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AC electrical-power calculator

Calculate active, reactive and apparent power for a sinusoidal single-phase or balanced three-phase consuming load; inspect RMS values and power factor.

ELECTRICAL POWER · 1.0.0

Active, reactive and apparent power

Calculate P, Q and S from RMS voltage, current and displacement power factor for sinusoidal single-phase or balanced three-phase loads.

S = kVI P = S cosφ Q = ±S √(1 − cos²φ) k = 1 or √3

Sinusoidal steady state and a consuming load. Three-phase operation is assumed fully balanced. True power factor from a distorted waveform may not be a valid input here.

Inputs and units

Use a decimal point or comma. Do not use thousands separators. Scientific notation is accepted.

0 or 10⁻⁶–10⁶ V equivalent. Three phase: line-to-line. Single phase: voltage across the load.
0 or 10⁻⁶–10⁶ A equivalent. Three phase: line current. Single phase: load current.
0 or 10⁻¹²–1. A dimensionless ratio, not a percentage. Select leading or lagging separately.

Calculation result

Calculator loading. The method and worked example remain readable without interactive controls.

This calculator processes its inputs, calculation and CSV in your browser. The calculator does not send or store them.

From formula to result

RMS is the effective value of a sinusoidal signal. For single phase, take the voltage across the load and the current through it: S(VA) = V(V) × I(A). A single load connected between two lines still uses the single-phase relationship.

For a balanced three-phase load, S(VA) = √3 × Vline-to-line(V) × Iline(A). This is total power across all three phases. Do not mix line-to-line voltage with one winding’s phase current; √3 applies to the stated line quantities.

cosφ refers to the angle between corresponding phase voltage and phase current. Entering line quantities here does not mean cosφ can be found directly from the angle between line-to-line voltage and line current. The same total-power formula using line quantities applies to a balanced star or delta load.

P = S cosφ and |Q| = S√[(1 − cosφ)(1 + cosφ)]. This second form remains numerically stable near unity power factor. Lagging current uses φ ≥ 0 and Q ≥ 0; leading uses φ ≤ 0 and Q ≤ 0. S is a magnitude and is never negative.

Convert kV to V and kA to A first. Core results are VA, W and var; divide each by 1,000 for kVA, kW and kvar. In this sinusoidal model, S² = P² + Q² and P/S = cosφ when S > 0. With harmonics, displacement power factor and true power factor need not be equal.

Worked example

An invented balanced ship auxiliary load has 440 V line-to-line RMS, 100 A line RMS, cosφ = 0.8 and lagging current. Frequency is not a separate input to this ideal sinusoidal power identity.

  1. S = √3 × 440 × 100 / 1,000 = 76.210236 kVA.
  2. P = 76.210236 × 0.8 = 60.968188 kW.
  3. sin|φ| = √(1 − 0.8²) = 0.6; Q = +76.210236 × 0.6 = +45.726141 kvar.
  4. φ = arccos(0.8) ≈ +36.869898°. With the same RMS values and cosφ but leading current, only the signs of Q and φ change.
  5. For single phase at 230 V, 10 A and cosφ = 0.8: S = 2.3 kVA, P = 1.84 kW and Q = +1.38 kvar for lagging current.
Worked example
QuantityPQS
Three phase, lagging60.968188 kW+45.726141 kvar76.210236 kVA
Three phase, leading60.968188 kW−45.726141 kvar76.210236 kVA
Single phase, lagging1.84 kW+1.38 kvar2.3 kVA

Limits of the result

  • Harmonics, phase unbalance, distorted voltage/current waveforms, inverter outputs and reverse active-power flow are excluded. Real measurements require suitable power-quality instruments and correct wiring and sign conventions.
  • P is electrical active power, not motor shaft power. Efficiency, losses, load factor, duty cycle, starting and transients are not inferred. kW is power; energy in kWh requires time as well.
  • This tool does not size conductors, breakers, fuses, protection coordination, short-circuit capacity, earthing or generators. Marine rules, equipment limits and safe electrical work require separate assessment.
  • The power-factor comparison is not an operating instruction or a compensation recommendation. A tested software relationship does not demonstrate suitability for a real installation or compliance with a standard.

Method references

Sources support the underlying relationships. Numerical examples and software bounds were chosen for this educational tool. Links checked 8 October 2026.

Read the method and its limits

Related project: ShipExact

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