Power Factor & Power Triangle Calculator
AC power has three flavors: real power P (watts, the energy actually consumed), reactive power Q (volt-amperes reactive, the energy sloshing back and forth in inductors and capacitors), and apparent power S (volt-amperes, the total the source must deliver). They form a right triangle — the power triangle — with S² = P² + Q², P = S·cos φ, Q = S·sin φ, and power factor PF = P/S = cos φ. A resistive load has PF = 1 (P = S, no reactive part); an inductive motor has PF < 1 with current lagging (positive Q); a capacitive load leads (negative Q). Enter voltage, current, and PF to get P, Q, and S — single-phase S = V·I, three-phase S = √3·V·I — or solve the power triangle from any two of P/Q/S, and work out the capacitive vars needed to correct a poor power factor. Everything runs locally in your browser.
From voltage, current & power factor
Power triangle solver (any two of P, Q, S)
Power-factor correction
The math. In a sinusoidal AC circuit, if the current lags the voltage by angle φ, the instantaneous power averages to P = V·I·cos φ watts — the real power that does useful work. The product S = V·I is the apparent power (VA), what the wiring and transformer must carry, and the difference Q = V·I·sin φ is the reactive power (var) exchanged with the magnetic/electric fields — it does no net work but still occupies capacity. The three sit on a right triangle: S² = P² + Q², PF = P/S = cos φ. For three-phase, replace V·I with √3·VL·IL (line-line voltage and line current). An inductive load (motors, transformers) has current lagging → positive Q and PF < 1; a capacitive load leads → negative Q. Low power factor means the source must supply extra current for the same real power, so utilities penalize it; power-factor correction adds capacitors that supply the reactive vars locally, raising PF from cos φ₁ toward cos φ₂. The required capacitive reactive power is Qc = P·(tan φ₁ − tan φ₂) where φ = arccos(PF) — the capacitor bank's var rating. Pairs with the Reactance & Impedance, Voltage Drop, Ohm's Law, and AC True RMS tools. Everything runs locally — nothing leaves your browser.