Apparent power and real power are not the same thing
kVA is apparent power: volts times amps, without regard to what the load does with them. kW is real power: the part that actually does work and shows up on your meter. The ratio between them is the power factor.
For a purely resistive load such as a heater, the two are equal and the power factor is 1. For motors, transformers and anything with a magnetic field or a rectifier front end, current and voltage fall out of step and kVA exceeds kW.
This matters commercially because equipment is rated in kVA while you are billed, for the most part, in kW. A transformer or generator must supply the apparent power, so a 100 kVA set with a load at 0.75 power factor can only deliver 75 kW of useful work — a quarter of the machine is capacity you are paying for and cannot use.
The formulas, by system
| System | kVA | Amps from kVA |
|---|---|---|
| DC | V × I ÷ 1000 | kVA × 1000 ÷ V |
| Single-phase AC | V × I ÷ 1000 | kVA × 1000 ÷ V |
| Three-phase AC | √3 × V × I ÷ 1000 | kVA × 1000 ÷ (√3 × V) |
The square root of 3, about 1.732, appears in three-phase formulas because the three phase voltages are offset by 120 degrees and the resulting vector sum is larger than any single phase. In a three-phase system, V is the line-to-line voltage, not the line-to-neutral voltage.
That last point is where most on-site errors happen. A 208Y/120 system is 208 V line-to-line for the calculation, not 120 V. Using 120 V in a three-phase formula gives an answer that is 73% too high — the machine gets sized for a load it will never carry.
Three-phase and single-phase are not interchangeable
The same nameplate kVA means very different current depending on how the power is delivered.
| 100 kVA delivered as | Voltage | Current |
|---|---|---|
| Single-phase | 240 V | 416.7 A |
| Three-phase | 208 V line-to-line | 277.6 A |
Three-phase delivers the same kVA with two-thirds the current (0.666×). That is not a rounding detail — it is the whole reason three-phase exists. A 100 kVA single-phase load needs conductors, breakers and transformer bushings sized for 416.7 A, where the same capacity three-phase needs 277.6 A. When you compare two quotes, check that they quote the same phase configuration before you compare prices.
Standard service sizes, converted to kVA
Residential and light-commercial services are sold in amperes, and the transformer behind them is quoted in kVA. These are the two views of the same thing, for a 208Y/120 three-phase service:
| Service | kVA at PF 1.0 | kVA at PF 0.9 | kVA at PF 0.8 |
|---|---|---|---|
| 100 A | 36.0 kVA | 32.4 kVA | 28.8 kVA |
| 125 A | 45.0 kVA | 40.5 kVA | 36.0 kVA |
| 200 A | 72.1 kVA | 64.8 kVA | 57.6 kVA |
| 225 A | 81.1 kVA | 73.0 kVA | 64.8 kVA |
| 400 A | 144.1 kVA | 129.7 kVA | 115.3 kVA |
| 600 A | 216.2 kVA | 194.5 kVA | 172.9 kVA |
Read the middle column for the case that actually bites: a 125 A service is a 45 kVA transformer at unity power factor, but the real load behind it is unlikely to be unity. At PF 0.8 the same 125 A of service carries only 36 kVA of useful work, which is why a building full of motors can trip a breaker that looks correctly sized on the panel label.
Transformer sizes and their secondary current
Dry-type transformers are sold in a standard series. This is the current each one puts on the secondary, which is the number that matters when you are coordinating breakers and buswork:
| kVA | 208 V three-phase | 240 V single-phase |
|---|---|---|
| 15 | 41.6 A | 62.5 A |
| 30 | 83.3 A | 125.0 A |
| 45 | 124.9 A | 187.5 A |
| 75 | 208.2 A | 312.5 A |
| 100 | 277.6 A | 416.7 A |
| 125 | 347.0 A | 520.8 A |
| 167 | 463.5 A | 695.8 A |
| 200 | 555.1 A | 833.3 A |
| 250 | 693.9 A | 1041.7 A |
| 333 | 924.3 A | 1387.5 A |
The 45 kVA row is the one that makes people look twice: 124.9 A on a three-phase 208 V secondary is why 45 kVA is the standard size behind a 125 A service. The numbers line up exactly, which is why a 125 A panel is fed by 45 kVA rather than 50 kVA.
What a low power factor costs you, in watts
"Low power factor wastes money" is usually stated without a number. Here is the number. Take a 10 kW load on 480 V single-phase and hold the real power constant while the power factor falls. The current goes up, and because resistive loss in a conductor goes as the square of the current, the loss goes up faster than the current does. Over 1,000 ft of copper conductor:
| Power factor | Current at 10 kW, 480 V | I²R loss, 1,000 ft copper |
|---|---|---|
| 1.00 | 20.8 A | 133.8 W |
| 0.90 | 23.1 A | 165.2 W |
| 0.80 | 26.0 A | 209.1 W |
| 0.70 | 29.8 A | 273.1 W |
| 0.60 | 34.7 A | 371.7 W |
Dropping from PF 0.8 to PF 0.6 raises current by 33% and raises the loss in that conductor by 1.78× — for the same useful work. That heat has to be removed, and it comes out of the same efficiency you were trying to protect. Every conductor between the meter and the load is paying this penalty.
