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3-Phase Power Calculator

Find three-phase apparent and real power in kilowatts by entering line-to-line voltage, line current, and power factor. Formula and example included.

Result

37.41 kW

A 3-phase system at 480 V, 50 A, 0.9 PF draws about 37.41 kW

Quick Answer

A 3 phase power calculator multiplies the square root of 3 by line voltage, line current, and power factor, then divides by 1,000 to give real power in kilowatts. For a 480 V, 50 A circuit at a power factor of 0.9, P = √3 × 480 × 50 × 0.9 ÷ 1,000 = 37.4 kW.

Three-Phase Power Explained: How the Calculator Works

Three-phase electrical systems carry power on three conductors offset 120 degrees apart. Calculating power across all three phases requires accounting for the phase offset using the square root of 3 (approximately 1.7321). This calculator computes real power in kilowatts, which is the portion of apparent power that actually does work at the load. When the power factor is set to 1, the calculator effectively returns apparent power in kVA rather than real power, since the two are equal at unity power factor; the same voltage and current inputs can also be used to find reactive power separately using kVAR = √(kVA² − kW²). The power factor input accounts for the phase angle between voltage and current caused by inductive or capacitive loads.

The 3 Phase Power Formula and All Required Variables

P (kW) = √3 × V × I × PF ÷ 1,000

  • P (kW) = √3 × V × I × PF ÷ 1,000
  • Apparent power (kVA) = √3 × V × I ÷ 1,000
  • Reactive power (kVAR) = √(kVA² − kW²)

Calculate 3 Phase Power in 4 Straightforward Steps

Inputs

  • Voltage (V): measure between any two phase conductors (L1-L2, L2-L3, or L1-L3) with a true-RMS voltmeter
  • Current (A): the line current in one phase conductor measured with a clamp meter
  • Power factor: from a power quality meter, motor nameplate, or drive output specification; use 0.85 if unknown for an induction motor estimate

Steps

  1. Record line-to-line voltage from a true-RMS voltmeter across any two phase conductors.
  2. Record line current from a clamp meter on one phase conductor.
  3. Record or estimate the power factor.
  4. Enter voltage, current, and power factor and read the real power in kW.

Three-Phase Power Calculation: A Fully Worked Example

A balanced three-phase circuit operating at 480 V line-to-line, 50 A line current, and 0.90 power factor.

  1. Apply formula: P = √3 × 480 × 50 × 0.90.
  2. Resolve √3 × 480 = 831.41 V-equivalent.
  3. Multiply by current: 831.41 × 50 = 41,569 W.
  4. Apply power factor: 41,569 × 0.90 = 37,412 W.
  5. Convert to kW: 37,412 ÷ 1,000 = 37.4 kW.

The three-phase circuit delivers 37.4 kW of real power to the load.

When a 3 Phase Power Calculator Is the Correct Tool

Use this calculator when sizing transformers, generators, or distribution panels for three-phase loads; when checking whether an existing circuit can supply a new piece of equipment; or when comparing motor nameplate data to measured field values. It gives accurate results for balanced three-phase systems where voltage and current are equal across all three phases. For unbalanced loads where each phase carries a different current, calculate each phase separately and sum the results.

Assumptions

  • The system is a balanced three-phase supply; voltage and current are equal across all three phases.
  • Voltage is the line-to-line value, not phase-to-neutral; for a wye system, phase-to-neutral voltage = V ÷ √3.
  • Power factor is entered as a decimal between 0 and 1, not as a percentage.
  • Result is real power (kW); the formula gives apparent power (kVA) when PF = 1.

Limitations

  • Does not handle unbalanced three-phase systems; sum individual phase calculations for unbalanced loads.
  • Does not compute reactive power or power factor from real and apparent power; use the kVAR formula separately.
  • Does not account for harmonic distortion in the current waveform; non-linear loads require a true-power meter.
  • Does not verify voltage class or system configuration (delta vs. wye); confirm line-to-line vs. phase-to-neutral before entry.

In Practice

The most common input error on this calculator is entering phase-to-neutral voltage instead of line-to-line voltage on a wye system. On a 480 V wye, the phase-to-neutral voltage is 480 ÷ √3 = 277 V. Entering 277 instead of 480 gives a result that is 1/√3 of the correct value (roughly 57% of the true power). Always verify which voltage you are reading before entry.

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Frequently Asked Questions: 3 Phase Power Calculator

What is the formula for three-phase power?

Real power in a three-phase circuit is P = √3 × V × I × PF, where V is line-to-line voltage, I is line current, and PF is power factor. Dividing the result by 1,000 gives kilowatts. The √3 factor (1.7321) accounts for the 120-degree phase offset between the three waveforms.

What is the difference between kW, kVA, and kVAR in three-phase?

kW is real power, the energy actually consumed by the load. kVA is apparent power, which is what the source supplies including the reactive component. kVAR is reactive power, the energy that oscillates between source and load due to inductance or capacitance. They are related by kVA² = kW² + kVAR², and power factor equals kW ÷ kVA.

How do I measure three-phase power in the field?

Clamp a true-RMS clamp meter around one phase conductor to read line current. Measure voltage across any two phase conductors with a true-RMS voltmeter to get line-to-line voltage. Obtain power factor from a power quality meter, the motor nameplate, or the drive output screen. Enter all three values into the calculator.

Why does the formula use √3 and not 3?

The √3 factor comes from the vector sum of three sinusoidal voltages displaced 120 degrees apart. While there are three phases, their combination is not simply triple the single-phase power because the phase angle offsets mean the voltages and currents do not all peak simultaneously. The correct multiplier for balanced three-phase is √3, not 3.

Can I use this calculator for a delta-connected load?

Yes, but confirm the voltage and current definitions. In a delta connection, line-to-line voltage equals phase voltage, and line current equals phase current × √3. The formula P = √3 × V × I × PF uses line values in both cases, so it applies to both wye and delta systems as long as you enter line-to-line voltage and line current.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.