Capacitor energy calculator
A 1000 µF capacitor charged to 12 V holds 0.072 J. Enter the capacitance in farads and the voltage in volts to get the stored energy; a negative voltage gives the same energy as the positive one, because voltage is squared. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Capacitance C in farads
- 0.001
- Voltage
- 12
- Energy
- 0.072 J
- Precision
- 10
This capacitor energy calculator finds the electrostatic energy stored in an ideal linear capacitor when you know its capacitance and the voltage across the plates. The definition is the closed form E equals one-half C times V squared, which is the standard introductory model used in circuit homework, energy budgets for pulsed loads, and first-order engineering checks on storage capacitors. When capacitance is given in farads and voltage in volts, the result is reported in joules; any consistent charge-per-voltage and potential pair works the same way. Zero capacitance or zero voltage is valid and yields zero stored energy; a negative voltage means reversed polarity and produces the same energy as the equal positive magnitude because of the square; a negative capacitance is rejected because it has no physical meaning for a passive storage element in this model. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
What the stored energy figure tells you
In classical electrostatics, an ideal linear capacitor with constant capacitance C stores energy when a voltage V is established between its terminals. With those two quantities, the stored energy is E equals one-half C times V squared. Capacitance is the charge per unit voltage in the linear regime: Q equals C V, and integrating the work to assemble charge yields the familiar one-half C V squared form, equivalently one-half Q V or Q squared over two C.
Voltage may be positive or negative relative to a chosen polarity; because energy depends on V squared, the sign of the voltage does not change the stored energy magnitude for a given absolute V. Capacitor energy is not the same as instantaneous power, peak current during a discharge, or the thermal energy dissipated in series resistance: under the ideal model it is a state variable of the present voltage and capacitance. Zero C or zero V is valid and yields zero energy when the other factor is finite.
Where capacitor energy fits in study, design, and software
Students meet E equals one-half C V squared when a textbook introduces electrostatic energy, when a homework problem asks how much energy is stored at a given bias, or when a contest problem gives microfarads and volts and asks for joules without calculus. Teachers can pre-generate answer keys for modest capacitances and voltages without trusting opaque calculator apps that silently switch units or confuse charge with energy.
Developers call the same contract from scripts to seed deterministic test vectors for power-electronics demos, to normalize user-entered storage parameters before an energy budget, or to satisfy programming-challenge statements that demand joules rather than a hand-waved sketch. Product and first-order electrical checks use E equals one-half C V squared when only capacitance and a design voltage are known before ESR, derating, or multi-cap banks are modeled.
What you can do with it
Homework and lab checks
Compute E = ½CV² from capacitance and voltage before grading worksheets or comparing energy budgets.
Tutoring and teaching software
Normalize user-entered capacitance and voltage into stored energy for interactive lessons and step helpers.
FAQ
What does the capacitor energy calculator cost?
It is free in your browser on this page.
What formula is used for capacitor energy?
Energy stored in an ideal linear capacitor is E = ½ · C · V², where C is capacitance and V is the voltage across the plates. With SI inputs (farads and volts) the unit is joules (J). Equivalent forms include ½QV and Q²/(2C).
What happens if capacitance is negative?
A negative capacitance is not accepted because E = ½CV² has no standard meaning for a negative C in this calculator.
Can the voltage V be negative?
Yes. A negative V means reversed polarity. Because energy depends on V², E is the same for +V and −V of equal magnitude. Zero V yields zero energy for any finite C.
Is this the same as electrical power P = VI?
No. Electrical power is energy per unit time from voltage and current. This tool computes electrostatic energy stored at a given capacitance and voltage (½CV²). Use the electrical power calculator when you need watts from V, I, or R.
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/capacitor-energy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"capacitance":0.001,"voltage":12}'const res = await fetch("https://api.kit.forhosting.com/elec/capacitor-energy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"capacitance": 0.001,
"voltage": 12
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/capacitor-energy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"capacitance": 0.001,
"voltage": 12
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/capacitor-energy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"capacitance":0.001,"voltage":12}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"capacitance":0.001,"voltage":12}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/capacitor-energy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"capacitance": 0.001,
"voltage": 12
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.capacitor_energy",
"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_c | 1000000000000000 |
max_abs_v | 1000000000000000 |
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
What capacitor energy means and what the response contains
This calculator returns the normalized inputs capacitance and voltage, the computed energy, the precision used, a method tag capacitor_energy, a short formula reminder, and a unit hint J for SI inputs. There is no numerical integration of a nonlinear dielectric, no multi-capacitor network reduction, and no Monte Carlo sampling: the engine either evaluates one-half C V squared inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing capacitance or voltage, non-finite values, magnitudes above the documented ceilings, and any capacitance that is negative, because a negative C is not accepted in this calculator.
How capacitance and voltage are read and how energy stays reproducible
Zero capacitance is allowed and returns zero energy. Voltage may be positive, zero, or negative; negative values mean reversed polarity and produce the same energy as the equal positive magnitude because of the square, which is intentional for bidirectional rail and bipolar bias problems. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces and non-numeric tokens are rejected. The preferred field for capacitance is capacitance, but aliases C, c, farads, and cap are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Capacitance must be finite and non-negative: a negative value fails with invalid_input and a message that names the field and explains that E equals one-half C V squared is undefined for a negative capacitance in this calculator, so a bad cell does not become a silent nonsense result. The preferred field for voltage is voltage, with aliases V, v, volts, and potential. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the capacitor energy formula yourself.
Where capacitor energy fits in study, design, and software
Education tools use the endpoint when a learner types capacitance and voltage and the UI must show joules. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with electrical power or resistor-network helpers when you need related circuit quantities, and with other math endpoints when you are building a small lab of free, deterministic electronics calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible capacitor energy values for unit tests, power-electronics demos, and CI assertions on E = ½CV².