Calculate real power (W), reactive power (VAR), apparent power (VA) and power factor for any AC circuit. Choose your known values below.
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Power Triangle
AC Power Formulas
The three types of AC power are related by the power triangle (S² = P² + Q²):
Key Formulas
Apparent Power
S = V × I (VA)
Real Power
P = V × I × cos(φ) (W)
Reactive Power
Q = V × I × sin(φ) (VAR)
Power Factor
PF = cos(φ) = P / S
Power Triangle
S² = P² + Q²
Phase Angle
φ = arccos(PF)
Worked Examples
1Electric motor (PF 0.85)
V = 230 V, I = 5 A
S = 230 × 51150 VA
P = 1150 × 0.85977.5 W
Q = 1150 × sin(31.8°)≈ 605 VAR
2Resistive heater (PF 1.0)
V = 230 V, I = 8.7 A
S = 230 × 8.72001 VA
P = 2001 × 1.02001 W
Q = 0 VAR (pure resistive)
3From P & Q
P = 1000 W, Q = 500 VAR
S = √(1000²+500²)1118 VA
PF = 1000/11180.894
φ = arccos(0.894)26.6°
4UPS sizing (S & PF)
S = 2000 VA, PF = 0.8
P = 2000 × 0.81600 W
Q = 2000 × sin(36.9°)1200 VAR
φ = arccos(0.8)36.9°
Frequently Asked Questions
What is the difference between real, reactive and apparent power? ▾
Real power (P, watts) does useful work. Reactive power (Q, VAR) is stored and returned by inductors and capacitors — it doesn't do useful work but increases the current drawn. Apparent power (S, VA) = V × I is the total power the source must supply. They relate as S² = P² + Q².
What is power factor and why does it matter? ▾
Power factor PF = P/S = cos(φ). A PF of 1 means all supplied power does useful work. A low PF (e.g. 0.7) means high reactive power, causing larger currents, higher cable losses and larger supply infrastructure. Most utilities penalise commercial customers with PF below 0.9.
What is the difference between VA and Watts? ▾
Watts (W) is real power consumed. VA is apparent power — what the supply must deliver. For resistive loads (heaters, incandescent bulbs) W = VA. For inductive loads (motors, transformers) VA > W because of reactive power.
How can I improve power factor? ▾
Add power factor correction capacitors in parallel with inductive loads. The capacitors supply the reactive power locally, reducing the reactive current from the supply. This lowers apparent power and improves efficiency.