Not all electrical power does useful work. Motors, transformers, and fluorescent lamps produce reactive power — energy that oscillates back and forth without performing any work. This is what separates active power (energy actually used) from apparent power (total power drawn). Our calculator computes all quantities including the power factor cos φ.
Step by Step: How to Use the Electrical Power Calculator
- Select the system type: Single-phase (230 V, household appliances) or three-phase (400 V, motors, industrial equipment).
- Enter the known values: Voltage (V), current (A), and power factor cos φ (0–1).
- Active power (P): P = U × I × cos φ (single-phase). P = √3 × U × I × cos φ (three-phase).
- Apparent power (S): S = U × I (single-phase). S = √3 × U × I (three-phase).
- Reactive power (Q): Q = √(S² - P²) or Q = U × I × sin φ.
Practical Examples
Electric motor 3 kW, 400 V three-phase, cos φ = 0.85: Apparent power S = 3000/0.85 = 3,529 VA. Current I = S / (√3 × 400) = 5.1 A. Reactive power Q = √(3529²−3000²) = 1,859 VAr.
Household appliance 230 V, 8 A, cos φ = 0.95: Active power P = 230 × 8 × 0.95 = 1,748 W. Apparent power S = 230 × 8 = 1,840 VA. Reactive power Q = 575 VAr.
Capacitor compensation: The motor above requires 1,859 VAr of reactive power. A compensation capacitor offsets this → power factor improves to 0.99. Industrial benefit: grid operators otherwise charge a reactive power surcharge.
Power Formulas
- Active power: P = U × I × cos φ (W)
- Apparent power: S = U × I (VA)
- Reactive power: Q = √(S²−P²) (VAr)
- Three-phase: multiply by √3 = 1.732
- cos φ = P/S (power factor)
Frequently Asked Questions
What does cos φ = 1 mean?
When cos φ = 1, apparent power equals active power — there is no reactive component. This applies to purely resistive loads (incandescent bulbs, heaters). Motors and transformers typically have cos φ = 0.7–0.9.
Why do industrial customers pay for reactive power?
Reactive power burdens the grid (cables and transformers must be sized larger) without delivering any useful output. Grid operators charge reactive power fees above a certain threshold. Compensation systems (capacitor banks) improve the power factor and reduce this cost.
What is the difference between a single-phase and three-phase supply?
Single-phase (230 V): used for household appliances, lighting, and small motors. Three-phase / three-wire (400 V): used for larger motors, industrial equipment, and EV charging (22 kW AC). Three-phase power formulas always include the factor √3 (≈ 1.732).
