Intermediate
AC Power Formulas
AC power triangle formulas — real power (kW), reactive power (kVAR), apparent power (kVA), and power factor relationships.
Formulas
P = V × I × cos(φ)
Real (active) power — single-phase
S = V × I
Apparent power — single-phase
Q = V × I × sin(φ)
Reactive power — single-phase
S = √(P² + Q²)
Power triangle relationship
PF = P / S = cos(φ)
Power factor
Variable Definitions
P=Real power(watts (W) or kilowatts (kW))
S=Apparent power(volt-amperes (VA) or kVA)
Q=Reactive power(volt-amperes reactive (VAR) or kVAR)
V=Voltage(volts (V))
I=Current(amperes (A))
φ=Phase angle(degrees (°))
PF=Power factor(dimensionless (0 to 1))
Worked Example
A 240V motor draws 15A at 0.85 power factor. Find P, S, and Q.
- S = V × I = 240 × 15 = 3,600 VA (3.6 kVA)
- P = S × PF = 3,600 × 0.85 = 3,060W (3.06 kW)
- Q = √(S² − P²) = √(3600² − 3060²) = 1,897 VAR (1.9 kVAR)
Answer: P = 3.06 kW, S = 3.6 kVA, Q = 1.9 kVAR
When to Use
- •Calculating actual power consumption of motors and inductive loads
- •Sizing transformers and generators (using kVA, not kW)
- •Power factor correction capacitor sizing
- •Understanding utility demand charges (billed in kW or kVA)
Standards & References
- NEC 220 — uses VA (apparent power) for load calculations
- NEC 430 — motor calculations use power factor for current determination