Impedance from R and X calculator
Resistance 3 Ω and reactance 4 Ω give an impedance of 5 Ω, plus its phase angle in degrees and radians. Enter X with its sign, positive for inductive loads and negative for capacitive ones, and the angle lands in the right quadrant. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Resistance
- 3
- Reactance
- 4
- Magnitude
- 5
- Impedance magnitude
- 5
- Phase rad
- 0.927295218
- Phase deg
- 53.1301023542
Impedance is the complex generalization of resistance for alternating-current circuits: a series combination of resistance R and reactance X forms Z equals R plus jX, and designers constantly need the polar pair of magnitude and phase rather than the rectangular parts alone. This impedance magnitude from R and X calculator accepts finite resistance and reactance in ohms, applies the Pythagorean identity |Z| equals the square root of R squared plus X squared, and reports the phase angle with the two-argument arctangent atan2 of X and R so every quadrant is correct, including pure capacitive loads in the fourth quadrant and pure inductive loads in the first. Results include magnitude in ohms, phase in radians and degrees, rectangular and polar display strings, and short formula steps you can paste into lab notes. Zero R and zero X is valid and yields a short circuit of zero ohms at phase zero.
What impedance magnitude and phase mean from R and X
In phasor circuit analysis a series impedance is written in rectangular form as Z equals R plus jX, where R is the real resistance in ohms and X is the imaginary reactance in ohms. Positive X means the net reactive part is inductive; negative X means capacitive. Magnitude |Z| is the length of that phasor on the complex plane and is always non-negative: |Z| equals the square root of R squared plus X squared, which is the same Euclidean norm used for any two-dimensional vector.
Phase φ is the angle of the phasor relative to the positive real axis; it is recovered with the two-argument arctangent atan2 of X and R so the result lands in the correct quadrant when R is negative or X is negative, unlike a naive arctan of X over R that fails when R is zero. Magnitude alone does not tell you whether a load is lagging or leading; phase carries that information and is essential for power-factor work, filter matching, and reading impedance analyzer printouts.
Where an R-and-X impedance calculator earns its keep
Students meet |Z| equals square root of R squared plus X squared when a homework set gives series resistance and reactance and asks for magnitude and phase without a full network solve. Teachers pre-generate answer keys for mixed inductive and capacitive loads and need a deterministic oracle that never flips the sign of capacitive phase. Lab technicians convert impedance analyzer rectangular readouts into polar form for lab notebooks and reports.
Product and first-order design checks convert a measured real and imaginary pair into |Z| and angle before deciding whether a matching network is required. Education platforms show live magnitude and phase when a learner types ohms for R and X.
What you can do with it
Homework and exam checks
Convert textbook series R and X into |Z| and phase so students can verify polar answers and lagging versus leading sign without calculator quadrant mistakes.
Lab and analyzer post-processing
Turn rectangular ohms from an impedance analyzer or LCR meter into magnitude and degrees for lab notebooks, reports, and quality logs.
FAQ
How do I get impedance magnitude from resistance and reactance?
Send finite numbers resistance (R) and reactance (X) in ohms.
Why use atan2 instead of arctan(X/R)?
atan2(X, R) keeps the correct quadrant when R is negative or zero.
What does a negative reactance mean?
Negative X is capacitive reactance; positive X is inductive. Magnitude stays non-negative; the phase angle becomes negative for capacitive loads with positive R.
Why do I need the phase if I already have the magnitude?
Magnitude alone does not tell you whether a load is lagging or leading. The phase carries that information, which matters for power-factor work, filter matching and reading the printout of an impedance analyzer.
Can it work out reactance from frequency and inductance or capacitance?
No. You enter X already in ohms. Getting reactance from frequency and L or C is a different calculation, handled by the inductive and capacitive reactance calculators, and this tool does not convert impedance into admittance either.
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/impedance-from-rx \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"resistance":3,"reactance":4}'const res = await fetch("https://api.kit.forhosting.com/elec/impedance-from-rx", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"resistance": 3,
"reactance": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/impedance-from-rx",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"resistance": 3,
"reactance": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/impedance-from-rx", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"resistance":3,"reactance":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"resistance":3,"reactance":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/impedance-from-rx", 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": 3,
"reactance": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.impedance_from_rx",
"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
Missing or non-finite inputs fail with invalid_input and are not billed.
What impedance magnitude and phase mean from R and X
When R and X are both zero the magnitude is zero and this calculator reports phase zero by the stable IEEE convention for atan2 of zero and zero. This endpoint does not compute reactance from frequency and L or C—that is a different search intent served by inductive and capacitive reactance tools—nor does it invert Z into admittance.
Input contract, response shape, and validation behaviour
Negative resistance is allowed because measurement conventions and active-source models sometimes place a negative real part on the plane; negative reactance is the normal capacitive case. Example: R equals three ohms and X equals four ohms yields |Z| equals five ohms and phase equals approximately fifty-three point one three degrees, the classic three-four-five right triangle used in every AC textbook. POST a JSON body with two required finite numbers: resistance R and reactance X, both in ohms. Preferred field names are resistance and reactance; aliases R, r, res, ohms_r for resistance and X, x, react, ohms_x for reactance are accepted so spreadsheets and query forms can reuse the same contract. 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. On success the body echoes rounded resistance and reactance, magnitude under both magnitude and impedance_magnitude, phase in radians and degrees under phase_rad, phase_deg, and synonym keys, rectangular and polar strings, formula and equation lines, unit hints, a short message, and ordered steps. 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 hypotenuse and atan2 yourself.
Where an R-and-X 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 for unit tests of meters, filters, and simulation export pipelines that must not hand-edit expected JSON.
Technical questions
Is R = 0 and X = 0 allowed?
Yes. The calculator returns magnitude 0 Ω and phase 0 (radians and degrees) using the stable atan2(0, 0) convention. Missing or non-finite fields are rejected instead.
What does the impedance from R and X calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.