3-Phase Amps to kW Calculator and Formula

Use this 3-phase amps-to-kW calculator to estimate real electrical power from line current, line voltage, and power factor. Enter current in amperes, voltage in volts, and power factor from 0 to 1; the calculator returns kilowatts, plus the corresponding apparent power in kVA.

Formula

For a balanced three-phase system, real power is kW = √3 × V × I × PF ÷ 1,000. Here, V is line-to-line voltage in volts, I is line current in amperes, and PF is power factor, a dimensionless value between 0 and 1 for the usual lagging or leading loads. The factor √3 (about 1.732) comes from the relationship between phase and line quantities in a balanced three-phase system. Dividing watts by 1,000 expresses the result in kilowatts.

The related apparent-power equation is kVA = √3 × V × I ÷ 1,000. Apparent power does not include power factor; real power does. This calculator assumes the voltage entered is line-to-line voltage, as commonly specified for a three-phase supply, and that current is the line current.

Worked Example

Using the calculator defaults—10 A, 400 V, and power factor 0.8:

1. Multiply voltage by current: 400 × 10 = 4,000.
2. Apply the three-phase factor and power factor: √3 × 4,000 × 0.8 ≈ 5,542.56 W.
3. Convert watts to kilowatts: 5,542.56 ÷ 1,000 ≈ 5.54 kW.
4. For apparent power, omit power factor: √3 × 400 × 10 ÷ 1,000 ≈ 6.93 kVA.

The real-power result is the estimated rate of useful electrical energy transfer under the stated assumptions. The kVA result describes apparent power, which combines real and reactive power.

How the Three-Phase Calculation Works

In a balanced three-phase system, three alternating voltages and currents are spaced evenly in phase. Their combined power is not calculated by simply multiplying voltage by current and then by three when the inputs are line voltage and line current. The appropriate line-value expression includes √3, giving P = √3 × V_L × I_L × PF.

There is another valid way to calculate power using phase voltage and phase current: P = 3 × V_phase × I_phase × PF. These are different sets of quantities. Mixing phase voltage with line current, or line-to-neutral voltage with a formula expecting line-to-line voltage, can produce a wrong answer.

When to Use the Calculator

Use it when you know the current, nominal line-to-line voltage, and power factor and want a quick estimate of three-phase real power. It can help with basic load comparisons, interpreting equipment data, or checking an arithmetic calculation. It is not a substitute for a meter reading or a detailed electrical assessment.

• Current: Enter amperes (A), not milliamperes. For example, 10 A is entered as 10.
• Voltage: Enter line-to-line volts. A system described as 400 V three-phase normally means 400 V between phases.
• Power factor: Use a known value from relevant equipment data or measurement. A value of 1 means the idealized real and apparent powers are equal; lower values mean real power is less than apparent power at the same voltage and current.

If power factor is unknown, the calculator cannot determine real kW from current and voltage alone. It can still calculate kVA, but treating kVA as kW implicitly assumes a power factor of 1 and may overstate real power.

Reading kW, kVA, and Power Factor

Kilowatts measure real power, the component associated with net energy transfer to a load. Kilovolt-amperes measure apparent power, based on voltage and current without accounting for their phase relationship. Power factor is the ratio of real power to apparent power for the applicable system, so kW = kVA × PF.

For example, 10 kVA at a power factor of 0.8 corresponds to 8 kW. This is why amperes and voltage alone do not establish real power for many AC loads. Motors and other inductive equipment can draw current that contributes to apparent power without contributing the same amount to real power.

Assumptions and Common Mistakes

The calculation is an estimate based on balanced three-phase operation and the values entered. Real systems may have changing loads, voltage variation, harmonic distortion, or phase imbalance. A single current and power-factor value may not describe every moment or operating condition. For an actual measurement, use suitable instruments and interpret their readings in the context of the system.

• Using the wrong voltage: Check whether a stated voltage is line-to-line or line-to-neutral. This calculator expects line-to-line voltage.
• Omitting power factor: Doing so yields kVA, not real kW, unless PF is 1.
• Using single-phase arithmetic: For a balanced three-phase system with line values, include √3; do not use the single-phase V × I × PF formula by itself.
• Rounding too early: Keep the power factor and intermediate result at reasonable precision, then round the final kW or kVA to suit the purpose.
• Assuming every load is balanced: For substantially unbalanced loads, calculate each phase appropriately or use a measurement method designed for that system.

The result is power, not energy. To find energy use over time, multiply power in kW by operating time in hours; for example, 5 kW used for 2 hours represents 10 kWh, assuming the power remains constant.

Frequently Asked Questions

How do I convert 3-phase amps to kW?
For balanced three-phase line values, calculate kW = 1.732 × volts × amps × power factor ÷ 1,000. Use line-to-line voltage and line current.

What power factor should I enter?
Enter the power factor that applies to the load and operating condition, ideally from reliable equipment information or measurement. Do not assume it is 0.8 for every load; if it is unknown, kW cannot be determined precisely from current and voltage alone.

Is 3-phase kVA the same as kW?
No. kVA is apparent power and kW is real power. They are equal only when the power factor is 1; otherwise, kW = kVA × power factor.

Can I use phase-to-neutral voltage?
Not directly in this calculator, which expects line-to-line voltage. A calculation using phase voltage requires the corresponding phase current and the formula 3 × phase voltage × phase current × power factor.

Does this formula work for an unbalanced load?
The simple √3 formula assumes a balanced three-phase system. For an unbalanced load, use phase-specific measurements and calculations or an appropriate power analyzer.

Does the answer tell me what size wire or breaker to use?
No. This is a power conversion, not a design or safety-sizing calculation. Equipment selection depends on system conditions, applicable requirements, and other factors; consult a qualified electrical professional.

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in amps | Current | A | 10 | 0
in volts | Line voltage | V | 400 | 0
in pf | Power factor | - | 0.8 | 0 | 1
out kw | Real power | kW | sqrt(3) * volts * amps * pf / 1000 | 2
out kva | Apparent power | kVA | sqrt(3) * volts * amps / 1000 | 2