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Capacitors in Series and Parallel Calculator

Computes the total capacitance of a list of capacitors connected all in parallel (sum) and all in series (reciprocal of the sum of reciprocals), and optionally the energy stored at a given voltage.

When to use

You have two or more capacitor values and need the equivalent capacitance for a parallel or a series connection.

Do not use when: The network mixes series and parallel groups (reduce it group by group), the components are resistors (use resistors-series-parallel), or you need charging time (use rc-time-constant).

Formula

parallel_total_uf = C1 + C2 + …; 1 / series_total_uf = 1/C1 + 1/C2 + …; energy_j = ½ × C_farad × voltage_v²

Capacitors combine the opposite way to resistors: parallel adds plate area (capacitances add), series adds plate separation (reciprocals add). In series each capacitor carries the same charge, so the smallest one sees the largest share of the voltage.

Inputs

Parameter	Type	Unit	Required	Description
`capacitances_uf`	number_list	µF	yes	Capacitor values in microfarads, comma-separated (1 nF = 0.001 µF, 1 pF = 1e-6 µF). All values must be positive.
`voltage_v`	number	V	no	Optional voltage across the combination; enables the stored-energy outputs (E = ½ C V²). Range: ≥ 0

Outputs

Output	Type	Unit	Description
`capacitor_count`	integer		How many values were combined.
`parallel_total_uf`	number	µF	C1 + C2 + … (always larger than the largest capacitor).
`series_total_uf`	number	µF	1 / (1/C1 + 1/C2 + …) (always smaller than the smallest capacitor).
`parallel_total_nf`	number	nF	Parallel total in nanofarads.
`series_total_nf`	number	nF	Series total in nanofarads.
`energy_parallel_j`	number	J	½ × parallel_total × V² (only when voltage_v is given).
`energy_series_j`	number	J	½ × series_total × V² (only when voltage_v is given).

Example

10, 22 and 47 µF at 12 V: {"capacitances_uf":[10,22,47],"voltage_v":12} → {"capacitor_count":3,"parallel_total_uf":79,"series_total_uf":5.99768,"parallel_total_nf":79000,"energy_parallel_j":0.005688,"energy_series_j":0.000432}

Two 100 nF capacitors: {"capacitances_uf":[0.1,0.1]} → {"capacitor_count":2,"parallel_total_uf":0.2,"series_total_uf":0.05,"series_total_nf":50}

GET https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel?capacitances_uf=10%2C22%2C47&voltage_v=12

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/capacitors-series-parallel · Markdown: https://tttkmbb.com/engineering/capacitors-series-parallel.md · JSON definition: https://tttkmbb.com/engineering/capacitors-series-parallel.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="capacitors-series-parallel"
OpenAPI operationId: calculate_capacitors_series_parallel
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Series and parallel circuits – capacitors (reference)
HyperPhysics – Capacitance (reference)

FAQ

Why put capacitors in series at all?

To raise the voltage rating (the applied voltage divides across them) or to obtain a small, non-standard value. Balancing resistors are usually needed so the voltage shares equally.

Do the units matter?

Any unit works as long as all values use it; the calculator assumes microfarads and also reports nanofarads. Energy needs farads, which is handled internally.

Related calculators

Resistors in Series and Parallel Calculator — The mirror-image rules for resistors.
RC Time Constant Calculator — Charging time of the resulting capacitance through a resistor.
LC Resonance Calculator — Resonant frequency with an inductor.