Three-Phase Power Calculator

Three-Phase Power Calculator

Calculate Power (kW), Current (Amps), or Voltage for balanced 3-phase systems.

Enter any 3 values to calculate the 4th.
i The system voltage. Select Line-to-Line or Line-to-Neutral on the right.
i The current flowing in each phase line.
i The ratio of Real Power to Apparent Power (0 to 1).
cosφ
i The actual power consumed by the load (kW).
Derived Results
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3 Phase Power Calculator by VersaCalculator

How to Use This Calculator

This tool uses the relationship between four primary electrical variables: Power (P), Voltage (V), Current (I), and Power Factor (PF).

  1. Select Voltage Type: Choose whether your voltage reading is Line-to-Line (VLL) or Line-to-Neutral (VLN). Most industrial equipment specs use Line-to-Line.
  2. Input Known Values: Enter the three parameters you have measured or know from the nameplate.

The Formulas: Line-to-Line vs. Line-to-Neutral

The most common source of error in three-phase calculations is applying the wrong formula for the voltage type. The math changes depending on how you measure voltage relative to the neutral wire.

1. Line-to-Line (VLL)

This is the standard measurement between any two live phases (e.g., 480V or 208V in many US industrial systems). Because the phases are 120 degrees apart, we use the square root of 3 (√3 ≈ 1.732) as a multiplier.

Real Power (kW):
P =
√3 × V × I × PF 1000
Current (Amps):
I =
1000 × P √3 × V × PF

2. Line-to-Neutral (VLN)

This measures the potential between a single phase and the neutral point. Here, the multiplier is simply 3, representing the three distinct phases.

Real Power (kW):
P =
3 × V × I × PF 1000
Current (Amps):
I =
1000 × P 3 × V × PF

Power Triangle

In alternating current (AC) systems, “power” isn’t a single number. It is composed of three distinct parts that form a right-angled triangle.

Real Power (P) – kW

Measured in Kilowatts (kW) or Watts (W).

This is the “working” power that actually performs the task turning the motor shaft, heating the element, or lighting the bulb. It is the portion of electricity that is converted into useful work.

Reactive Power (Q) – kVAR

Measured in Kilovolt-Amperes Reactive (kV-AR).

This power doesn’t do useful work but is necessary to maintain the magnetic and electric fields in inductive loads like motors and transformers. Think of it as the “pressure” required to keep the magnetic field sustained so the motor can spin.

Apparent Power (S) – kVA

Measured in Kilovolt-Amperes (kV-A).

This is the total power being drawn from the supply. It is the vector sum of Real and Reactive power. Transformers and generators are usually rated in kVA because they must handle the total current, regardless of how much of it is used for real work vs. magnetic fields.

What is Power Factor?

Power Factor (PF) is a measure of efficiency, represented as a decimal between 0 and 1 (or a percentage). It is the ratio of Real Power (kW) to Apparent Power (k-VA).

  • 1.0 (Unity): 100% efficiency. All power drawn is being used for work. This typically only happens with purely resistive loads like electric heaters.
  • 0.8 to 0.95: Common for industrial motors.
  • Low PF (< 0.8): Indicates wasted energy. You are drawing more current than you need to do the work, often resulting in utility surcharges.

Why Use Three-Phase Power?

You will rarely see single-phase power used for heavy industrial machinery (typically anything over 5HP or 3.7kW). Three-phase systems offer distinct engineering advantages:

  1. Constant Power Transfer: In single-phase AC, power drops to zero 120 times per second (at 60Hz). In three-phase, the power waves overlap, providing a continuous, smooth delivery of energy. This reduces vibrations and stress on motors.
  2. Efficiency: Three-phase systems can transmit the same amount of power using less conductor material (copper or aluminum) than an equivalent single-phase system.
  3. Self-Starting Motors: Three-phase induction motors create a rotating magnetic field naturally, meaning they don’t require startup capacitors or centrifugal switches, making them more reliable and easier to maintain.

FAQs

Q1. Why does the calculator assume a balanced load?

A: This tool calculates based on a “balanced” system, where the current is identical in all three phases. In perfectly optimized industrial systems, loads are balanced. If you have significant imbalances (different currents on each leg), you should calculate each phase individually as a single-phase load and sum them up.

Q2. How do I convert kW to Amps for a 3-phase motor?

A: To find the full-load current (FLA), you need the voltage and the power factor.

Formula: Amps = (kW x 1000) / (Volts x 1.732 x PF).

If you don’t know the Power Factor, 0.8 is a standard estimation for estimation purposes.

Q3. What is the difference between kVA and kW?

A: kW is the power you use (and pay for). kVA is the power the infrastructure must deliver. If your Power Factor is low, your kVA will be much higher than your kW, meaning you need larger wires and transformers to do the same amount of work.

Sources: JCalc, DigiKey, RapidTables, MyElectrical, Blackhawk Supply, eMotors Direct, Omni Calculator, NEPSI, CalcTool, Generator Source.