Three-Phase Power Calculator Formula
Understand the math behind the three-phase power calculator. Each variable explained with a worked example.
Formulas Used
Real Power (P)
real_power = sqrt(3) * voltage_ll * current * pf / 1000Apparent Power (S)
apparent_power = sqrt(3) * voltage_ll * current / 1000Reactive Power (Q)
reactive_power = sqrt(3) * voltage_ll * current * sqrt(1 - pow(pf, 2)) / 1000Variables
| Variable | Description | Default |
|---|---|---|
voltage_ll | Line-to-Line Voltage (V_LL)(V) | 400 |
current | Line Current (I)(A) | 50 |
pf | Power 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.
- 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
Frequently Asked Questions
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.
Learn More
Guide
Understanding Electrical Circuits: Fundamentals for Engineers
Learn the fundamentals of electrical circuits including Ohm's law, Kirchhoff's laws, series and parallel circuits, AC vs DC, power calculations, and three-phase systems.
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Open Three-Phase Power Calculator