Convert line voltage and line current into apparent, active and reactive power for a three-phase or single-phase supply. Returns the power factor angle, phase voltage, the capacitor rating needed to reach 0.95, and the annual energy and running cost at your tariff.
| Symbol | Meaning | Unit |
|---|---|---|
| S | Apparent power — sizes cables and transformers | VA |
| P | Active power — what the meter bills | W |
| Q | Reactive power — magnetising, no useful work | VAr |
| VL | Line-to-line voltage | V |
| Vφ | Phase voltage, line to neutral | V |
| IL | Line current | A |
| cos φ | Power factor, P / S | — |
| φ | Phase angle between voltage and current | ° |
| Qc | Capacitor rating to reach the target PF | VAr |
| η | Efficiency | — |
| h | Operating hours per year | h |
A three-phase distribution board draws 100 A from a 415 V supply at 0.8 lagging power factor. The connected equipment is 92 % efficient, runs 6000 hours a year, and energy costs 8 per kWh.
| Input | Unit | Accepted range | Default |
|---|---|---|---|
| Phase system | — | Single or three phase | Three phase |
| Line voltage | V | > 0 | 415 |
| Line current | A | > 0 | 100 |
| Power factor | — | > 0 and ≤ 1 | 0.80 |
| Efficiency | % | > 0 and ≤ 100 | 92 |
| Operating hours | h/year | > 0 and ≤ 8760 | 6000 |
| Tariff | per kWh | ≥ 0 | 8 |
| Load type | Typical PF | Nature | Correction worthwhile |
|---|---|---|---|
| Resistive heating | 1.00 | Unity | No |
| Incandescent lighting | 1.00 | Unity | No |
| LED / electronic ballast | 0.90–0.95 | Often leading | Rarely |
| Induction motor, full load | 0.85–0.90 | Lagging | Marginal |
| Induction motor, half load | 0.70–0.80 | Lagging | Yes |
| Induction motor, no load | 0.10–0.30 | Lagging | Yes — avoid idling |
| Welding set | 0.50–0.70 | Lagging, intermittent | Yes |
| Arc furnace | 0.70–0.85 | Lagging, harmonic-rich | Detuned banks only |
| VFD-driven load | 0.95–0.98 | Displacement near unity | No — filter harmonics instead |
| System | Line voltage | Phase voltage | Region |
|---|---|---|---|
| Three phase LV | 400 V | 230 V | Europe, IEC standard |
| Three phase LV | 415 V | 239.6 V | India, UK legacy, Australia |
| Three phase LV | 380 V | 219.4 V | China, parts of Asia |
| Three phase LV | 480 V | 277 V | North America industrial |
| Three phase LV | 208 V | 120 V | North America commercial |
| Three phase MV | 3.3 / 6.6 / 11 kV | 1.9 / 3.8 / 6.35 kV | India, UK distribution |
| Three phase MV | 4.16 / 13.8 kV | 2.4 / 7.97 kV | North America distribution |
Apparent power in volt-amperes equals √3 multiplied by the line voltage and the line current. Active power in watts is that result multiplied by the power factor. For a 415 V supply drawing 100 A, apparent power is 71880 VA or 71.88 kVA, and at a power factor of 0.8 the active power is 57504 W. The √3 appears because line current and phase voltage in a three-phase system are separated by 30°, not because there are three phases.
kVA is the total power flowing, the product of voltage and current, and is what determines cable and transformer size. kW is the portion doing useful work, and is what the energy meter bills. kVAr is the portion that oscillates between the supply and the load's magnetic fields without doing work. The three form a right triangle where S² = P² + Q², and power factor is the ratio of active to apparent power.
The capacitor rating equals the active power multiplied by the difference between the tangent of the existing phase angle and the tangent of the target angle. This calculator targets a power factor of 0.95, which is the threshold most tariffs use. A 57.5 kW load at 0.8 power factor needs about 24.2 kVAr to reach 0.95. Correcting all the way to unity is usually avoided because it risks leading power factor at light load and resonance with system harmonics.
In a star or wye connection, the line voltage measured between any two phases is the vector difference of two phase voltages that are 120° apart, and that vector difference is √3 times the individual phase voltage. So a 415 V line-to-line system has 239.6 V between each phase and neutral. In a delta connection there is no neutral and the line voltage equals the phase voltage, while the line current becomes √3 times the phase current instead.
Most utilities set the threshold at 0.95 lagging, below which a penalty applies, and many industrial tariffs offer a rebate above it. Anything below 0.85 is usually worth correcting on cost alone, because the reactive current inflates cable losses, consumes transformer capacity and often attracts a direct charge. Above 0.98 the remaining gain is small and the risk of overcorrection at light load rises, so 0.95 to 0.98 is the usual target band.
Results are for estimation and preliminary design. Energy cost is a simple product of power and hours — real billing adds demand charges, power factor penalties and time-of-day tariffs. Verify against your tariff schedule and a qualified engineer.
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