Two capacitor series calculator
10 and 20 in series give about 6.6667 in the same unit: the product, 200, divided by the sum, 30. Enter two capacitor values and get the equivalent with each step shown, always below the smaller of the two. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- C1
- 10
- C2
- 20
- Product
- 200
- Sum
- 30
- Equivalent capacitance
- 6.6666666667
- Series capacitance
- 6.6666666667
When exactly two capacitors share the same series branch, every textbook reduces the network to one equivalent value with the product-over-sum formula: multiply the two capacitances and divide by their sum. Bench technicians use that identity constantly—pairing a stocked 10 µF with a 22 µF, checking a ceramic pair on a timing rail, or verifying a coupling network before soldering—because it is faster than writing out the reciprocal sum and less error-prone than a multi-value list when only two parts are on the table.
What two capacitors in series mean and why product-over-sum works
Two capacitors in series sit on the same current path so they store the same charge magnitude while their voltages add. Charge Q equals C times V for each device, so V1 equals Q over C1 and V2 equals Q over C2; the total voltage is Q times (1/C1 plus 1/C2). Defining an equivalent capacitance Ceq by V_total equals Q over Ceq immediately yields 1/Ceq equals 1/C1 plus 1/C2.
Clearing the common denominator for exactly two terms produces the product-over-sum form that every secondary-school and first-year engineering course teaches: Ceq equals (C1 times C2) divided by (C1 plus C2). That algebraic rewrite is not a different physics story—it is the reciprocal identity specialized to two positive values—but it is the form students and techs type into a calculator when only two numbers are known.
The series equivalent is always strictly smaller than the smaller of the two capacitances when both are positive, which is a quick sanity check on the bench: if your computed Ceq is larger than min(C1, C2), a sign or unit error slipped in. Equal capacitors collapse further to half the single value, so two identical 100 nF parts in series behave like 50 nF. Units cancel: microfarads in give microfarads out, provided both inputs use the same scale.
This capability implements only the two-value product-over-sum contract with named fields c1 and c2; if you need an arbitrary-length series list, use a multi-capacitor series tool instead of stretching this focused landing.
Where a two-capacitor series calculator earns its keep
Electronics labs and maker benches constantly pair two stocked values when a single catalog part is unavailable or when a higher voltage rating is needed by stacking capacitors in series with balancing resistors. Exam-prep generators and LMS plugins need a fixed two-field contract so item templates map directly onto c1 and c2 without parsing comma lists of variable length.
Curriculum authors ranking for two capacitor series calculator or product over sum capacitance benefit from a dedicated landing whose free browser path matches the paid automation path on the same pure module. Content sites that already host a general n-value series capacitance tool still win a distinct long-tail query when learners type the textbook phrase for exactly two capacitors and expect the product-over-sum formula rather than a reciprocal-sum array.
What you can do with it
Bench pairing of two stocked capacitors
Enter two catalog values in µF or nF and get the series equivalent from product-over-sum before soldering a timing or coupling network.
BOM and LMS automation
Mark two-capacitor series items or generate drop-in equivalents with a deterministic oracle that rejects zero and negatives instead of returning NaN.
FAQ
How do I compute two capacitors in series?
Send strictly positive finite c1 and c2 in the same unit.
Why is the series equivalent smaller than each capacitor?
For positive values that always yields Ceq < min(C1, C2).
What units should I use for c1 and c2?
Any consistent unit—farads, microfarads, nanofarads, or picofarads. Units cancel; the equivalent uses the same scale as the inputs.
What if c1 or c2 is zero or negative?
Product-over-sum requires two strictly positive finite capacitances; zero and negative values are not billed.
Why put two capacitors in series at all?
To reach a value you don't have in stock, or to get a higher voltage rating by stacking two parts, usually with balancing resistors. In exchange, the total capacitance falls below the smaller of the two.
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/two-capacitors-series \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"c1":10,"c2":20}'const res = await fetch("https://api.kit.forhosting.com/elec/two-capacitors-series", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"c1": 10,
"c2": 20
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/two-capacitors-series",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"c1": 10,
"c2": 20
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/two-capacitors-series", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"c1":10,"c2":20}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"c1":10,"c2":20}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/two-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
{
"c1": 10,
"c2": 20
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.two_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.
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
This two capacitor series calculator accepts two strictly positive finite values in any consistent unit, returns the cleaned equivalent capacitance together with product, sum, and step strings, and rejects zero or negative inputs with invalid_input instead of a silent NaN.
Input contract, response shape, and validation rules
Zero is rejected because a shorted or non-physical capacitor would make the reciprocal path undefined and the product-over-sum form divide by a sum that no longer represents two real series parts. Wire the free browser form for quick bench checks, then call the identical contract from scripts when you generate BOM checks or lab answer keys. POST a JSON object with two required fields named c1 and c2 (aliases capacitance1/capacitance2, cap1/cap2, and c_1/c_2 are also accepted). Each must be a finite number strictly greater than zero; JSON numbers and plain numeric strings are both allowed. Missing fields, empty strings, non-numeric tokens, NaN, Infinity, zero, and any negative value fail with invalid_input and are not billed. On success the response echoes cleaned c1 and c2, the intermediate product and sum, equivalent_capacitance (also mirrored as series_capacitance for clients that expect that name), the smaller of the two inputs as min, the formula string Ceq = (C1 · C2) / (C1 + C2), a short message, and a steps array that walks product, sum, and division for display. Successful API calls cost the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where a two-capacitor series calculator earns its keep
A deterministic product-over-sum oracle returns cleaned JSON without pulling a full circuit simulator for a two-node question. Field service scripts that read two measured ceramic or film values from a BOM and must emit the series equivalent for a drop-in replacement also prefer a tiny parse endpoint over a multi-part netlist. Keep c1 and c2 positive and finite in the same unit, pin the rounded equivalent_capacitance in tests, and you get reproducible series totals for homework, LMS plugins, and edge workers without standing up SPICE infrastructure of your own.
Integration use cases
Lab homework and product-over-sum drills
Let students submit c1 and c2 and verify that (C1·C2)/(C1+C2) matches the textbook series pair, including equal-value and decade fixtures.
Technical questions
What does the two capacitor series calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.