Three-Phase Power Calculator
Calculate real, apparent, and reactive power for a balanced three-phase electrical system.
Real Power (P)
29.44 kW
Real Power (P) vs Line-to-Line Voltage (V_LL)
Formula
## 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.
Exemplo Resolvido
A 400 V three-phase supply with 50 A line current at 0.85 power factor.
- 01S = sqrt(3) x 400 x 50 = 34,641 VA = 34.64 kVA
- 02P = 34,641 x 0.85 = 29,445 W = 29.44 kW
- 03Q = 34,641 x sin(acos(0.85)) = 34,641 x 0.5268 = 18.25 kVAR
Perguntas Frequentes
What is the difference between line and phase voltage?
In a three-phase system, line-to-line voltage (V_LL) = sqrt(3) x phase voltage (V_LN). For a 400V system, phase voltage is 400/sqrt(3) = 231V. Wye-connected loads see phase voltage; delta loads see line voltage.
Why is power factor important?
Low power factor means the system draws more current than necessary for the real power delivered. This increases cable size requirements, transformer loading, and utility bills (many utilities penalise power factor below 0.9).
How do I convert between single-phase and three-phase?
Three-phase power = sqrt(3) x V_LL x I x PF. Single-phase power = V x I x PF. Three-phase delivers 73% more power than single-phase at the same voltage and current because of the sqrt(3) factor.
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