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Free calculator

Use this calculator to

  • Convert line current on a 400 V three-phase supply into kVA and kW
  • Check how much real power your agreed supply capacity can deliver at your power factor
  • Break a balanced three-phase load into kVA, kW, kVAR, phase voltage and phase angle
  • Sanity-check a connection offer: what 100 A or 400 A per phase means in kilowatts

3-Phase Power Calculator

Full power calculator for balanced three-phase AC circuits — kW, kVA, kVAR, amps.

V
A
PF
3-Phase Power

Formulas

  • Apparent power: S (kVA) = √3 × VL × IL / 1000
  • Real power: P (kW) = S × PF
  • Reactive power: Q (kVAR) = √(S² − P²)
  • Phase voltage: Vph = VL / √3
  • √3 ≈ 1.7321

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Common scenarios

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For business

Why this matters for businesses

Almost every UK commercial supply above the smallest shop is three-phase, so the maths underpinning kW, kVA and amps is the maths underpinning every capacity decision you make. A finance lead approving a new compressor, a chiller, an EV charger array or a CNC machine is, whether they realise it or not, betting that the kW load fits inside the kVA capacity of the supply and the breaker protection on the panel. Get the three-phase conversion wrong and you either trip the head of the building or pay for a connection uplift you did not need.

Power factor is the variable that catches out most non-electrical decision makers. A 100 kW load at 0.85 power factor draws 118 kVA from the supply and roughly 170 amps per phase at 400 V, but the supplier still bills the kW for energy and the kVA (or reactive kVArh) for capacity charges. That gap between nameplate kW and supply-side kVA is exactly where DUoS capacity charges and reactive-power penalties accumulate. Knowing how to translate between the three figures makes it possible to spot a bill anomaly, sanity check a quote, or justify a capacitor bank.

For Purely Energy clients, the three-phase conversion is the bridge between the engineering side of the site and the procurement side of the bill. When we review a multi-site account, the first question is almost always whether the MIC is sensibly matched to actual kW demand, and the second is whether the power factor is high enough to avoid reactive charges. Both questions need the kW, kVA and amps to be reconciled against meter data. Use this calculator to translate between them quickly, and to spot mismatches before they become a written-off capacity uplift.

Common questions

How do I calculate power in a three-phase system?

For a balanced load, apparent power is S (kVA) = 1.732 x VL x IL / 1000, using the line-to-line voltage and line current. Real power is P (kW) = S x PF, and reactive power is Q (kVAR) = the square root of (S squared minus P squared). On a UK 400 V supply drawing 100 A per line at a power factor of 0.9, that gives 69.3 kVA and 62.4 kW.

Why does the formula use 1.732?

1.732 is the square root of 3, and it comes from the geometry of three phases spaced 120 degrees apart. In a star-connected system the line-to-line voltage is root 3 times the line-to-neutral voltage, which is why a UK supply is 400 V between lines but 230 V from any line to neutral: 400 / 1.732 = 230. The same factor carries through into the three-phase power formula.

How many kW can a 100 A three-phase supply deliver?

The apparent power ceiling is 1.732 x 400 x 100 / 1000 = 69.3 kVA. The real power depends on your power factor: at 0.9 you get about 62 kW, at 0.8 only 55 kW. This is why power factor matters when a site is approaching the limit of its supply: correcting from 0.8 to 0.95 releases around 10 kW of usable capacity from the same 100 A connection without any network upgrade.

What is the difference between line-to-line and phase voltage?

Line-to-line voltage is measured between any two of the three lines, 400 V nominal in the UK. Phase voltage, or line-to-neutral, is measured from one line to neutral, 230 V nominal, and the ratio between them is the square root of 3. Three-phase equipment such as motors connects across the lines at 400 V, while single-phase circuits for sockets and lighting take one line and neutral at 230 V.

What do the kVA, kW and kVAR results each mean?

kVA is the apparent power, the total your supply must carry and the unit your agreed supply capacity is set in. kW is the real power doing useful work, and the only part you are billed energy for as kWh over time. kVAR is the reactive power magnetising motors and transformers. They relate as a right-angled triangle: kVA squared = kW squared + kVAR squared, with the power factor as kW divided by kVA.

Does this calculator work for unbalanced loads?

It assumes a balanced load, meaning the same current in all three lines, which holds well for three-phase motors and most fixed machinery. Real distribution boards mixing single-phase circuits are rarely perfectly balanced. For an unbalanced system, measure each line separately and sum the per-phase powers: P = V line-to-neutral x I x PF for each phase. A large imbalance also drives current in the neutral and is worth correcting in its own right.

Related calculators

The conversions that procurement and engineering use alongside this one.

3-Phase Power Calculator (kW, kVA, A) | Purely Energy