Three figures describe one three-phase load: kVA, kW and kvar. A clamp meter reads only amps. One relation converts between them, and it holds in both directions.
The question
A board feeds a load drawing 50 A per phase at 400 V. The power factor is 0.9. The task is to state that load in kVA, in kW and in kvar. The same relation runs the other way, from a known kVA figure to the current it draws at 400 V.
The inputs
- Phases: 3
- Line voltage: 400 V
- Line current: 50 A
- Power factor: 0.9
The voltage is the line to line figure, not the 230 V phase to neutral figure. Mixing the two is the most common error in this calculation. The current is the current in one line, the figure a clamp meter gives on a single conductor.
The clause
Cl 2.2.2 of AS/NZS 3000:2018 covers maximum demand. It is the clause that consumes this result. A demand figure in amps becomes a kVA figure for the network application. The relation below is how it gets there.
The steps
The tool works in three moves.
- Apparent power: 34.64 kVA. It multiplies 400 V by 50 A by the square root of three, then divides by 1000.
- Real power: 31.18 kW. It multiplies the apparent power by the power factor of 0.9.
- Reactive power: 15.1 kvar. It takes the component at right angles to the real power.
The square root of three carries all the three-phase content. It appears because the tool starts from the line voltage while the power flows in three phase to neutral paths.
The result
50 A at 400 V and 0.9 power factor is 34.64 kVA, 31.18 kW and 15.1 kvar. The tool reports no warnings.
Read the same line backwards to go from kVA to amps. Divide 34.64 kVA by 400 V and by the square root of three and the 50 A comes back. A 34.64 kVA supply application and a 50 A per phase demand describe the same load.
Three habits keep the result honest.
Name the power you mean. A generator plate is kVA. A motor plate is usually output kW. A heater plate is kW drawn. The three are not interchangeable, and the power factor is what separates the first two.
Watch the power factor. At 0.9 the 34.64 kVA supplies 31.18 kW. Drop the power factor and the kilowatts fall while the amps stay the same. The cable, the device and the network connection all size on the amps.
Use the reactive figure. The 15.1 kvar is the quantity a correction study works on. Capacitors reduce it, which reduces the apparent power and the current. The real power does not change.
The relation assumes a balanced load. Three phases carrying different currents need a per-phase calculation and a neutral current check. The tool treats the current you enter as the current in every phase.
This page is a design aid. Verify every value against the current edition of the standard.
See also: Motor full load current: 11 kW 400 V DOL, 22 kW EV charger amps at 400 V three-phase and Current-carrying capacity and derating.