RC circuit calculator
With 5 V through 1 kΩ into 1 µF, the capacitor reaches about 3.16 V after 1 ms, exactly one time constant. Enter source voltage, resistance, capacitance and elapsed time to get the capacitor voltage and the time constant. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Source voltage
- 5
- Resistance
- 1,000
- Capacitance
- 0.000001
- Time
- 0.001
- Time constant
- 0.001
- Capacitor voltage
- 3.1606027941
An RC charging circuit is the textbook first-order network: a DC source, a series resistor, and a capacitor that starts uncharged. Closing the switch does not slam the capacitor to the rail; the voltage climbs along a smooth exponential whose speed is set by the product RC. Students checking lab traces, technicians sizing a delay, and firmware authors picking a brown-out window all need the capacitor voltage at a chosen elapsed time rather than a graph they have to read by eye. This RC circuit calculator takes source voltage, resistance, capacitance, and elapsed time, then returns the capacitor voltage from Vc(t) = Vs times one minus e to the minus t over RC.
How capacitor voltage follows from the RC exponential
Start from Kirchhoff's voltage law on a series loop that contains a constant source Vs, a resistor R, and a capacitor C that is initially uncharged. The loop equation is R C dVc over dt plus Vc equals Vs. With Vc of zero equal to zero at the switching instant, the unique solution is Vc of t equals Vs times one minus e to the minus t over tau, where the time constant tau equals R times C.
That closed form is what this RC circuit calculator evaluates: four finite numbers in, one capacitor voltage out, plus the echoed inputs and tau so you can check the arithmetic. After one time constant the voltage is about sixty-three point two percent of the source; after ln two times tau it is fifty percent; after three tau roughly ninety-five percent; and after five tau about ninety-nine point three percent, the classic settling rule of thumb.
At t equals zero the exponential is one and the capacitor voltage is zero, matching the initial condition. As t grows without bound the exponential vanishes and the capacitor voltage approaches the source but never quite reaches it in finite time.
Where an RC circuit voltage calculator earns its keep
Lab courses ask for the capacitor voltage at one tau, three tau, and five tau so students can place scope cursors on the ideal exponential before they move on to discharge and filters. Power-on delay networks, reset supervisors, and RC soft-start blobs are sized so a capacitor voltage sits at a known fraction of the rail at a chosen instant; evaluating V of t is the forward check after you pick R and C.
Embedded bring-up teams convert a firmware timeout into the voltage the analog node should have reached, then add margin so brown-out detectors and PLL lock windows are not racing the exponential. Keep the inverse charge-time landing, the bare tau equals R C page, and capacitor energy tools on separate URLs so each search intent has one clear tool rather than an overloaded multi-formula page that confuses both students and search engines.
What you can do with it
Lab RC charging drills
Compute capacitor voltage at 1τ, 3τ, and 5τ so students can place scope cursors on the ideal exponential without reading a graph by eye.
Power-on delay and reset networks
Check the capacitor voltage at a firmware timeout or comparator window after choosing R and C for a supervisor or soft-start blob.
FAQ
What happens if resistance or capacitance is zero or negative?
A series RC charging circuit needs strictly positive R and C so the time constant is well defined; those failures are not billed.
What voltage do I get after one time constant?
About 63.2 percent of the source: Vc(τ) = Vs × (1 − 1/e). After five time constants the capacitor is about 99.3 percent of Vs, the usual settling rule of thumb.
Do I pass microfarads and kilohms or SI base units?
Always SI base units: volts, ohms, farads, and seconds. For 1 µF pass 1e-6; for 1 kΩ pass 1000. Prefix strings like "1uF" are not parsed.
What does the RC circuit calculator cost?
The browser tool is free and runs locally.
How long does a capacitor take to charge fully?
In theory it never quite gets there. It passes about 95% of the source after three time constants and about 99.3% after five, the usual rule of thumb for settled.
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/rc-circuit \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"source_voltage":5,"resistance":1000,"capacitance":0.000001,"time":0.001}'const res = await fetch("https://api.kit.forhosting.com/phys/rc-circuit", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"source_voltage": 5,
"resistance": 1000,
"capacitance": 0.000001,
"time": 0.001
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/rc-circuit",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"source_voltage": 5,
"resistance": 1000,
"capacitance": 0.000001,
"time": 0.001
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/rc-circuit", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"source_voltage":5,"resistance":1000,"capacitance":0.000001,"time":0.001}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"source_voltage":5,"resistance":1000,"capacitance":0.000001,"time":0.001}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/rc-circuit", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"source_voltage": 5,
"resistance": 1000,
"capacitance": 0.000001,
"time": 0.001
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.rc_circuit",
"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
Zero or negative resistance or capacitance is rejected with invalid_input because a non-positive time constant is not a charging circuit.
Input contract, response shape, and illegal RC values
Numeric values and numeric strings are both accepted so form widgets and spreadsheet paste stay convenient; SI prefix strings such as one microfarad written as text are not parsed, so pass one times ten to the minus six for a microfarad part and one thousand for a one-kilohm resistor. Resistance and capacitance must be strictly greater than zero. Elapsed time must be greater than or equal to zero; a negative clock is rejected rather than producing a nonsense discharge-looking number from the charging formula. A classroom check is one kilohm and one microfarad at five volts after one millisecond, which is one tau and must return about 3.16 V, or sixty-three percent of the source. POST a JSON body with four required finite numbers: source_voltage in volts, resistance in ohms, capacitance in farads, and time in seconds since charging began. Aliases are accepted for convenience—vs, Vs, supply_voltage, or voltage for the source; r, R, or ohms for resistance; c, C, or farads for capacitance; t, elapsed_time, or seconds for time—but only one key may appear for each quantity. Zero or negative resistance or capacitance fails with invalid_input, because tau would not be a positive charging time constant and the exponential is undefined or instantaneous in a way this tool does not model. On success the body echoes the cleaned inputs, time_constant as R times C, capacitor_voltage as the primary result, and a formula string. Successful API calls use the published base of $0.002 per item; validation failures do not consume prepaid balance.
Integration use cases
CI fixtures and answer keys
Script Vc(t)=Vs(1−e^(−t/RC)) with the same module the browser uses so automated graders share one ground truth for RC circuit problems.
Technical questions
How do I calculate capacitor voltage in an RC circuit?
Send finite source_voltage Vs in volts, resistance R in ohms, capacitance C in farads, and time t in seconds. The API returns Vc(t) = Vs × (1 − e^(−t/(R×C))) and the time constant τ = R×C.