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 (P)

real_power = sqrt(3) * voltage_ll * current * pf / 1000

Apparent Power (S)

apparent_power = sqrt(3) * voltage_ll * current / 1000

Reactive Power (Q)

reactive_power = sqrt(3) * voltage_ll * current * sqrt(1 - pow(pf, 2)) / 1000

Variables

VariableDescriptionDefault
voltage_llLine-to-Line Voltage (V_LL)(V)400
currentLine Current (I)(A)50
pfPower Factor (cos phi)0.85

How It Works

Three-Phase Power Calculations

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

Formulas

P = sqrt(3) x V_LL x I x cos(phi) (real power in watts)

S = sqrt(3) x V_LL x I (apparent power in VA)

Q = sqrt(3) x V_LL x I x sin(phi) (reactive power in VAR)

where V_LL is the line-to-line voltage, I is the line current, and cos(phi) is the power factor. These apply to balanced loads.

Worked Example

A 400 V three-phase supply with 50 A line current at 0.85 power factor.

voltage_ll = 400current = 50pf = 0.85
  1. 01S = sqrt(3) x 400 x 50 = 34,641 VA = 34.64 kVA
  2. 02P = 34,641 x 0.85 = 29,445 W = 29.44 kW
  3. 03Q = 34,641 x sin(acos(0.85)) = 34,641 x 0.5268 = 18.25 kVAR

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