\[P=\sqrt{3}\,V_L I_L \cos(\phi)\]
Variables
Pthree-phase real power (W)
VLline-to-line voltage (V)
ILline current (A)
PFpower factor
Description
What is this formula?
The three-phase power equation calculates the real power delivered by a balanced three-phase AC electrical system using line voltage, line current, and power factor.
When to use it
Use this formula when analyzing industrial electrical systems, motors, generators, transformers, power distribution networks, and large commercial electrical installations operating with balanced three-phase loads.
Example
A factory motor operates at:
Line voltage = 480 V
Line current = 120 A
Power factor = 0.85
Formula:
P = √3 × VL × IL × PF
Substitution:
P = 1.732 × 480 × 120 × 0.85
Result:
P = 84,822 W
P ≈ 84.8 kW
Applications
Industrial motor systems
Electrical power distribution
Generator sizing
Energy audits
Transformer loading analysis
Three-phase equipment design