Inductance from reactance calculator
A reactance of 31.416 Ω at 50 Hz calls for a coil of about 0.1 H. Enter the ohms your design needs and the signal frequency, and the calculator divides by two pi times f to give the inductance in henries. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- XL
- 31.4159265359
- F
- 50
- Inductive reactance
- 31.4159265359
- Frequency
- 50
- L
- 0.1
- Inductance
- 0.1
An inductance from reactance calculator turns a target inductive reactance and a chosen signal frequency into the coil inductance that produces that reactance. Reactance must be non-negative for this passive inductor model.
What L = XL / (2 π f) means for coil sizing
In elementary AC circuit theory, an ideal inductor of inductance L henries driven by a sinusoidal source at frequency f hertz has inductive reactance XL equals two pi times f times L, measured in ohms. When the design brief already states the ohms you need at a known frequency—for example a choke that should present about thirty-one ohms at fifty hertz—you invert that identity: L equals XL divided by two pi f. Angular frequency omega equals two pi f in radians per second, so L is also XL over omega.
Doubling the target reactance doubles the required inductance; doubling frequency halves the inductance needed for the same XL. At DC the classical XL formula collapses to zero reactance for any finite L, so you cannot uniquely recover L from XL when f is zero; this tool therefore rejects non-positive frequency rather than returning infinity or an arbitrary default. Typical classroom numbers: XL about thirty-one point four ohms at fifty hertz implies L about one-tenth of a henry; the same XL at sixty hertz implies a slightly smaller coil.
Teachers and automated graders care about the zero-frequency rejection as much as the arithmetic: a student who forgets that L equals XL over two pi f needs f greater than zero has left the domain of the inverse formula.
Practical tips, limits, and related searches
Keep reactance and frequency inside the published absolute range so the quotient XL over two pi f cannot overflow into a non-finite inductance that the solver must reject. Convert millihenries by multiplying the returned L by one thousand when you need mH on a datasheet, and microhenries by one million, rather than feeding non-SI mix-ups into XL or f. Prefer this capability when you already have scalar XL and f and only need L in henries; if you know L and need XL instead, use the companion inductive reactance calculator.
Round-trip checks are easy: recompute two pi f L by hand and confirm it recovers the published XL within the same twelve-decimal rounding, and confirm that scaling XL alone scales L proportionally as the inverse formula predicts.
What you can do with it
Homework checks for L = XL/(2πf)
Students enter target XL and f from textbook inductor-sizing problems and compare hand-written L against a deterministic result before submitting.
Choke and filter coil pre-sizing
Designers pick the henries needed so a coil presents a budgeted reactance at line or switching frequency before ordering parts.
FAQ
How do I find inductance from inductive reactance?
For an ideal inductor, L = XL / (2πf) henries when XL is in ohms and f is in hertz.
What happens when frequency is zero or negative?
Zero and negative frequency are outside this inverse model.
Is the inductance from reactance calculator free?
The browser tool is free and runs locally.
How does the frequency change the inductance I need?
Inversely. For the same reactance, doubling the frequency halves the inductance required, so the 31.416 Ω that needs about 0.1 H at 50 Hz needs a slightly smaller coil at 60 Hz. Doubling the target reactance doubles the inductance.
Is this the same as the inductive reactance calculator?
No, it works the other way round. Here you start from the ohms you need and get the inductance; if you already know the inductance and want its reactance, use the inductive reactance calculator.
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/inductance-from-reactance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"XL":31.415926535898,"f":50}'const res = await fetch("https://api.kit.forhosting.com/elec/inductance-from-reactance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"XL": 31.415926535898,
"f": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/inductance-from-reactance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"XL": 31.415926535898,
"f": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/inductance-from-reactance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"XL":31.415926535898,"f":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"XL":31.415926535898,"f":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/inductance-from-reactance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"XL": 31.415926535898,
"f": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.inductance_from_reactance",
"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 | 1000000000000 |
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
Frequency must be strictly positive: zero and negative f make L equals XL over two pi f undefined or out of domain, so the API returns a clear invalid_input error instead of inventing a signed or infinite inductance.
What L = XL / (2 π f) means for coil sizing
Prefer SI throughout: convert millihenries-oriented answers yourself after the call if you want mH display, and keep XL already in ohms so comparisons stay consistent. The check path recomputes XL over two pi f with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets without floating-point ambiguity between the Worker and the browser.
How to call the API and what comes back
Negative reactance is also rejected for this passive inductor model. 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 two required finite numbers: XL (aliases reactance, inductive_reactance, xl, and ohms) for target inductive reactance in ohms, 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 quotients remain finite in IEEE double precision on the Worker and in the browser. Frequency must be strictly positive; any zero or negative f is rejected as invalid_input. On success the response echoes rounded XL and inductive_reactance, f and frequency, sets L and inductance to the same non-negative henry value, omega and angular_frequency to two pi f in rad/s, formula to the string L equals XL over two pi f, equation to a human-readable substitution line, unit_L to H, unit_XL to ohm, unit_f to Hz, unit_omega to rad/s, message to a short English summary, and steps to an ordered array of given values, formula, omega line, substitution, and summary. Failed validation—missing fields, non-numeric strings, non-finite numbers, values outside absolute limits, non-positive frequency, negative reactance, or a non-finite quotient—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
When teaching, pair examples: XL equals about thirty-one point four one six ohms with f equals fifty hertz yields L about zero point one henry; doubling XL doubles L; setting f to zero correctly returns invalid_input; and a negative reactance demonstrates the hard domain rejection path. This landing targets people searching for an inductance from reactance calculator, L equals XL over two pi f, or inductor henries from ohms and frequency online; it is not the forward inductive reactance XL equals two pi f L tool, not a capacitive reactance XC calculator, not a series R-L impedance magnitude solver, and not a resonant-frequency finder. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set frequency to zero.
Integration use cases
Unit tests for inverse AC solvers
Generate known-good L cases plus deliberate zero-frequency rejections for coding kata expected values that invert XL = 2πfL.
Technical questions
Does zero reactance mean zero inductance?
Yes. When XL = 0 and f > 0, the solver returns L = 0 for this ideal passive model.
Is this the same as the inductive reactance calculator?
No. That tool computes XL = 2πfL from known f and L. This tool inverts the formula to find L from a target XL and frequency—different search intent and input contract.