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Single and Three-Phase AC Real Power, Voltage, Current and Factor

Relate RMS voltage, line current, real electrical power and power factor, with single-phase and balanced three-phase voltage conventions.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Single-phase 100 V RMS, 2 A RMS and power factor 0.5 give 100 W real power. Balanced three-phase with the same line-to-neutral voltage and line current gives 300 W.

Single-phase: P = VI PF; balanced three-phase: P = √3 VLL I PF = 3 VLN I PF.

Worked example

Enter these known values and leave the other values blank.

RMS voltage V
100 V
RMS line current I
2 A
Power factor PF
0.5
Single-phase real power P
100 W

Assumptions and limitations

  • Use RMS voltage and current magnitudes. Power is real electrical consumed power in W, not apparent power in VA or motor shaft output. Power factor is real power divided by apparent power.
  • Three-phase formulas assume a balanced sinusoidal supply. Select line-to-line or line-to-neutral voltage explicitly; the result represents total three-phase real power and current is current in each line.
  • Nonnegative voltage, current and power are permitted, with 0 ≤ PF ≤ 1. Zero power factor with known voltage and current gives zero real power. Zero power with zero current or zero PF cannot uniquely determine missing voltage/current; that inverse stays blank.
  • The initial PF=0.95 is an illustrative default. Replace it with your known value, or unlock and clear it before solving PF from known nonzero voltage and current. Clear another unknown before entering an inverse.
  • This finite magnitude model does not supply phase direction, generation sign, reactive power, harmonic or imbalance analysis, starting current, motor efficiency, conductor/protection sizing or equipment ratings.

Common questions

Is this apparent power or motor output?

It is real electrical power. Apparent power omits the power-factor multiplier, while shaft output also depends on motor efficiency.

Why can zero power leave an inverse blank?

A zero product has no unique missing factor when another factor is already zero. Known voltage/current with PF=0 gives zero power, but zero power and PF=0 do not identify current.

Which three-phase voltage should I enter?

Use the selected RMS convention: line-to-line for √3 VLL I PF or line-to-neutral for 3 VLN I PF. The line current refers to each line.

References

RMS voltage, current and real consumed power are nonnegative magnitudes. Positive real power requires positive voltage, current and power factor. Zero power factor remains valid for forward zero-real-power calculations; a zero product does not identify a missing factor. Nine source-pinned voltage, current and power-factor inverses are skipped when their known denominator factors are zero. Forward zero-power results remain valid, and indeterminate zero-product inverses leave the unknown blank.

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