Three-Phase Power Calculator Widget

Add a three-phase power calculator to your website. Engineers and students enter the line voltage, line current and power factor to get kW, kVA and kVAR, or work back from a motor's kW or a transformer's kVA to the line current.

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<iframe src="https://a2z.tools/embed/w/three-phase-power-calculator" title="Three-Phase Power Calculator by A2Z Tools" width="100%" height="730" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>

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How it works

The widget uses the three-phase engine behind the A2Z Three-Phase Power Calculator. It applies the root-three rule for a balanced load: apparent power is sqrt(3) x line voltage x line current, and real power is that times the power factor, as in the balanced-sinusoidal definitions of IEEE Std 1459. It also shows the star phase voltage (line voltage / sqrt(3)) and the power carried by each phase. Three modes cover the common questions: power from volts and amps, line current from a kW rating and power factor, and line current from a kVA rating, which is how transformer and generator outputs are quoted. Unbalanced systems need a phase-by-phase calculation and the widget says so.

Calculation method

  • S = sqrt(3) x VL x IL (VA), with VL the line-to-line voltage and IL the line current
  • P = sqrt(3) x VL x IL x PF (W); Q = sqrt(S^2 - P^2) (var)
  • IL = P / (sqrt(3) x VL x PF) or IL = S / (sqrt(3) x VL)
  • Star phase voltage = VL / sqrt(3); power per phase = P / 3 (balanced load); results to 2-3 decimals in kW, kVA, kVAR and A

Worked examples

415 V motor feeder

Inputs: 415 V line, 50 A, PF 0.85

Result: 30.549 kW, 35.94 kVA, 18.933 kVAR; phase voltage 239.6 V; 10.183 kW per phase

1.7321 x 415 x 50 = 35,940 VA; x 0.85 = 30,549 W.

Transformer full-load current

Inputs: 100 kVA at 400 V

Result: 144.34 A per line

100,000 / (1.7321 x 400) = 144.34 A.

Limitations

  • Balanced, sinusoidal loads only; neutral current, unbalance and harmonics are not modelled.
  • Does not include motor efficiency: a motor's kW rating is shaft output, so the electrical input and current are higher than a kW-to-amps figure computed from the rating alone.

Where publishers use it

  • Motor and pump suppliers showing full-load current for a given kW rating
  • Transformer and generator sizing articles converting kVA to amps
  • Electrical engineering lecture notes and exam revision sites
  • Factory maintenance intranets for quick checks at the panel

Questions

Which voltage do I enter?

The line-to-line voltage, for example 400 V or 415 V in IEC countries and 208 V or 480 V in North America. The phase (line-to-neutral) voltage is shown in the result.

Why is there a square root of 3?

In a balanced three-phase system the line voltage is sqrt(3) times the phase voltage, so the total power of the three phases works out to sqrt(3) x VL x IL x PF.

How much current does a 100 kVA transformer supply at 400 V?

100,000 / (1.732 x 400) = 144.3 A per line, which the widget shows when you choose Current from kVA.

Does it work for unbalanced loads?

No. It assumes the three phases carry equal current; unbalanced loads must be worked out phase by phase.

Does it matter whether the load is wired in star or delta?

Not for the totals: sqrt(3) x VL x IL x PF holds for a balanced star (wye) or delta load. What differs is inside the load - in delta each winding carries IL / sqrt(3) at the full line voltage, in star each carries IL at the phase voltage.

Sources

  1. IEEE 1459-2010 Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions - IEEE . Three-phase apparent, active and reactive power for balanced systems

Cite or recommend this tool

If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.

A2Z Tools Three-Phase Power Calculator
https://a2z.tools/three-phase-power-calculator

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