Power-Factor Correction Capacitance

C = \frac{Q_{c}}{2\pi f V^{2}}

C =

Q_c =

f =

V =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

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A capacitor's vars are Q = V²/X_C, and since X_C = 1/(2πfC), that rearranges to Q = 2πfCV² — solve it for C and you have your capacitor. Getting 5 kvar at 240 V and 60 Hz takes 5000/(2π × 60 × 240²) ≈ 230 µF, a physically large oil-filled can, which is why correction capacitors are bulky and why higher voltages are so much cheaper per var. The var field here uses watts: vars and watts share dimensions.

The V² is the sting. A capacitor bank rated 25 kvar at 480 V delivers only 25 × (240/480)² ≈ 6.25 kvar if someone installs it on a 240 V system — a mistake that shows up as a stubbornly unimproved power factor. Frequency matters the same way, so a bank imported from a 50 Hz country loses a fifth of its vars at 60 Hz... and gains 20% the other way, along with the overcurrent that comes with it.

Power-Factor Correction Capacitance

C = \frac{Q_{c}}{2\pi f V^{2}}

Where

$C$ = Capacitance
$Q_{c}$ = Reactive power wanted (var)
$f$ = Supply frequency
$V$ = Voltage across the capacitor

Missing one of these? Work it out first, then come back

Capacitance — Q Factor of a Series Resonant Circuit, RC Time Constant
Reactive power wanted (var) — Reactive Power (Power Triangle), Power-Factor Correction kvar
Supply frequency — Synchronous Speed from Frequency and Poles, 555 Astable Frequency
Voltage across the capacitor — Three-Phase Real Power, Single-Phase Real Power with Power Factor

Part of this formula set

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.