# What is the kVA?

Works out apparent power in kVA from volts and amps for single-phase or three-phase circuits, or the current from kVA and volts, with real power in kW from the power factor.

- Page: https://www.acalculator.org/physics/kva-calculator
- JSON spec: https://www.acalculator.org/physics/kva-calculator.json
- Version: 54d0b1aa1d04

## Default answer

Example with the default inputs (Supply Single-phase, Find kVA, Voltage 240 V, Current 50 A, Power factor 0.8): 240 V at 50 A is 12 kVA (9.6 kW at the power factor given).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| ph | Supply | Single-phase, or balanced three-phase with the line-to-line voltage. |
| find | Find | Work out kVA from volts and amps, or amps from kVA and volts. |
| v | Voltage | The RMS voltage; for three-phase, the line-to-line voltage. |
| i | Current | The RMS current in each line. |
| kva | Apparent power (kVA) | The apparent power in kilovolt-amperes, such as a transformer or generator rating. |
| pf | Power factor | The share of the apparent power that does work, from 0 to 1: 1 for heaters, about 0.8 to 0.95 for motors. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| kva | Apparent power (kVA) | Volts × amps (× √3 for three-phase) ÷ 1,000. |
| amps | Current (A) | The current in each line, in amperes. |
| kw | Real power (kW) | kVA × power factor: the power that does work. |
| kvar | Reactive power (kVAR) | kVA × √(1 − power factor²). |
| va | Apparent power (VA) | The apparent power in volt-amperes. |

## Method

Single-phase: kVA = V × I ÷ 1,000, I = kVA × 1,000 ÷ V. Three-phase: kVA = √3 × V × I ÷ 1,000, I = kVA × 1,000 ÷ (√3 × V). kW = kVA × pf; kVAR = kVA × √(1 − pf²).

## Assumptions

- RMS values on a sinusoidal supply; for three-phase, a balanced load with the line-to-line voltage and the line current.
- The power factor only changes kW and kVAR; kVA and amps do not depend on it.

## Worked examples

1. ph = single, find = kva, v = 240, i = 50, pf = 0.8 gives kva = 12, kw = 9.6, kvar = 7.2, va = 12,000. Source: OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit (average power = I_rms V_rms cos φ; power factor cos φ), https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05).
2. ph = three, find = kva, v = 480, i = 100, pf = 1 gives kva = 83.138439, kw = 83.138439, kvar = 0. Source: Wikipedia, "Three-phase electric power" (balanced load: apparent power = √3 × line voltage × line current), https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05).
3. ph = three, find = amps, v = 208, kva = 75, pf = 0.9 gives i = 208.179184, kw = 67.5. Source: Wikipedia, "Three-phase electric power" (balanced load: apparent power = √3 × line voltage × line current), https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05).
4. ph = single, find = amps, v = 120, kva = 1.8, pf = 1 gives i = 15. Source: OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit (average power = I_rms V_rms cos φ; power factor cos φ), https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05).

## FAQ

### How do I calculate kVA?

For single-phase, multiply volts by amps and divide by 1,000: 240 V × 50 A = 12,000 VA = 12 kVA. For balanced three-phase, multiply by √3 (about 1.732) as well, using the line-to-line voltage: √3 × 480 V × 100 A ÷ 1,000 = 83.1 kVA.

### How do I convert kVA to amps?

Single-phase: amps = kVA × 1,000 ÷ volts, so 1.8 kVA at 120 V is 15 A. Three-phase: amps = kVA × 1,000 ÷ (√3 × volts), so a 75 kVA load at 208 V draws about 208.2 A per line.

### What is the difference between kVA and kW?

kVA is apparent power: volts times amps. kW is real power, the part that does work, and equals kVA × power factor. A motor drawing 12 kVA at a power factor of 0.8 uses 9.6 kW. For a heater, with a power factor of 1, the two are the same.

### What is kVAR?

Reactive power, in kilovolt-amperes reactive. It flows back and forth between the supply and coils or capacitors and does no work. kW, kVAR and kVA form a right triangle: kVA² = kW² + kVAR².

### Why are transformers and generators rated in kVA?

Their heating depends on the current, and the current depends on kVA, not on the power factor of the load. A kVA rating holds for any load; the kW they can deliver depends on the power factor of what is connected.

### Which voltage do I use for three-phase?

The line-to-line voltage, such as 208 V, 400 V or 480 V, and the current in one line. The √3 in the formula assumes a balanced load, with the same current in each line.

## Sources

- OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit: average power = I_rms V_rms cos φ, and the power factor cos φ. https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05)
- Wikipedia, "Three-phase electric power": for a balanced load, power = √3 × line voltage × line current. https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05)