Capacitor Calculator (Series/Parallel)

The mathematics of series and parallel capacitor combinations follow directly from conservation of charge and Kirchhoff's voltage law, both established by the mid-1840s. In parallel, each capacitor holds its own charge Q_i = C_iV at the common voltage V, and total charge adds: C_total = ΣC_i. In series, the same charge Q flows into every capacitor (series implies same current, same charge), and voltages add: 1/C_total = Σ(1/C_i) — the reciprocal sum familiar from parallel resistors.

This inverse symmetry between resistor and capacitor combinations was one of the first "dualities" to appear in circuit theory. When Oliver Heaviside formalized the impedance concept in the 1890s, the duality became exact: replacing R with 1/(jωC) in any resistor formula gives the capacitor equivalent, which is why capacitor series/parallel math looks "backwards" compared to resistor math. The pattern generalizes — inductors (jωL) combine like resistors do; capacitors (1/jωC) combine inversely — and is the basis of every filter synthesis textbook.

Choose series or parallel, add as many capacitors as you need, pick engineering units (pF, nF, µF), and this calculator returns the equivalent capacitance plus energy stored at a reference voltage. For mixed banks (some series, some parallel), break the network into sub-blocks and combine step by step.

Practical reminder: in parallel, the lowest voltage rating limits safe operation. In series, real caps rarely share voltage equally because leakage currents differ — use balancing resistors or matched caps where voltage is close to the rating. Everything runs client-side; no values leave your browser.