Capacitors are the standard fix because they supply reactive current locally instead of pulling it down the feeder. The kVAR needed to move a given load from PF 0.7 to PF 0.95:
| Real load | kVAR at PF 0.7 | kVAR at PF 0.95 | Capacitor to install |
|---|---|---|---|
| 50 kW | 51.0 kVAR | 16.4 kVAR | 34.6 kVAR |
| 100 kW | 102.0 kVAR | 32.9 kVAR | 69.2 kVAR |
| 200 kW | 204.0 kVAR | 65.7 kVAR | 138.3 kVAR |
A 100 kW load needs about 69 kVAR of correction. The correction is a fraction of the running load, which is why a capacitor bank pays for itself in a utility tariff with a reactive charge or a minimum power factor requirement — commonly 0.90 or 0.95 on commercial tariffs.
Sizing a generator on kVA, not kW
A generator nameplate is in kVA for the same reason a transformer is: it is the machine's thermal and current limit, not its output. The load schedule people write down, however, is in kW. Converting between them is the difference between a machine that starts and one that trips on pickup:
| Load | PF 1.0 | PF 0.9 | PF 0.8 | PF 0.7 |
|---|---|---|---|---|
| 50 kW | 50 kVA | 55.6 kVA | 62.5 kVA | 71.4 kVA |
| 80 kW | 80 kVA | 88.9 kVA | 100 kVA | 114.3 kVA |
| 100 kW | 100 kVA | 111.1 kVA | 125 kVA | 142.9 kVA |
| 200 kW | 200 kVA | 222.2 kVA | 250 kVA | 285.7 kVA |
Size the set on the right-hand columns, then add margin for motor starting. An 80 kW load at PF 0.8 needs a 100 kVA machine, and a 125 kVA set gives 25% headroom — the kind of margin that absorbs the inrush of a large motor starting while the rest of the load is already running.
Three worked examples
1. Sizing a standby generator
A facility has 80 kW of load at a power factor of 0.8. The apparent power is 80 ÷ 0.8 = 100 kVA, so a 125 kVA set gives the 25% headroom that absorbs motor starting and future load. Size the machine on kVA, not on the 80 kW figure that appears on the load schedule.
2. Checking a service in amps
A 45 kVA transformer secondary at 208 V three-phase. Current equals 45,000 ÷ (1.732 × 208) = 124.9 A, which is why 45 kVA is the common transformer size for a 125 A service.
3. A single-phase machine
A 10 kW single-phase load at 240 V and 0.9 power factor draws 10,000 ÷ (240 × 0.9) = 46.3 A. Ignoring the power factor would give 41.7 A and a circuit sized about 11% too small.
What a low power factor costs you in equipment
Beyond the heat in the conductors, a poor power factor shows up as capacity you pay for and cannot use — cables, transformers, switchgear and generators all carry the full apparent current, so every one of them is oversized for the real work, and voltage drop along the feeder rises for the same reason. Most commercial tariffs also carry a reactive power charge or a minimum power factor requirement, commonly 0.90 or 0.95, so falling below it adds a line item to the bill. Correcting it with capacitors is usually straightforward; the power factor calculator on this site sizes the correction.
How this calculator is verified
The relationships implemented here are the standard definitions of apparent, real and reactive power in single-phase and balanced three-phase systems. Results assume a sinusoidal supply and a balanced load. Non-linear loads such as variable frequency drives and switch-mode supplies need harmonic analysis, which this calculator does not perform.
- IEEE — IEEE 1459, the standard for definitions of power quantities under sinusoidal, non-sinusoidal, balanced and unbalanced conditions.
- NIST — SI definitions of the watt, volt and ampere.
- NEMA — motor and generator rating standards, including the kVA basis for machine ratings.
- NFPA — NFPA 70, the National Electrical Code, and NFPA 70E for electrical safety in the workplace, including the grounding and bonding articles that the service sizes above are built on.
- CESA — the Canadian Electricity Association, for utility and grid context on power quality and power factor.
- US Department of Energy — Office of Electricity, for the demand-side and power factor programs utilities run.
Formulas and worked examples last verified: 27 October 2026.
Instruments for reading kVA, amps and power factor
Every conversion on this page needs two of the four values, and the honest way to get them is to measure. These are the instruments for a single or three-phase supply.
- Clamp meter — The amps side of every conversion is best read, not assumed. A clamp meter reads line current in place.
- Power quality analyzer — If the power factor is unknown, the kW-to-kVA conversion is a guess. An analyzer measures it directly, along with the harmonics a simple meter misses.
- True-RMS multimeter — Voltage is the other input, and a true-RMS meter reads it correctly on the non-sinusoidal supplies the page flags.
- Phase rotation meter — On three-phase work, confirming rotation before connecting saves a motor running backwards.
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