Capacitance calculator
Plates of 0.01 m² with a 0.001 m gap in vacuum give 8.854 × 10⁻¹¹ F; double the area or halve the gap and the capacitance doubles. Enter area, separation and absolute permittivity in SI units to get farads. 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
- Separation
- 0.001
- Permittivity
- 0
- Capacitance
- 0.0000000001
This capacitance calculator returns the capacitance of an ideal parallel-plate capacitor in farads from three SI quantities: overlapping plate area in square metres, plate separation in metres, and the absolute dielectric permittivity of the medium between the plates in farads per metre. The closed-form relation is C equals epsilon times A divided by d, so larger plates, a thinner gap, or a higher permittivity each raise the charge stored per volt.
What C = εA/d means and which permittivity to enter
Model the device as two overlapping conducting plates of area A that face each other across a uniform gap d filled with a linear dielectric whose absolute permittivity is epsilon. When fringing at the edges is neglected, the electric field between the plates is uniform and the capacitance — the charge stored per volt — collapses to C equals epsilon times A divided by d. All three quantities are SI: area in square metres, separation in metres, permittivity in farads per metre, and capacitance in farads.
Vacuum permittivity is about eight point eight five four times ten to the minus twelve farads per metre; a linear dielectric is that baseline multiplied by a relative permittivity, and this calculator asks for the product already in SI form so a laboratory epsilon, a datasheet absolute permittivity, or vacuum itself can be entered without a hidden conversion step. Capacitance grows linearly with area and permittivity and inversely with gap: doubling the plates doubles C, filling the gap with twice the permittivity doubles C, and halving the gap doubles C.
That inverse dependence is why a vanishing or reversed gap is not a physical capacitor in this model — the formula diverges at contact — so the engine refuses zero and negative separation instead of emitting infinity or a huge denormal.
Where a quick capacitance check helps
Classrooms and tutoring platforms use a capacitance calculator so learners can check farad results for arbitrary area, gap, and permittivity without unit-conversion slips by hand. Exam-prep generators need a deterministic oracle that marks wrong the case of a zero or negative gap instead of silently returning infinity that a buggy grader might treat as success. Sensor and PCB teams size sense electrodes and stack-up gaps with this analytic baseline before running a full field extractor.
Failed validation does not consume balance. Keep requests in SI units end to end, convert centimetre plates and millimetre gaps to metres before calling, and pin the farad value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up an electrostatics solver of your own. Fringing, patterned electrodes, and multilayer stacks remain outside the ideal formula, so treat the number as the classic textbook baseline rather than a three-dimensional extraction.
What you can do with it
Sensor and electrode geometry estimates
Size sense plates and dielectric gaps with a deterministic C = εA/d baseline before a full field extractor or a lab measurement.
FAQ
How is capacitance computed from area, gap, and permittivity?
Send finite numbers area (m²), separation (m), and permittivity ε (F/m).
Is permittivity the relative dielectric constant or the SI value?
This calculator wants absolute dielectric permittivity ε in farads per metre, not the unitless κ. For vacuum use about 8.854e-12 F/m; for a dielectric use ε = εr · ε0.
What happens if the plate separation is zero or negative?
The calculation is refused with a message, because capacitance grows without limit as the gap closes and a reversed gap is not a physical capacitor. You never get an infinite value in place of an answer.
What does the parallel-plate model leave out?
Fringing at the plate edges, patterned electrodes and multilayer stacks. It assumes a uniform field across a uniform gap, which makes it the analytic baseline to check before running a full field solver.
Can I enter plates in centimetres and the gap in millimetres?
Convert them to metres first: square centimetres to square metres and millimetres to metres. The calculator works in SI units from end to end, so a value in another unit would give the wrong capacitance.
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/phys/capacitance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"area":0.01,"separation":0.001,"permittivity":8.854187817e-12}'const res = await fetch("https://api.kit.forhosting.com/phys/capacitance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"area": 0.01,
"separation": 0.001,
"permittivity": 8.854187817e-12
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/capacitance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"area": 0.01,
"separation": 0.001,
"permittivity": 8.854187817e-12
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/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,"permittivity":8.854187817e-12}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"area":0.01,"separation":0.001,"permittivity":8.854187817e-12}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/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,
"permittivity": 8.854187817e-12
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.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.
Limits
max_abs_area | 1000000 |
max_abs_separation | 1000000 |
max_abs_permittivity | 1 |
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
Input contract, response shape, and error behaviour
Area and permittivity must be strictly positive. Separation must be strictly greater than zero: both a zero gap and a negative gap fail with a message that zero or negative plate separation is invalid, matching the product promise that the one-over-d singularity never masquerades as a finite answer. Magnitude ceilings keep pathological inputs from overflowing isolate arithmetic while still covering classroom centimetre plates and ordinary millimetre-scale engineering gaps. POST a JSON body with three required finite numbers: area, the overlapping plate area in square metres; separation, the gap in metres; and permittivity, the absolute dielectric permittivity in farads per metre. Each field may arrive as a JSON number or as a numeric string; aliases A and plate_area, d, gap, distance and plate_separation, and epsilon, eps, dielectric_permittivity and varepsilon are accepted so notebooks and CAD exports map without renaming columns. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes the three inputs, reports capacitance in farads, and includes formula C equals epsilon A over d, method parallel_plate, and a units object documenting farads, square metres, metres, and farads per metre. Pair the response with your own circuit equations if you next need stored energy or reactance; this endpoint computes geometric capacitance only and does not emit plots, netlists, or field solutions.
Integration use cases
Homework and exam checks
Enter plate area, gap, and absolute permittivity, compare farad results with hand work, and get a clear invalid_input when separation is zero or negative.
Curriculum fixtures and lab notebooks
Produce SI-unit capacitance checks for demos, auto-graded drills, and lab write-ups without embedding an electromagnetic solver.
Technical questions
What happens if plate separation is zero or negative?
The task fails with invalid_input. Zero or negative gap makes the ideal formula divide by d, so the engine rejects it and does not bill the call.
What does a successful capacitance response contain?
Echoed area, separation, and permittivity, capacitance in farads, formula C = ε A / d, method parallel_plate, and a units object for F, m², m, and F/m.
What does the capacitance calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.