Power Factor Calculator

In alternating current (AC) systems, power factor (PF) measures how effectively incoming electrical power is converted into useful work output. Mathematically, power factor is defined as the ratio of true power (measured in watts, W) to apparent power (measured in volt-amperes, VA), expressed as PF = P / S. Alternatively, when working with circuit impedance, the power factor equals the cosine of the phase angle ($ heta$) between voltage and current, or the ratio of resistance ($R$) to impedance ($Z$). The underlying physics rely on the power triangle, where apparent power forms the hypotenuse, while true power and reactive power form the adjacent and opposite legs respectively.

Consider an industrial AC circuit operating with a current of 10 amperes passing through a circuit component with a resistance of 15 ohms. First, calculate the true power using the formula P = I² * R. Squaring the current yields 10² = 100, and multiplying by the 15-ohm resistance gives a true power of 1,500 watts (1.5 kW). Next, assume the total circuit impedance is 20 ohms, making the apparent power S = I² * Z = 100 * 20 = 2,000 VA. Finally, divide true power by apparent power: PF = 1,500 / 2,000 = 0.75. This indicates a 75% efficiency rating for the circuit load.

When analyzing electrical systems, always ensure your units are consistent—convert kilowatts to watts and kilovolt-amperes to volt-amperes before running calculations. A low power factor indicates high reactive power waste, which can be mitigated using capacitor banks for power factor correction. Furthermore, regular monitoring of phase angles helps prevent overheating in transformers and distribution lines caused by excessive current draw.