3 Phase Power Calculation: Formula and Examples

Calculate three-phase real power from line voltage, line current, and power factor using this calculator. Enter voltage in volts, current in amperes, and power factor as a decimal from 0 to 1; it returns power in kilowatts, along with apparent power and the equivalent single-phase formula result for comparison.

Formula

For a balanced three-phase system using line-to-line voltage and line current, real power is:

P = √3 × V_L × I_L × PF

• P is real power in watts (W). Divide by 1,000 for kilowatts (kW).
• V_L is line-to-line voltage in volts (V), measured between two phase conductors.
• I_L is line current in amperes (A).
• PF is power factor, a dimensionless value between 0 and 1 for ordinary loads.

The calculator uses kW for its headline result, so it divides the watt result by 1,000. Apparent power is S = √3 × V_L × I_L, expressed in volt-amperes (VA) or kilovolt-amperes (kVA). The single-phase comparison is V × I × PF; it is not the three-phase total.

Worked Example

Using the calculator defaults—400 V line-to-line, 10 A line current, and power factor 0.8:

1. Calculate the voltage-current product: 400 × 10 = 4,000 VA before the three-phase factor and power factor.
2. Apply the three-phase factor: √3 × 4,000 ≈ 6,928.20 VA.
3. Apply the power factor: 6,928.20 × 0.8 ≈ 5,542.56 W.
4. Convert to kilowatts: 5,542.56 ÷ 1,000 = 5.54 kW (rounded to two decimal places).

The corresponding apparent power is √3 × 400 × 10 ÷ 1,000 = 6.93 kVA. The comparison value from V × I × PF is 400 × 10 × 0.8 ÷ 1,000 = 3.20 kW; it represents the single-phase expression, not the total three-phase load.

Why Three-Phase Power Uses √3

Three-phase systems have three alternating voltages, separated in phase by 120 degrees. In a balanced system, each phase contributes power, and the relationship between line measurements and phase measurements introduces the √3 factor. This gives a convenient total-power calculation using the voltage measured between lines and the current in a line.

The expression assumes a balanced load: the three phases carry equal currents and have matching power-factor characteristics. It is common in calculations for motors, distribution equipment, and other three-phase loads. If the phases are significantly unbalanced, a single line voltage and current may not describe the total accurately; calculate each phase’s real power and add the results, or use appropriate measurements and equipment.

Line Values, Phase Values, and Connections

Do not confuse line voltage and current with phase voltage and current. Line values are measured at the supply conductors; phase values refer to one winding or load branch. In a star (wye) connection, line voltage is √3 times phase voltage, while line current equals phase current. In a delta connection, line voltage equals phase voltage, while line current is √3 times phase current. Those relationships explain why the balanced total-power equation can use line voltage and line current for either connection.

If you instead use phase voltage and phase current, the total for a balanced system is P = 3 × V_phase × I_phase × PF. Use one consistent set of values: do not multiply line voltage and line current by 3, or add another √3 to the line-value formula.

When to Use the Result and Its Limits

Use the real-power result to estimate the rate at which a balanced load converts electrical energy into useful work, heat, or other forms of energy. One kilowatt sustained for one hour corresponds to one kilowatt-hour of energy. The calculator’s kVA result is useful for distinguishing apparent power from real power; the power factor relates them as P = S × PF.

For direct current or a purely resistive load, power factor is effectively 1, so real power and apparent power have the same numerical value in compatible units. Motors and other alternating-current loads can have a power factor below 1. If the power factor is unknown, you can calculate apparent power but cannot determine real power accurately from voltage and current alone.

• Use the system’s actual line-to-line voltage and line current, not a nominal value if a more accurate measurement is needed.
• Enter power factor as a decimal: 0.8 means 80%, not 80.
• Use RMS AC voltage and current values for standard power calculations.
• For distorted waveforms or unbalanced loads, a simple power-factor figure and balanced formula may be inadequate; use a suitable power analyzer or phase-by-phase method.

The calculation returns electrical power, not energy use over time, motor shaft output, or required equipment capacity. Motor efficiency affects how much electrical input is needed for a specified mechanical output. For design or troubleshooting, account for the equipment rating, operating conditions, starting current, and applicable electrical requirements; a calculator is not a substitute for qualified assessment.

Common Calculation Mistakes

The most frequent error is leaving out √3 when using line-to-line voltage and line current. Another is using the single-phase equation V × I × PF as though it were the total three-phase power. Also check whether a voltage is line-to-line or line-to-neutral: a stated phase-to-neutral value cannot be substituted as line voltage without converting it appropriately.

Keep units consistent. This calculator expects volts and amperes; entering kilovolts or milliamperes without conversion changes the answer by a factor of 1,000. Finally, round only at the end. Displayed results are rounded to two decimal places, so small differences from hand calculations using fewer digits are normal.

Frequently Asked Questions

What is the formula for three-phase power?
For a balanced three-phase system using line-to-line voltage and line current, real power is P = √3 × V_L × I_L × power factor. The result is in watts when volts and amperes are used.

How do I calculate three-phase power in kW?
Multiply √3 by line voltage in volts, line current in amperes, and power factor, then divide by 1,000. For 400 V, 10 A, and PF 0.8, the result is about 5.54 kW.

Can I calculate three-phase power without power factor?
You can calculate apparent power in kVA with S = √3 × V_L × I_L. To calculate real power in kW, you need the power factor or a direct real-power measurement.

Is three-phase power √3 times voltage times current?
That expression gives apparent power in VA when voltage is line-to-line and current is line current. Multiply by power factor to get real power in W.

Does the same formula work for star and delta systems?
Yes, for a balanced system when you use line-to-line voltage and line current. If using phase values instead, use P = 3 × phase voltage × phase current × power factor.

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in v | Line voltage | V | 400 | 0
in i | Line current | A | 10 | 0
in pf | Power factor | - | 0.8 | 0
out p | Real power | kW | sqrt(3) * v * i * pf / 1000 | 2
out s | Apparent power | kVA | sqrt(3) * v * i / 1000 | 2
out single | V × I × PF comparison | kW | v * i * pf / 1000 | 2