Series and Parallel Capacitor Calculator

How it works

Capacitors in parallel share one voltage, so their charges simply add and the equivalent capacitance is the sum of the individual values. Capacitors in series carry the same charge, so their voltages add instead, and the equivalent capacitance is the reciprocal of the sum of reciprocals. A series string is always smaller than its smallest member; a parallel bank is always larger than its largest.

Because every value is entered in the same unit, the equivalent comes back in that unit too, and the charge carries the matching prefix: nanofarads times volts gives nanocoulombs, microfarads times volts gives microcoulombs.

In series, the applied voltage divides in inverse proportion to capacitance: each capacitor's voltage is the applied voltage times the equivalent capacitance divided by its own capacitance, so the smallest capacitor takes the largest share. In parallel, every capacitor sees the full applied voltage and holds its own capacitance times that voltage.

Formula

Parallel:  C = C1 + C2 + … + Cn
Series:    1/C = 1/C1 + 1/C2 + … + 1/Cn
Total charge:            Q = C × V
Series voltage on Ci:    Vi = V × C ÷ Ci     (each holds Q)
Parallel charge on Ci:   Qi = Ci × V        (each sees V)

Example

A 470 nF and a 1,000 nF (1 µF) capacitor in series across 12 V: 1/C = 1/470 + 1/1000, so C = 319.73 nF. The total charge is 319.73 × 12 = 3,836.73 nC. The 470 nF capacitor takes 12 × 319.73 ÷ 470 = 8.16 V and the 1 µF capacitor 12 × 319.73 ÷ 1000 = 3.84 V, which add back to 12 V.

The same two capacitors in parallel give 470 + 1000 = 1,470 nF (1.47 µF); each sees 12 V, holding 5,640 nC and 12,000 nC.

Assumptions and limitations

• Capacitors are ideal: no leakage, no equivalent series resistance and no tolerance. Real parts differ from their marked value by up to the tolerance given on the part or its data sheet, which shifts both the equivalent and the voltage split.
• The series voltage split is the steady-state DC split for capacitors that started uncharged. In practice leakage currents decide the long-term split across series capacitors, which is why balancing resistors are often fitted across each one.
• The applied voltage is shared across the group; the calculator does not check any capacitor's voltage rating. Operating a capacitor above its rated voltage, given in the manufacturer's data sheet, can cause it to fail.
• Results are estimates for learning and circuit sketching, not a substitute for the manufacturer's data sheet or a qualified engineer's design review.

Frequently asked questions