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Three-Phase Power Calculator

Three-phase distribution delivers steadier power over less copper than single phase. The catch is keeping line and phase quantities apart — they differ by √3, and which one differs depends on whether the load is star or delta connected.

Three-Phase Power — P = √3·V_L·I_L·cos φ

Balanced three-phase load from line quantities — the formula is the same for star and delta; only the phase values differ.

Real power P
Reactive power Q
Apparent power S
Phase voltage V_ph
Phase current I_ph
  1. 1.Given (star): V_L = 400 V, I_L = 10 A, cos φ = 0.8
  2. 2.FormulaStar: V_ph = V_L ÷ √3, I_ph = I_LSubstituteV_ph = 400 ÷ 1.732ResultV_ph = 230.9401 V, I_ph = 10 A
  3. 3.FormulaS = √3 × V_L × I_LSubstituteS = 1.732 × 400 × 10ResultS = 6.9282 kVA
  4. 4.FormulaP = S × cos φSubstituteP = 6928.2032 × 0.8ResultP = 5.5426 kW
  5. 5.FormulaQ = √(S² − P²)SubstituteQ = √(6928.2032² − 5542.5626²)ResultQ = 4.1569 kVAR
Common trap: √3 appears once, not twice. P = √3·V_L·I_L·cos φ already accounts for all three phases — multiplying by 3 as well is the classic exam mistake. (Per phase it's P = 3·V_ph·I_ph·cos φ — the two forms are equal.)

The formula

S = √3 × V_L × I_L ; P = S × cos φ ; Star: V_ph = V_L/√3, I_ph = I_L ; Delta: V_ph = V_L, I_ph = I_L/√3

V_L, I_L
line voltage and line current (volts, amperes)
V_ph, I_ph
voltage across and current through one phase of the load
S, P, Q
apparent, real and reactive power
cos φ
power factor of the load

Worked example

A star-connected load on a 415 V line drawing 10 A at 0.85 power factor.

  1. S = √3 × 415 × 10 = 1.732 × 4150 = 7188 VA
  2. P = 7188 × 0.85 = 6110 W
  3. Q = √(7188² − 6110²) = 3786 VAr
  4. Star connection: V_ph = 415 / √3 = 239.6 V, I_ph = I_L = 10 A

7.19 kVA total, delivering 6.11 kW with 3.79 kVAr reactive; each phase sees 239.6 V.

Where you'll use it

Industrial load calculations, motor ratings and distribution design. The 415 V / 240 V pair in the example is the standard Indian LT supply — 415 V between lines, 240 V from any line to neutral.

The laws behind it

Parts this applies to

Resistor (fixed)Capacitor (aluminium electrolytic)Capacitor (tantalum)LED (light-emitting diode)MOSFETRectifier DiodeSchottky DiodeZener Diode

Related calculators

Power Triangle CalculatorS² = P² + Q²Power Factor Correction CalculatorQ_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf)Synchronous Speed and Slip CalculatorN_s = 120f / PTransformer Turns Ratio CalculatorN_p / N_s = V_p / V_s = I_s / I_p