Calculation 3 Phase Power

Calculate real power (kW), apparent power (kVA), and reactive power (kVAR) for three-phase AC electrical systems. Enter the line-to-line voltage, current, and power factor below.

Standard default is 0.85 for inductive loads.

Calculation Results

Real Power (P)

0 kW

Apparent Power (S)

0 kVA

Reactive Power (Q)

0 kVAR

function calculateThreePhasePower() { var v = parseFloat(document.getElementById('voltage').value); var i = parseFloat(document.getElementById('current').value); var pf = parseFloat(document.getElementById('powerFactor').value); if (isNaN(v) || isNaN(i) || isNaN(pf) || v <= 0 || i <= 0) { alert('Please enter valid positive numbers for Voltage and Current.'); return; } if (pf 1) { alert('Power Factor must be between 0 and 1.'); return; } var sqrt3 = Math.sqrt(3); // S = sqrt(3) * V * I (Apparent Power in VA) var s_va = sqrt3 * v * i; var s_kva = s_va / 1000; // P = sqrt(3) * V * I * PF (Real Power in Watts) var p_w = s_va * pf; var p_kw = p_w / 1000; // Q = sqrt(S^2 – P^2) (Reactive Power in VAR) // Or Q = sqrt(3) * V * I * sin(acos(pf)) var q_var = Math.sqrt(Math.pow(s_va, 2) – Math.pow(p_w, 2)); var q_kvar = q_var / 1000; document.getElementById('realPower').innerText = p_kw.toFixed(2) + ' kW'; document.getElementById('apparentPower').innerText = s_kva.toFixed(2) + ' kVA'; document.getElementById('reactivePower').innerText = q_kvar.toFixed(2) + ' kVAR'; document.getElementById('resultsArea').style.display = 'block'; }

How to Calculate 3-Phase Power

Calculating electrical power in a three-phase AC system is more complex than single-phase because it involves a phase shift and a square root multiplier of 3. Whether you are sizing a generator, a motor, or balancing an industrial load, understanding these formulas is critical.

The 3-Phase Power Formulas

There are three primary types of power calculated in 3-phase systems:

• Real Power (P): Measured in Watts (W) or Kilowatts (kW). This is the power that actually does work.
  Formula: P = √3 × V × I × PF
• Apparent Power (S): Measured in Volt-Amps (VA) or Kilovolt-Amps (kVA). This is the total power delivered to the circuit.
  Formula: S = √3 × V × I
• Reactive Power (Q): Measured in VAR or kVAR. This is "borrowed" power used to create magnetic fields in inductive loads (like motors).
  Formula: Q = √3 × V × I × sin(Φ)

Example Calculation

Imagine an industrial motor operating on a 480V 3-phase line with a measured current of 50 Amps and a Power Factor of 0.80.

1. Apparent Power: 1.732 × 480V × 50A = 41,568 VA (or 41.57 kVA).
2. Real Power: 41,568 VA × 0.80 = 33,254 W (or 33.25 kW).

Why Power Factor (PF) Matters

The Power Factor represents the efficiency of the electrical system. A PF of 1.0 (unity) means all electricity is being converted into work. A lower PF (like 0.70) means a large portion of the current is used for the reactive component (magnetizing), requiring thicker wires and larger transformers for the same amount of useful work.