RLC impedance calculator
At 50 Hz, a series circuit of 100 Ω, 0.2 H and 10 µF is dominated by the capacitor, so its phase is negative and voltage lags current. Enter R, L, C and frequency to get the impedance magnitude in ohms and the phase angle. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Resistance
- 100
- Inductance
- 0.2
- Capacitance
- 0.00001
- Frequency
- 50
- Angular frequency
- 314.159265359
- Inductive reactance
- 62.8318530718
- Capacitive reactance
- 318.3098861838
- Reactance
- -255.478033112
A series RLC circuit is the elementary AC filter: one resistor, one inductor, and one capacitor in a single loop, driven by a sinusoidal source at a known frequency. Designers, students, and technicians need the complex impedance of that branch — not resonant frequency, not a polar conversion of already-known R and X — so they can size current, drop voltage, and read power factor from the four quantities they actually measure. This series RLC impedance calculator accepts resistance in ohms, inductance in henries, capacitance in farads, and signal frequency in hertz, then returns the impedance magnitude |Z| in ohms and the phase angle of Z.
What series RLC impedance is and how magnitude and phase arise
In a series RLC circuit a resistor, an inductor, and a capacitor share one current, and the individual voltage drops add as phasors on the complex plane. The resistor contributes a real impedance R in ohms. Net reactance X is XL minus XC, so the total series impedance is the complex number Z equals R plus jX.
Impedance magnitude |Z| is the Euclidean length of that phasor — the square root of R squared plus X squared — and is the ratio of voltage amplitude to current amplitude at the driving frequency. Phase angle φ is the argument of Z, recovered with the two-argument arctangent atan2 of X and R so the quadrant is correct: a positive phase means the net reactance is inductive and voltage leads current; a negative phase means the net reactance is capacitive and voltage lags current.
At the series resonant frequency XL equals XC, X vanishes, |Z| collapses to R, and the phase is zero. This landing does not compute that resonant frequency or the quality factor Q — those are a different search intent served by an RLC resonance calculator — and it does not convert a precomputed rectangular pair R and X into polar form. It starts from the four circuit quantities a student, technician, or script actually has: resistance, inductance, capacitance, and signal frequency in SI units.
Where a series RLC impedance calculator earns its keep
Students meet series RLC impedance when a homework set gives R, L, C, and the source frequency and asks for |Z| and the phase without a full nodal solve. Teachers pre-generate answer keys for mixed below-resonance and above-resonance loads and need a deterministic oracle that never flips the sign of capacitive phase. Lab technicians convert an LCR-meter's component values and a chosen test frequency into the branch impedance they will see on an analyzer.
Product and first-order filter checks evaluate |Z| at the mains frequency, at a switching harmonic, or at a radio carrier before deciding whether a matching network is required. Education platforms show live magnitude and phase when a learner types ohms, henries, farads, and hertz.
What you can do with it
Homework and exam checks
Convert textbook series R, L, C, and source frequency into |Z| and phase so students can verify polar answers and lagging versus leading sign without calculator quadrant mistakes.
Lab and filter first-order checks
Turn LCR-meter component values and a chosen test frequency into branch impedance magnitude and degrees for notebooks, reports, and matching-network decisions.
FAQ
How do I compute series RLC impedance from R, L, C, and frequency?
Send finite numbers resistance (Ω), inductance (H), capacitance (F), and frequency (Hz).
When is the phase positive and when is it negative?
Phase is positive (inductive, voltage leads current) when XL > XC, negative (capacitive, voltage lags current) when XL < XC, and zero at series resonance where XL = XC and |Z| = R.
Is this the same as an RLC resonant-frequency calculator?
No. Resonance tools return f0 and Q from L, C, and R. This calculator evaluates |Z| and phase at a given driving frequency. Impedance-from-R-and-X tools start after reactance is already known.
Can I leave out the inductor or the resistor?
