Series capacitance calculator
Capacitors of 10, 20 and 47 µF in series come out a little under 6 µF, always below the smallest one. Enter as many values as you need in one unit and get the total with every step of the working. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Capacitors
- 10, 20, 47
- Quantity
- 3
- Series capacitance
- 5.8385093168
- Total capacitance
- 5.8385093168
- Reciprocal sum
- 0.1712765957
A series capacitance calculator turns a list of capacitor values into the single equivalent capacitance of a series string. Enter two or more capacitances in the same unit—farads, microfarads, nanofarads, or picofarads—and the tool returns C from the reciprocal sum one over C equals one over C1 plus one over C2 plus continuing for every device on the string, plus the intermediate reciprocal sum, min and max, and step-by-step substitution you can paste into homework or design notes. Series networks always yield an equivalent smaller than the smallest individual capacitor, which is exactly what designers need when they stack ceramics or electrolytics to raise voltage rating or trim a value.
What series capacitance means and why the reciprocal sum appears
When capacitors share the same current and sit end to end, charge conservation forces the same charge magnitude on each series member while the voltages add. Capacitance is charge over voltage, so the total voltage is the sum of Qi over Ci for a common Q, which rearranges to one over C_eq equals the sum of one over each Ci.
For two equal capacitors of value C the series total is C over two; for two unequal values C1 and C2 it is the product over the sum, C1 C2 over C1 plus C2, which is identical to the reciprocal form. With three or more parts you rarely want the expanded multi-product expression by hand—the reciprocal scan stays linear in the number of devices and is numerically stable for ordinary component decades from picofarads through farads.
The series total is always strictly less than the smallest Ci when n is greater than one, which is a quick sanity check after any manual or automated run. Teachers and firmware tests also care about the zero rejection: a student or sensor feed that inserts a zero microfarad reading must not produce Infinity or NaN downstream. Near-zero floating values at or below one times ten to the minus fifteen are treated as zero and rejected the same way so noise does not invent a huge reciprocal term.
Practical tips, limits, and related searches
Keep every value in the same unit before you call: mixing microfarads with nanofarads without converting will produce a nonsense equivalent that looks numeric but is wrong by three orders of magnitude. Prefer sending numbers rather than pre-formatted engineering strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. When teaching, show that adding more series capacitors always lowers the total further, and that the total never exceeds the smallest device on the string.
This landing targets people searching for a series capacitance calculator, capacitors in series, or equivalent series capacitance online; it is not a parallel network sum, not an RC time-constant solver, and not a frequency-domain impedance tool. Prefer this capability when you already have a flat list of series members and only need C_eq; if your schematic mixes series and parallel branches, reduce each pure series chain with this tool first, then combine branches by the parallel sum rule outside.
What you can do with it
BOM and stack design for voltage rating
Designers stack series ceramics or electrolytics and need the equivalent capacitance after the voltage-sharing string is fixed.
FAQ
What happens if one capacitor value is zero?
A zero capacitance makes a reciprocal undefined and is not allowed in a series list.
Is the series total larger or smaller than each capacitor?
For two or more positive capacitors, the series equivalent is always smaller than the smallest individual value on the string.
Does this handle parallel capacitors?
No. Parallel networks sum capacitances (C = C1 + C2 + …). This page is only for series strings.
Is the series capacitance calculator free?
The browser tool is free and runs locally.
How do I work out three or more capacitors in series?
Invert each value, add the reciprocals, then invert that sum once. The calculator does this for the whole list and shows each step, so you can paste the working into homework or design notes.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/capacitors-series \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"capacitors":[10,20,47]}'const res = await fetch("https://api.kit.forhosting.com/elec/capacitors-series", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"capacitors": [
10,
20,
47
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/capacitors-series",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"capacitors": [
10,
20,
47
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/capacitors-series", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"capacitors":[10,20,47]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"capacitors":[10,20,47]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/capacitors-series", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"capacitors": [
10,
20,
47
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.capacitors_series",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_n | 100000 |
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Any zero in the list is rejected with a clear invalid_input error because a zero farad device would make a reciprocal undefined and is not a physical series member.
What series capacitance means and why the reciprocal sum appears
That is the closed formula this calculator implements: invert every positive capacitance, add those reciprocals, then invert the sum once to obtain series_capacitance in the same unit you supplied.
How to call the API and what comes back
Numeric strings inside the array are coerced; a comma or whitespace separated string is also accepted for simple text forms. Send a JSON body with one required field named capacitors: a non-empty array of strictly positive finite numbers in a single consistent unit. Aliases values, capacitances, caps, and list are accepted and behave the same. Absolute values must stay within the published limit of one trillion so intermediate reciprocals remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes count as n, capacitors as the rounded input list in order, series_capacitance and total_capacitance as the same equivalent C, reciprocal_sum as the intermediate sum of one over each Ci, min and max of the sample, formula as the string one over C equals sum of one over Ci, message as a short English summary, and steps as an ordered array of substitution lines. Failed validation—missing field, empty list, non-finite entries, zero or near-zero values, negatives, values outside absolute limits, or a list longer than one hundred thousand entries—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately type a zero.
Integration use cases
Homework checks for series networks
Students enter textbook capacitor lists and compare hand-written series totals and reciprocal sums against a deterministic browser or API result.
Firmware and unit-test expected values
Generate known-good series totals and deliberate zero rejections for embedded calculators or coding kata expected JSON.
Technical questions
How do you calculate capacitors in series?
Use 1/C_eq = 1/C1 + 1/C2 + … + 1/Cn, then invert: C_eq = 1 / sum(1/Ci). All values must share the same unit.