Series RL impedance calculator
A 100 Ω resistor in series with 0.1 H at 50 Hz gives about 104.8 Ω of impedance, with current lagging by about 17.4°. You also get the coil's reactance, about 31.4 Ω here, and the angular frequency. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- R
- 100
- L
- 0.1
- F
- 50
- Resistance
- 100
- Inductance
- 0.1
- Frequency
- 50
- XL
- 31.4159265359
A series RL impedance calculator turns resistance, inductance, and signal frequency into the AC opposition of a resistor and inductor connected end to end. Students checking phasor homework, firmware engineers sizing choke filters, and coding-kata authors all need that same |Z| and phase without opening a full SPICE deck or impedance analyzer.
What series RL impedance means on the phasor diagram
In elementary AC circuit theory, a series combination of resistance R ohms and inductance L henries driven by a sinusoidal source at frequency f hertz has complex impedance Z equals R plus j XL, where inductive reactance XL equals two pi times f times L ohms and j is the imaginary unit. The magnitude |Z| is the Euclidean length of that phasor: the square root of R squared plus XL squared, also in ohms.
The phase angle phi equals the two-argument arctangent of XL over R, measured from the positive real axis so that current lags voltage by a lagging angle between zero and ninety degrees for non-negative passive R and L. At DC (f equals zero) XL collapses to zero, |Z| equals R, and the phase is zero—an ideal series inductor behaves as a short for steady current and only the resistor remains.
Doubling frequency doubles XL; when XL is much larger than R the network looks nearly inductive and the phase approaches ninety degrees. Typical classroom numbers: one hundred ohms and one hundred millihenries at fifty hertz give XL about thirty-one point four ohms and |Z| about one hundred four point eight ohms with a modest lag angle near seventeen point four degrees.
Teachers and automated graders care about the negative-input rejection as much as the arithmetic: a student who plugs a negative frequency has left the domain of the formula, and a silent absolute-value fallback would hide that mistake.
Practical tips, limits, and related searches
Keep R, L, and f inside the published absolute range so products with two pi and the subsequent square root cannot overflow into a non-finite magnitude that the solver must reject. Convert millihenries by dividing by one thousand, microhenries by one million, and kilohertz by multiplying by one thousand before you call if you want |Z| already in ohms without mental rescaling afterward.
Prefer this capability when you already have scalar R, L, and f and need both magnitude and phase of the series combination; if you only need XL without R, use the inductive reactance calculator instead.
Round-trip checks are easy: recompute XL equals two pi f L and |Z| equals sqrt of R squared plus XL squared by hand and confirm they match the published fields within the same twelve-decimal rounding, and confirm that pure resistive (L or f zero) and pure inductive (R zero with XL positive) edge cases return phase zero and ninety degrees respectively as the phasor diagram predicts.
What you can do with it
Homework checks for series RL phasors
Students enter R, L, and f from textbook AC problems and compare hand-written |Z| and lag angle against a deterministic result before submitting.
Filter and choke pre-flight estimates
Designers estimate series resistor-plus-inductor impedance magnitude and phase at line or switching frequency before budgeting drop and phase margin.
FAQ
Is the series RL impedance calculator free?
The browser tool is free and runs locally.
What happens at zero frequency, with direct current?
The coil's reactance drops to zero, so the impedance equals R and the phase is zero. An ideal series inductor behaves as a short for steady current and only the resistor remains.
What if I enter a negative resistance, inductance or frequency?
It is rejected. A negative value lies outside this passive resistor-and-coil model, and quietly taking its absolute value would hide the mistake, which matters when the result is used to check homework.
Why does the phase approach 90 degrees at high frequency?
Reactance grows with frequency: doubling f doubles it. Once the coil's reactance is much larger than R, the circuit looks almost purely inductive, so the current lags the voltage by an angle close to 90 degrees.
Is this the same as the inductive reactance calculator?
No. That calculator gives only the coil's reactance. This one adds the series resistor and returns the combined impedance and phase; use the inductive reactance calculator when you need the reactance without 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/impedance-rl-series \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"R":100,"L":0.1,"f":50}'const res = await fetch("https://api.kit.forhosting.com/elec/impedance-rl-series", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"R": 100,
"L": 0.1,
"f": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/impedance-rl-series",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"R": 100,
"L": 0.1,
"f": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/impedance-rl-series", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"R":100,"L":0.1,"f":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"R":100,"L":0.1,"f":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/impedance-rl-series", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"R": 100,
"L": 0.1,
"f": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.impedance_rl_series",
"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
Negative resistance, inductance, or frequency is outside this passive model, so the API returns a clear invalid_input error instead of inventing non-physical values.
What series RL impedance means on the phasor diagram
Prefer SI throughout: convert millihenries to henries and kilohertz to hertz before the call so comparisons stay consistent across worksheets and API clients.
How to call the API and what comes back
Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern including optional scientific notation. Send a JSON body with three required finite numbers: R (aliases resistance, resistor, and ohms) for series resistance in ohms; L (aliases inductance, henry, and henries) for inductance in henries; and f (aliases frequency, freq, and hz) for signal frequency in hertz. Absolute values must stay within the published limit of one trillion so intermediate products and the square root remain finite in IEEE double precision on the Worker and in the browser. Resistance, inductance, and frequency must each be non-negative; any strictly negative value is rejected as invalid_input for this passive series RL model. On success the response echoes rounded R and resistance, L and inductance, f and frequency; sets XL and inductive_reactance to the same non-negative ohm value; sets Z and impedance_magnitude to the impedance magnitude in ohms; sets phase_rad, phase_deg, and phase_angle_deg for the lag angle; sets omega and angular_frequency to two pi f in rad/s; formula to the combined |Z| and phase identity; equation to a human-readable substitution line; unit labels for Z, XL, R, L, f, omega, and phase; message to a short English summary; and steps to an ordered array covering given values, omega, XL, magnitude, phase, and summary. Failed validation—missing fields, non-numeric strings, non-finite numbers, values outside absolute limits, negative R, L, or f, or a non-finite result—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item.
Practical tips, limits, and related searches
When teaching, pair examples: R equals one hundred ohms, L equals zero point one henry, f equals fifty hertz yields XL about thirty-one point four ohms and |Z| a little above one hundred ohms; setting f to zero correctly returns |Z| equals R and phase zero; and a negative frequency demonstrates the hard invalid_input path. This landing targets people searching for a series RL impedance calculator, |Z| magnitude and phase of resistor plus inductor, or AC impedance of series RL online; it is not a pure inductive-reactance-only tool (that is a separate XL equals two pi f L landing), not an RL time-constant tau equals L over R calculator, not an RL filter cutoff finder, and not a parallel RL or full RLC resonance solver. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set frequency negative.
Integration use cases
Unit tests for AC circuit solvers
Generate known-good series RL impedance cases plus deliberate negative-input rejections for coding kata expected values.
Technical questions
How is series RL impedance calculated?
XL = 2πfL, then |Z| = sqrt(R² + XL²) and phase φ = atan2(XL, R). Send non-negative R (Ω), L (H), and f (Hz); the API returns magnitude, phase in rad and deg, XL, and steps.
What happens when frequency is negative?
Negative frequency is outside this model. The tool returns invalid_input instead of taking an absolute value or inventing a signed reactance.
Does zero frequency mean |Z| equals R?
Yes. At DC (f = 0) XL = 0, so |Z| = R and the phase angle is zero for any non-negative R.
Is this the same as inductive reactance alone?
No. Pure XL = 2πfL ignores the series resistor. This calculator includes R and returns full |Z| and phase for the series combination.