Last updated: 2026-06-16

Power Factor Correction

Inductive loads such as motors and transformers draw reactive power that flows back and forth without doing useful work, dragging the power factor below 1. Adding a capacitor in parallel supplies that reactive power locally, raising the power factor and cutting the current the supply has to carry. This calculator sizes the shunt capacitor for a single-phase line-to-neutral connection, given the real power, voltage, frequency, and the power factors before and after correction.

Formula

The reactive power the capacitor must supply is

and the capacitance that delivers it is

where each phase angle comes from its power factor, $\varphi = \arccos(\text{PF})$.

Worked example

A 10 kW single-phase load runs at 230 V, 50 Hz with a power factor of 0.7, and we want to raise it to 0.95.

The phase angles are $\varphi_1 = \arccos(0.7) \approx 45.6^\circ$ and $\varphi_2 = \arccos(0.95) \approx 18.2^\circ$. Substituting into the formula:

Why it matters

A low power factor forces the supply to carry reactive current that heats cables and loads transformers without delivering useful power, which is why many utilities apply a power factor penalty to industrial bills. Installing a correction capacitor reduces the current drawn for the same real power, freeing up capacity in the distribution system and often lowering the electricity bill. Note that this single-shunt formula assumes a single-phase line-to-neutral connection; three-phase systems and harmonic-rich loads need additional analysis.