Yes. An inductance of zero gives the series RC case and a resistance of zero gives the series LC case, both valid. The capacitance, however, must stay above zero.
What is the impedance at resonance?
At the frequency where inductive and capacitive reactance are equal, they cancel: the impedance magnitude falls to the resistance alone and the phase angle is zero.
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/rlc-impedance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"resistance":100,"inductance":0.2,"capacitance":0.00001,"frequency":50}'const res = await fetch("https://api.kit.forhosting.com/phys/rlc-impedance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"resistance": 100,
"inductance": 0.2,
"capacitance": 0.00001,
"frequency": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/rlc-impedance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"resistance": 100,
"inductance": 0.2,
"capacitance": 0.00001,
"frequency": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/rlc-impedance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"resistance":100,"inductance":0.2,"capacitance":0.00001,"frequency":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"resistance":100,"inductance":0.2,"capacitance":0.00001,"frequency":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/rlc-impedance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"resistance": 100,
"inductance": 0.2,
"capacitance": 0.00001,
"frequency": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.rlc_impedance",
"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
Internally it forms net reactance as inductive reactance minus capacitive reactance, XL = 2πfL and XC = 1/(2πfC), then converts the rectangular pair R + jX into polar form with a Euclidean magnitude and a two-argument arctangent. Frequency must be a positive number; zero, negative, or non-finite frequency fails with invalid_input and is not billed.
What series RLC impedance is and how magnitude and phase arise
The inductor contributes an imaginary inductive reactance XL equal to two pi times the driving frequency times the inductance, XL = 2πfL, always non-negative for L ≥ 0 and f > 0. The capacitor contributes an imaginary capacitive reactance XC equal to the reciprocal of two pi times frequency times capacitance, XC = 1/(2πfC), which is defined only when both frequency and capacitance are strictly positive.
Input contract, response shape, and validation behaviour
Frequency must be a positive number: zero hertz would make capacitive reactance infinite in this AC model, and a negative frequency is not a physical driving rate, so those cases fail rather than returning Infinity. Capacitance must be strictly positive because XC is the reciprocal of ωC. Resistance and inductance must be finite and non-negative; a zero inductance is the valid series RC special case, and a zero resistance is the valid series LC special case. On success the body echoes the cleaned inputs, reports angular frequency ω = 2πf, inductive and capacitive reactances, net reactance, impedance magnitude, and phase in radians and degrees, plus formula and method tags. Example: one hundred ohms, two tenths of a henry, ten microfarads, and fifty hertz yields a capacitive (negative) phase because fifty hertz sits below the series resonance of that LC pair. POST a JSON body with four required finite numbers in SI units: resistance R in ohms, inductance L in henries, capacitance C in farads, and frequency f in hertz. Preferred field names are resistance, inductance, capacitance, and frequency; aliases R, r, ohms for resistance, L, l, henries, henry for inductance, C, c, farads, farad for capacitance, and f, freq, hz for frequency are accepted so spreadsheets and lab exports map without renaming columns. Each value may arrive as a JSON number or as a numeric string in ordinary decimal or scientific notation; blank strings, non-numeric tokens, and non-finite values fail with invalid_input naming the field. Magnitudes above one trillion in absolute value are rejected so accidental unit mistakes do not overflow the Worker. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside automated pipelines without re-implementing hypot and atan2 yourself. Successful API calls are billed at $0.002 per item; validation failures do not consume prepaid balance.
Where a series RLC impedance calculator earns its keep
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.
Integration use cases
Deterministic CI fixtures
Generate reproducible |Z| and atan2 phase pairs from R, L, C, and f for unit tests of meters, filters, and simulation export pipelines that must not hand-edit expected JSON.
Technical questions
Why must frequency be a positive number?
Capacitive reactance XC = 1/(2πfC) is undefined at f = 0, and a negative frequency is not a physical driving rate. Zero, negative, or non-finite frequency fails with invalid_input and is not billed.
What does the series RLC impedance calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.