR — three flavors of power
Real power (kW) is what does work — heat, motion, light. Reactive power (kVAR) is the energy that oscillates between the source and inductive components like motor windings or transformer cores. Apparent power (kVA) is the vector sum of the two, and it is what the wires actually carry.
The three are related by the power triangle: kVA² = kW² + kVAR². A 10 kW motor with 5 kVAR of reactive demand has an apparent power of √(100 + 25) = 11.2 kVA. The 1.2 kVA gap is wasted from the utility's perspective and shows up on the bill of large customers as a power-factor penalty.
Power factor and why it matters
Power factor is cos φ — the cosine of the phase angle between voltage and current waveforms. A purely resistive load (heater, incandescent bulb) has power factor 1.0; voltage and current peak together. An inductive load (motor, transformer) pulls current that lags voltage, dropping power factor below 1. Capacitive loads (some electronics, capacitor banks) push current to lead voltage and bring power factor back up.
Power factor correction with capacitor banks usually pays back in 18–36 months for industrial sites. Adding 100 kVAR of capacitance to a plant running at 0.8 pf can raise it to 0.95+, cut line losses by 10–15 %, and erase utility penalties altogether.
Generator and transformer sizing in kVA
Always specify generators and transformers in kVA, not kW. The kW rating is load-dependent; the kVA rating is what the equipment can physically supply. Standard practice adds a 20–25 % safety margin to handle motor inrush current (which can spike to six times the running current for 50–200 milliseconds during startup).
- Residential standby = 10–22 kVA covers a typical US home with central air conditioning.
- Small commercial = 50–150 kVA powers a restaurant, dental office, or small retail unit.
- Mid-size building = 250–1000 kVA serves a mid-rise office, hospital wing, or warehouse.
- Data center pod = 1500–3000 kVA per UPS module, with N+1 redundancy.
- Utility substation = 10,000+ kVA (10 MVA) per transformer, multiple per site.
- EV fast charger = 50–350 kVA per stall, 3-phase 400/480 V.
Typical kVA by appliance and building
A 230 V single-phase electric kettle pulls about 2 kW at unity power factor — call it 2 kVA. A 1.5 hp pool pump motor running 230 V single-phase at 0.85 power factor needs roughly 1.3 kVA. A 50 hp three-phase industrial motor at 460 V draws around 47 kVA at full load. Scale the numbers and you can spot-check any installation against its main feeder.
Why three-phase uses the √3 factor
Three-phase power uses three separate conductors carrying alternating currents offset by 120 degrees in time. At any instant, the sum of the three instantaneous currents is zero (in a balanced system), but the average power delivered is √3 times what a single phase at the same line-to-line voltage and current would deliver. The 1.732 multiplier is the geometric resolution of three balanced phasors.
In a 3-phase formula, V is the line-to-line voltage (e.g., 400 V or 480 V), not the phase-to-neutral voltage. Mixing them is the most common mistake — using 230 V (phase voltage) instead of 400 V (line voltage) in a European 3-phase formula undersizes the result by √3.
Common kVA calculation mistakes
Three patterns show up repeatedly. First, applying the single-phase formula to a three-phase circuit and missing the √3 factor — instant 73 % undersize. Second, confusing kW load with kVA capacity when sizing generators, leading to overload tripping when motors start. Third, ignoring power factor entirely and assuming 1.0 for an inductive load — guarantees a generator runs out of headroom and stalls under real load.