Helical coil inductance calculator
Ten turns on a 0.0254 m radius spread over 0.0508 m, a 1-inch by 2-inch air coil, give 3.44827586207 µH. Enter turns, radius and length in metres to size an air-core choke or check a physics answer in henries. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Turns
- 10
- Radius
- 0.0254
- Length
- 0.0508
- Inductance
- 0.0000034483 H
- Inductance uh
- 3.4482758621
This helical coil inductance calculator returns the inductance of a single-layer air-core helical winding in henries from three geometry values: the number of turns, the mean coil radius in metres, and the axial coil length in metres. It applies Wheeler's 1928 closed form for a helical solenoid, converting SI metres into the inch-based original so the result is a true henry rather than a leftover microhenry you still have to scale by hand. The engine is fully deterministic: it insists that the turn count is a positive integer, rejects a non-positive radius or length, and never calls a network, a clock, or a random generator.
What Wheeler's helical-coil formula means
Model the winding as a single-layer circular helix of N closely spaced turns, mean radius r, and axial length l, sitting in air or vacuum so the relative permeability is one. The long-solenoid textbook limit L equals mu zero times N squared times pi r squared over l is recovered only when the coil is much longer than it is wide; Wheeler's extra nine-r term is the finite-length correction that keeps a short helical coil from being wildly overestimated.
Inductance therefore grows with the square of the turns and with the square of the radius, and it falls as the winding is stretched along its axis: doubling N quadruples L, doubling r more than quadruples L because r also sits in the denominator, and stretching l reduces L. A vanishing or reversed length is not a physical helix in this model, and a fractional turn count is not a winding, so those cases fail instead of emitting infinity or a silent empty result.
Where helical coil inductance is useful
Classrooms and tutoring platforms use a helical coil inductance calculator so learners can check henry results for arbitrary N, r, and l without converting inches by hand and without mixing microhenries with henries. Exam-prep generators need a deterministic oracle that marks wrong a non-integer turn count instead of silently rounding three-point-seven turns into four. Radio amateurs and radio-frequency technicians size air-core chokes and matching coils with this analytic baseline before cutting wire or running a method-of-moments extractor.
Failed validation does not consume balance. Keep requests in SI metres end to end, convert millimetre drawings to metres before calling, and pin the henry value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up a magnetostatics solver of your own. Closely spaced turns, a circular former, and an air core remain the assumptions: multilayer pies, ferrite cores, and square formers stay outside Wheeler's original range, so treat the number as the classic helical baseline rather than a three-dimensional extraction.
What you can do with it
Air-core RF choke and matching-coil estimates
Size a single-layer helical winding with Wheeler's closed form before cutting wire or running a full electromagnetic extractor.
FAQ
How do I compute the inductance of a helical coil?
Send a positive integer turns N, mean radius r in metres, and axial length l in metres.
What happens if the number of turns is not a positive integer?
Zero, negative, and fractional turn counts are not a physical winding in this model and are not billed.
Does this model ferrite cores or multilayer windings?
No. It is Wheeler's single-layer air-core helix. Ferrite, powdered iron, square formers, and multilayer pies need a different extractor.
How do the turns and the radius change the inductance?
Doubling the number of turns quadruples the inductance, and doubling the radius more than quadruples it. Stretching the same winding over a longer length lowers the inductance.
Why not just use the long-solenoid formula?
Because it only holds when the coil is much longer than it is wide. Wheeler's formula adds a correction for finite length, so a short coil is not wildly overestimated.
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/helical-coil \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"turns":10,"radius":0.0254,"length":0.0508}'const res = await fetch("https://api.kit.forhosting.com/phys/helical-coil", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"turns": 10,
"radius": 0.0254,
"length": 0.0508
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/helical-coil",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"turns": 10,
"radius": 0.0254,
"length": 0.0508
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/helical-coil", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"turns":10,"radius":0.0254,"length":0.0508}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"turns":10,"radius":0.0254,"length":0.0508}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/helical-coil", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"turns": 10,
"radius": 0.0254,
"length": 0.0508
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.helical_coil",
"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_turns | 1000000 |
max_abs_radius | 1000 |
max_abs_length | 1000 |
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 Wheeler's helical-coil formula means
Wheeler's 1928 formula, still the workhorse for radio coils and student solenoids, states that inductance in microhenries is r_in squared times N squared, divided by nine r_in plus ten l_in, where both r_in and l_in are inches. This calculator accepts SI metres, divides each length by 0.0254, evaluates that expression, and multiplies by ten to the minus six so the published unit is the henry. The payload echoes the three inputs, reports inductance in henries and in microhenries, and tags the method as Wheeler helical so a notebook can cite the formula next to the number.
Input contract, response shape, and error behaviour
Radius and length must be strictly positive: a zero or negative dimension would make the Wheeler denominator non-physical or would describe a collapsed winding. Magnitude ceilings keep pathological kilometre-scale coils from overflowing isolate arithmetic while still covering classroom centimetre coils and ordinary millimetre-scale radio-frequency chokes. POST a JSON body with three required fields: turns, a positive integer N; radius, the mean coil radius in metres; and length, the axial winding length in metres. Radius and length may arrive as JSON numbers or as numeric strings; turns may arrive as an integer or as a digit string, but not as a fraction, not as zero, and not as a negative value. Aliases N, n and turns_count, r and coil_radius, and l and coil_length are accepted so lab notebooks and CAD exports map without renaming columns. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes turns, radius, and length, reports inductance in henries, reports inductance_uh in microhenries for radio-frequency work, and includes formula, method wheeler_helical, and unit H. Pair the response with your own circuit equations if you next need inductive reactance or stored energy; this endpoint computes geometric inductance only and does not emit plots, SPICE netlists, or a Nagaoka coefficient table.
Integration use cases
Homework and exam checks
Enter turns, mean radius, and axial length, compare henry results with hand work, and get a clear invalid_input when N is not a positive integer.
Notebooks and lab fixtures
Pin a reproducible L in henries from N, r, and l in calibration scripts without importing a magnetostatics library.
Technical questions
Are radius and length in metres or inches?
Inputs are SI metres. The original Wheeler formula is inch-based; the calculator converts internally (1 in = 0.0254 m) and still returns henries.
What does the helical coil inductance calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.