RLC resonant frequency calculator
With 1 mH, 1 µF and 10 Ω, a series RLC circuit resonates at about 5 kHz with a Q of about 3. Enter the three values to get the resonant frequency, the angular frequency, the quality factor and the bandwidth at once. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Inductance L in henries
- 0.001
- Capacitance C in farads
- 0.000001
- Resistance
- 10
- Resonant frequency hz
- 5,032.9212104487 Hz
- Angular frequency rad s
- 31,622.7766016838
- Quality factor
- 3.1622776602
- Bandwidth hz
- 1,591.549430919
This RLC resonant frequency calculator takes inductance L in henries, capacitance C in farads, and series resistance R in ohms, then returns the series resonant frequency f0, the angular frequency omega0, the quality factor Q, and the minus-three-decibel bandwidth BW. Resonance is the frequency where the inductive and capacitive reactances cancel, so the impedance of a series RLC network is purely resistive and equal to R. The closed forms used here are fully deterministic: f0 equals one over two pi times the square root of L times C, omega0 equals one over the square root of L times C, and Q equals one over R times the square root of L over C. Small checks you may already know include one millihenry with one microfarad and ten ohms yielding roughly five kilohertz and Q near three, and one hundred millihenries with one microfarad and fifty ohms yielding roughly five hundred hertz with a higher Q. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
What series RLC resonance means and what you get
In a series RLC circuit the inductor and capacitor exchange energy once per cycle, and at resonance their reactances are equal in magnitude and opposite in sign. That condition fixes the natural frequency of the LC tank: angular frequency omega0 equals one over the square root of L times C, and the ordinary frequency f0 in hertz is omega0 divided by two pi, which is the familiar one over two pi square-root of LC.
Resistance does not shift the ideal undamped resonant frequency in the series case, but it does set how sharp the resonance is. The quality factor Q equals one over R times the square root of L over C, which is the same as omega0 L over R or one over omega0 R C. High Q means a narrow peak and low damping; low Q means a broad, lossy response.
This calculator also returns the approximate half-power bandwidth BW equals f0 over Q in hertz, so you can estimate the width of the resonance without a full frequency sweep.
Where resonant frequency and Q fit in design, study, and software
Students meet series RLC resonance when a textbook introduces AC circuits, when a lab asks for the frequency of maximum current through a series string, or when they convert between f0 and the LC product before sizing a filter. Teachers can pre-generate answer keys for modest component values without trusting opaque calculator apps that silently switch between angular and ordinary frequency.
RF and audio designers use f0 and Q as first-cut targets when choosing L and C for a band-pass tank or when estimating how much series resistance the coil and wiring will tolerate before the peak flattens. Developers call the same contract from scripts to seed deterministic test vectors for impedance plotters, to normalize user-entered component triples before simulation demos, or to satisfy programming-challenge statements that demand f0 and Q rather than a hand-waved sketch.
Contest and homework practice often needs a fast, offline source of resonance numbers so solutions can be checked without a network of simulators under time pressure. Product and education tools use the evaluation when a learner types L, C, and R and the UI must show hertz, rad per second, and a clean quality factor.
What you can do with it
Homework and lab checks
Compute f0 and Q for textbook series RLC values and verify lab measurements against the closed-form peak.
Filter and tank design
Pick L, C, and R targets so resonant frequency and bandwidth match a band-pass or oscillator first cut.
FAQ
What does the RLC resonant frequency calculator cost?
It is free in your browser on this page.
How are f0 and Q defined for series RLC?
Angular frequency is ω0 = 1/√(LC) in rad/s.
What happens if L, C, or R is zero?
Zero or negative inductance, capacitance, or resistance makes the resonance or quality-factor formulas undefined in this calculator.
Is this for series or parallel RLC?
Series RLC only. Parallel tanks use a different Q expression; this page does not switch topologies.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
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/rlc-resonance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"inductance":0.001,"capacitance":0.000001,"resistance":10}'const res = await fetch("https://api.kit.forhosting.com/elec/rlc-resonance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"inductance": 0.001,
"capacitance": 0.000001,
"resistance": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/rlc-resonance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"inductance": 0.001,
"capacitance": 0.000001,
"resistance": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/rlc-resonance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"inductance":0.001,"capacitance":0.000001,"resistance":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"inductance":0.001,"capacitance":0.000001,"resistance":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/rlc-resonance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"inductance": 0.001,
"capacitance": 0.000001,
"resistance": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.rlc_resonance",
"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_l | 1000000000000000 |
max_abs_c | 1000000000000000 |
max_abs_r | 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 series RLC resonance means and what the response contains
The response includes the normalized inductance, capacitance, and resistance, resonant_frequency_hz, angular_frequency_rad_s, quality_factor, bandwidth_hz, the precision used, a method tag series_rlc_resonance, a short formula string, and the unit tag Hz for the frequency fields. There is no approximate symbolic CAS path and no random sampling: the engine either builds exact floating-point results inside the supported range or rejects the input with invalid_input. Rejected cases include missing L, C, or R, non-finite values, magnitudes above the documented ceiling, and any zero or non-positive value, because f0 and Q are undefined when the tank or the resistance is non-physical.
How L, C, and R are read and how f0 and Q stay reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong resonant peak. Cross-checks against omega0 L over R and one over omega0 R C keep the quality factor consistent across equivalent identities. The preferred fields are inductance for L in henries, capacitance for C in farads, and resistance for R in ohms, but aliases L, l, henries, and henry for inductance, C, c, farads, and farad for capacitance, and R, r, ohms, and ohm for resistance are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Zero for L, C, or R is invalid and fails with invalid_input, as is any negative value, because the square-root products and the division by R are not defined for non-positive circuit elements in this model. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for all 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 LC formulas yourself.
Where resonant frequency and Q fit in design, study, and software
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 inductor-energy or capacitor-energy tools when you need related passive-circuit helpers, and with other electronics endpoints when you are building a small lab of free, deterministic calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible f0, ω0, Q, and BW numbers for unit tests, property checks, and CI assertions.