# 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.

- Calculator id: `capacitors-series-parallel` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_capacitors_series_parallel`
- Canonical page: https://tttkmbb.com/engineering/capacitors-series-parallel · This document: https://tttkmbb.com/engineering/capacitors-series-parallel.md · JSON definition: https://tttkmbb.com/engineering/capacitors-series-parallel.json

## Purpose

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.

**Use when:** 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).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `capacitances_uf` | number_list | µF | required | 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 | optional | Optional voltage across the combination; enables the stored-energy outputs (E = ½ C V²). (min 0) |

## Output

| Field | 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). |

## 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.

## Data Sources

- Wikipedia – Series and parallel circuits – capacitors — https://en.wikipedia.org/wiki/Series_and_parallel_circuits#Capacitors (reference, retrieved 2026-09-24)
- HyperPhysics – Capacitance — http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capac.html (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel?capacitances_uf=…`
- `POST https://tttkmbb.com/api/v1/calculate/capacitors-series-parallel` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/capacitors-series-parallel · OpenAPI operationId `calculate_capacitors_series_parallel` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "capacitors-series-parallel", "inputs": {…}}`

## Example

- 10, 22 and 47 µF at 12 V: inputs `{"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: inputs `{"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
```

## Limitations

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). 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. All values are computed from the formula above; no measurement or live data is involved.

## 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

- [Resistors in Series and Parallel Calculator](https://tttkmbb.com/physics/resistors-series-parallel.md) — The mirror-image rules for resistors.
- [RC Time Constant Calculator](https://tttkmbb.com/engineering/rc-time-constant.md) — Charging time of the resulting capacitance through a resistor.
- [LC Resonance Calculator](https://tttkmbb.com/engineering/lc-resonance.md) — Resonant frequency with an inductor.