3-Phase Power Calculator

About the 3-Phase Power Calculator

Most homes run on single-phase power, but factories, farms, workshops, commercial buildings and data centres usually run on three-phase. A three-phase supply has three live conductors carrying alternating currents that peak one after another, a third of a cycle apart. The result is smooth, constant power that suits large motors, uses less copper for the same power and lets equipment run more efficiently. The formulas for three-phase power include a factor that often trips people up: the square root of three.

This 3-phase power calculator works in both directions. Given the line-to-line voltage, the current on each line and the power factor, it gives the real power in kilowatts, the apparent power in kVA and the reactive power in kVAR. Switch modes and it works out the current a three-phase load of known kilowatts will draw, which is what you need to size breakers, cables and generators.

How to Use the 3-Phase Power Calculator

Choose Power from current or Current from power.

Enter the line-to-line voltage, such as 208, 400 or 480 volts.

Enter the line current in amps or the real power in kW, and the power factor.

The Formulas

  kVA  = √3 × V × I ÷ 1,000
  kW   = kVA × power factor
  kVAR = √(kVA² − kW²)
  I    = kW × 1,000 ÷ (√3 × V × power factor)

√3 is about 1.732. V is the voltage between any two lines, and I is the current in each line.

Step-by-Step Examples

Power: 480 V, 50 A, power factor 0.85.

  kVA    1.732 × 480 × 50 ÷ 1,000 = 41.57 kVA
  kW     41.57 × 0.85 = 35.33 kW
  kVAR   √(41.57² − 35.33²) = 21.9 kVAR

Current: a 30 kW load at 480 V, power factor 0.85.

  I      30,000 ÷ (1.732 × 480 × 0.85) = 42.45 A per line

Where √3 Comes From

In a balanced three-phase system each phase voltage is 120° out of step with the others. The voltage measured between two lines is not twice the line-to-neutral voltage but √3 times it, because the two voltages are offset. A 480-volt system therefore has 277 volts from each line to neutral, and a 208-volt system has 120 volts to neutral. Total power is three times the power in one phase. Writing that in terms of line voltage gives 3 × (V ÷ √3) × I, which simplifies to √3 × V × I.

Real, Apparent and Reactive Power

Motors, transformers and fluorescent ballasts need magnetising current that flows back and forth without doing useful work. That makes the current larger than the real power alone would need. Real power, in kW, does the work. Reactive power, in kVAR, sustains the magnetic fields. Apparent power, in kVA, is what the wires and transformers actually carry. The ratio of real to apparent power is the power factor. Generators, transformers and UPS units are rated in kVA because their heating depends on current, not on how useful the power is.

Choosing a Power Factor

If you know the equipment's power factor, use it. Induction motors at full load usually run between 0.8 and 0.9, and much lower when lightly loaded, which is why oversized motors waste capacity. Resistive loads such as heaters and incandescent lamps have a power factor of 1. Modern variable-speed drives and switch-mode power supplies often have power factors close to 1 because of built-in correction. Utilities sometimes charge industrial customers for low power factor, and capacitor banks are installed to improve it.

Using the Current Result

The current per line is the starting point for choosing conductors and protection. Electrical codes usually require continuous loads, those running three hours or more, to be sized at 125% of their current. Motors have their own rules based on nameplate full-load current and starting current. The wire calculator and electrical code tables then turn the current into a conductor size, with voltage drop checked for long runs.

Horsepower

Motor ratings are often given in horsepower. One horsepower is 746 watts of mechanical output. The calculator shows the equivalent horsepower of the real power, but a motor's electrical input is larger than its output because motors are typically 85 to 95% efficient. To size the supply for a motor, start from its nameplate full-load amps where possible rather than its horsepower.

Single-Phase Comparison

For a single-phase load the formula has no √3: watts = volts × amps × power factor. The same power drawn from a three-phase supply needs less current per conductor, which is one of the main reasons three-phase is used for larger loads.

Unbalanced Loads

The formulas assume the three phases carry equal current. When single-phase loads are connected unevenly, the line currents differ and the neutral carries the imbalance. Measure each line and work out each phase separately in that case, adding the three phase powers together.

Understanding Your Result

The headline gives the real power in kW, or the current per line.

The power line gives kVA, kW and kVAR.

The current line gives the line current and line-to-neutral voltage.

The horsepower line converts the real power to horsepower.

When Should You Use This Calculator?

Use it to size breakers and cables for three-phase equipment.

Use it to choose a generator or transformer in kVA.

Use it to check motor loads in a workshop or plant.

Common Mistakes

Leaving out √3. Three-phase power uses 1.732.

Using line-to-neutral voltage. The formula uses line-to-line voltage.

Ignoring power factor. kW and kVA differ for motors.

Sizing generators in kW only. They are rated in kVA.