Parallel-plate capacitor calculator
Two plates of 0.01 m² (100 cm²) 1 mm apart in air make 88.542 pF. Enter the overlap area, the gap and the dielectric constant to get the ideal parallel-plate capacitance in farads, a textbook baseline for homework and layout checks. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Area
- 0.01
- Plate separation
- 0.001
- Relative permittivity
- 1
- Capacitance
- 0.0000000001
- Epsilon 0
- 0
An ideal parallel-plate capacitor stores charge on two conductive plates of overlapping area A separated by a gap d filled with a dielectric of relative permittivity kappa. The textbook formula C equals epsilon-zero times kappa times A over d converts those three SI quantities into capacitance in farads, which students, RF layout teams, and sensor designers use constantly when checking homework, sizing sense electrodes, or sanity-checking a board stack-up against a simple analytic baseline.
What parallel-plate capacitance returns and how to choose area, gap, and dielectric
Model the device as two overlapping plates of area A measured in square metres, separated by a uniform gap d measured in metres, with the volume between them filled by a linear dielectric of relative permittivity kappa equal to epsilon-r (unitless). The classical ideal formula states that capacitance C equals epsilon-zero times kappa times A divided by d, where epsilon-zero is approximately eight point eight five four times ten to the minus twelve farads per metre.
Vacuum and dry air use kappa approximately one; common plastics, ceramics, and glass use larger kappa values that multiply capacitance for the same geometry. Area and dielectric must be positive; separation must be strictly positive. Magnitude bounds keep pathological inputs from overflowing isolate arithmetic while still covering classroom centimetre plates and many millimetre-gap engineering checks.
Classroom use and practical limits
Call the free in-browser parallel-plate capacitor calculator for homework checks, lecture demos, and quick verification of hand calculations without installing a field solver or CAD capacitance extractor. Fringing fields, non-uniform dielectrics, and multilayer stacks are outside the ideal formula, so treat results as the classic textbook baseline rather than a full 3D extraction. Keep classroom centimetre plates and millimetre gaps within the published bounds and prefer SI units end to end.
Authors shipping SDKs can map capacitance, area, separation, and dielectric directly into tables students recognize from textbook parallel-plate problems, including clear errors when someone accidentally submits zero gap.
What you can do with it
Sensor and PCB geometry estimates
Designers size sense electrodes and stack-up gaps with a deterministic parallel-plate baseline before running a full field extractor or lab measurement.
Curriculum and lab notebooks
Lesson builders produce SI-unit capacitance checks for demos, auto-graded drills, and lab write-ups without embedding a full electromagnetic solver.
FAQ
How do I calculate parallel-plate capacitance?
Optional dielectric defaults to 1. The response includes capacitance in farads from C = ε0 · κ · A / d.
What units does the calculator use?
SI units: area in square metres, separation in metres, dielectric dimensionless, capacitance in farads. Convert cm² or mm gaps to metres before calling.
Is the parallel-plate capacitor calculator free?
The browser tool runs free on your device.
Is this the same as capacitors in parallel?
No. This computes geometry C = ε0 κ A / d for one parallel-plate device. Summing several discrete capacitors in a parallel circuit is a different calculator.
Does the result include fringing fields?
No. Fringing at the plate edges, uneven dielectrics and multilayer stacks are outside the ideal formula, so treat the result as the classic textbook baseline rather than a full three-dimensional field extraction.
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/parallel-plate-capacitance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"area":0.01,"separation":0.001}'const res = await fetch("https://api.kit.forhosting.com/elec/parallel-plate-capacitance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"area": 0.01,
"separation": 0.001
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/parallel-plate-capacitance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"area": 0.01,
"separation": 0.001
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/parallel-plate-capacitance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"area":0.01,"separation":0.001}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"area":0.01,"separation":0.001}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/parallel-plate-capacitance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"area": 0.01,
"separation": 0.001
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.parallel_plate_capacitance",
"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 capability evaluates that relation with a fixed vacuum permittivity, returns structured JSON including the capacitance and the constants used, and rejects zero plate separation so the singular one-over-d case never masquerades as a finite answer. The algorithm is pure arithmetic—no network, no random seed, no wall clock—so identical inputs always yield identical JSON.
What parallel-plate capacitance returns and how to choose area, gap, and dielectric
Send required fields area and separation as JSON numbers or numeric strings; aliases A, plate_area, d, gap, and distance are accepted so lab notebooks and CAD exports map without renaming columns. Optional dielectric defaults to one when omitted, with aliases k, kappa, er, epsilon_r, and relative_permittivity for homework forms that already use those names. Zero separation makes the one-over-d term diverge, so the engine raises invalid_input rather than inventing infinity. Identical inputs always produce identical JSON because the path is pure floating-point with a fixed constant and stable rounding—no model, no filesystem, and no external electromagnetics library.
Reading capacitance, constants, units, and common error cases
On success the response echoes area, separation, and dielectric after stable rounding, then reports capacitance as the farad value from C equals epsilon-zero kappa A over d. The field epsilon_0 is the exact vacuum permittivity used in the computation so reports and graded rubrics can cite it without ambiguity. Formula is always C equals eps0 star kappa star A over d, and method is always parallel_plate_capacitance so downstream code can branch without sniffing shapes. Units document capacitance in farads, area in square metres, separation in metres, and dielectric as a dimensionless one so UI tables and SDK demos stay SI-consistent. Use capacitance when you need the device value for circuit equations; use the echoed geometry and kappa when logging which stack produced that value; use epsilon_0 when documenting constants next to a lab notebook entry. Missing area or separation, non-finite numbers, non-positive area or dielectric, out-of-range magnitudes, and zero or negative separation all fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, classroom workflows, and practical limits
Send a JSON body with required numeric fields area and separation plus optional dielectric (or their aliases). Use the prepaid API when a tutoring platform, electronics curriculum generator, PCB sense-electrode estimator, or simulation pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with circuit combination tools when the next step is wiring several computed plate capacitors in series or parallel networks, or with energy and charge tools when you already have C and want stored energy one-half C V squared.
Integration use cases
Homework and exam verification
Students enter plate area, gap, and dielectric constant, compare farad results with hand work, and get a clear invalid_input when separation is zero by mistake.
Technical questions
What happens if plate separation is zero?
The request fails with invalid_input. Zero gap makes the ideal formula divide by d, so the engine rejects it and does not charge the call.