Calculate AC power: real watts, reactive VAR, and apparent VA from voltage, current, and power factor. Single and 3-phase with cost estimation.
In AC circuits, power is not simply voltage times current. The phase difference between voltage and current waveforms — caused by inductors, capacitors, and nonlinear loads — means that the "apparent" power drawn from the source is always greater than the "real" power doing useful work.
The power factor (cos φ) quantifies this relationship. A power factor of 1.0 means voltage and current are perfectly in phase — all power does useful work. A power factor of 0.8 means only 80% of the apparent power is real. The remaining "reactive" power oscillates between the source and load without doing work, but still heats up wires and transformers.
This calculator computes all three components of the AC power triangle: real power (watts), reactive power (VAR), and apparent power (VA). It supports both single-phase and three-phase systems, estimates energy costs, and calculates the capacitor size needed for power factor correction. Check the example with realistic values before reporting.
Understanding the full AC power picture — real, reactive, and apparent — is essential for electrical design, energy management, and utility cost optimization. Simply multiplying voltage by current gives apparent power, not the actual watts consumed, which can lead to oversized generators, incorrect UPS sizing, and surprising electricity bills.
This calculator breaks down all three power components, visualizes the power triangle, and estimates the cost impact. It also calculates power factor correction, helping engineers and facility managers reduce losses and avoid utility penalties.
P = V × I × cos(φ) for single-phase; P = √3 × V × I × cos(φ) for 3-phase. S = V × I (or √3 × V × I). Q = √(S² − P²). Phase angle φ = arccos(PF).
Result: 1020 W real, 1200 VA apparent
At 120V, 10A, and PF 0.85: apparent power = 1200 VA, real power = 1020 W, reactive power = 633 VAR. Phase angle is 31.8°.
The power triangle is a right triangle where the hypotenuse represents apparent power (S in VA), the adjacent side represents real power (P in watts), and the opposite side represents reactive power (Q in VAR). The angle between S and P is the phase angle φ, and cos(φ) is the power factor.
This geometric relationship means S² = P² + Q², just like the Pythagorean theorem. Real power performs useful work (heating, turning motors, computing). Reactive power supports the magnetic and electric fields needed by inductive and capacitive loads but does no net work over a full cycle.
A typical industrial facility might have a power factor of 0.75-0.85 due to induction motors, transformers, and old lighting. This means the utility must supply 18-33% more apparent power than the facility actually uses. Utilities respond by imposing power factor penalties — typically a surcharge when PF drops below 0.90 or 0.95.
Power factor correction capacitors counteract the inductive reactive power, reducing the apparent power and current drawn from the grid. This reduces line losses, frees up transformer capacity, and eliminates utility penalties. The recommended correction is usually to PF 0.95 — over-correction can create resonance problems.
Single-phase power uses two conductors (hot and neutral) carrying one alternating current. Three-phase power uses three conductors carrying currents offset by 120°. The √3 factor in the 3-phase formula arises from the vector sum of these three currents. Three-phase systems are more efficient for delivering large amounts of power because they use less conductor material for the same power level.
Watts (W) measure real power — the actual energy consumed. VA (volt-amperes) measures apparent power — the total power the source must supply. They differ by the power factor: W = VA × PF.
Low power factor means you draw more current than necessary for the same real power, increasing wire losses, transformer loading, and often utility bills. Many utilities penalize commercial customers for PF below 0.90-0.95.
Check the nameplate or data sheet. Common values: resistive heaters 1.0, computers with PFC 0.95-0.99, induction motors 0.75-0.90, older fluorescent lights 0.50-0.70.
Reactive power (VAR) represents energy that oscillates between the source and magnetic/electric fields in inductors and capacitors. It does no useful work but requires infrastructure to deliver.
Add capacitors in parallel with inductive loads. The calculator shows the VAR rating needed to bring PF from its current value up to 0.95.
Residential meters typically measure only real power (kWh), so PF does not directly affect the bill. Commercial and industrial customers may face demand charges or PF penalties based on apparent power or power factor.