Three-Phase Power Calculator Formula

Understand the math behind the three-phase power calculator. Each variable explained with a worked example.

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Formulas Used

Real Power

real_kw = real_power / 1000

Apparent Power

apparent_kva = apparent_power / 1000

Reactive Power

reactive_kvar = sqrt(pow(apparent_power, 2) - pow(real_power, 2)) / 1000

Phase Voltage

v_phase = v_line / sqrt(3)

Variables

VariableDescriptionDefault
v_lineLine-to-Line Voltage(V)480
i_lineLine Current(A)20
power_factorPower Factor0.85
apparent_powerDerived value= sqrt(3) * v_line * i_linecalculated
real_powerDerived value= sqrt(3) * v_line * i_line * power_factorcalculated

How It Works

Three-Phase Power Calculations

Three-phase systems are the standard for industrial and commercial power distribution.

Formulas (Balanced Load)

Apparent Power = sqrt(3) x V_line x I_line

Real Power = Apparent x Power Factor

Reactive Power = sqrt(Apparent^2 - Real^2)

Phase Voltage = Line Voltage / sqrt(3)

The sqrt(3) factor (approximately 1.732) arises from the 120-degree phase separation between the three phases.

Worked Example

480 V three-phase, 20 A line current, 0.85 power factor.

v_line = 480i_line = 20power_factor = 0.85
  1. 01Apparent: sqrt(3) x 480 x 20 = 16,627 VA = 16.63 kVA
  2. 02Real: 16,627 x 0.85 = 14,133 W = 14.13 kW
  3. 03Reactive: sqrt(16627^2 - 14133^2) = 8,744 VAR = 8.74 kVAR
  4. 04Phase voltage: 480 / 1.732 = 277.1 V

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