ForHosting KIT · Developer Utilities

Coupling coefficient calculator

This coupling coefficient calculator determines how strongly two coils are magnetically linked.

● BetaFree · in your browser

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Enter their mutual inductance and each coil's self inductance in the same unit, and it applies k = M / sqrt(L1 × L2). The result is a dimensionless coefficient from zero to one, accompanied by the equivalent percentage for quick interpretation. It is useful when checking transformer measurements, comparing winding arrangements, characterizing coupled inductors, evaluating laboratory prototypes, or validating measured values before circuit simulation and design review.

What the coupling coefficient tells you

The coupling coefficient describes the fraction of magnetic flux from one coil that links the other coil. A value near zero indicates weak magnetic interaction, while a value near one indicates that nearly all relevant flux is shared. Because the coefficient is a ratio, it has no unit and can be compared across components of very different sizes. This calculator uses the magnitude of mutual inductance, so its output focuses on coupling strength rather than winding polarity. Dot convention and winding orientation can give mutual inductance a sign in circuit equations, but that sign does not change the magnitude of the physical linkage. The returned percentage is simply the coefficient multiplied by one hundred. It can make comparisons easier to communicate, but the dimensionless coefficient is the value normally entered in circuit models. Real coils exhibit leakage flux, so perfect coupling is an ideal limit rather than the usual measured result.

How to enter inductance values correctly

Provide mutual inductance M and the two self inductances L1 and L2 using the same inductance unit. Henries are suggested in the field descriptions, but millihenries or microhenries also work when all three numbers share that unit, because the units cancel in the ratio. Do not mix 6 millihenries with 0.01 henry unless you first convert them to a common scale. Both self inductances must be positive, and mutual inductance may be zero. For a passive pair of coils, the magnitude of M cannot be greater than the geometric mean sqrt(L1 × L2). The calculator rejects a larger value because it would imply a coupling coefficient above one and usually signals a unit conversion, transcription, or measurement error. Use measured values taken under compatible test conditions. Frequency, nearby magnetic material, core position, and instrument setup can affect observed inductance, so combining figures from unrelated conditions may produce a mathematically valid but experimentally misleading result.

Interpreting and applying the result

Use the calculated coefficient as an input to transformer, coupled-inductor, resonant-link, and wireless-power models. For example, M = 6 mH, L1 = 10 mH, and L2 = 40 mH gives a coefficient of 0.3, or 30 percent. That number measures magnetic linkage; it is not efficiency. Copper resistance, core loss, switching loss, load matching, frequency, and geometry can all reduce power-transfer efficiency even when coupling is strong. Conversely, a design with modest coupling can still be useful when its resonant network and load are chosen appropriately. When comparing prototypes, keep the measurement method and frequency consistent and track k alongside resistance and quality factor. The deterministic calculation is also suitable for automated validation: a test system can send measured inductances, store the returned coefficient, and flag values outside an engineering tolerance. API requests cost $0.002, while the same arithmetic can be run in the browser without network-dependent computation.

What you can do with it

Characterize a transformer prototype

Convert measured mutual and self inductances into a comparable coupling value before evaluating leakage and loss.

Validate coupled-inductor model inputs

Check that laboratory measurements produce a physically valid coefficient before entering them into a simulator.

Compare coil placement experiments

Quantify how changes in spacing, alignment, or core position affect magnetic linkage between two coils.

FAQ

What formula does the calculator use?

It uses k = M / sqrt(L1 × L2), where M is mutual inductance and L1 and L2 are the individual self inductances.

Do all three inductance values need to be in henries?

No. Any inductance unit works as long as the same unit is used for all three values.

Why must the coupling coefficient be between zero and one?

For a passive coil pair, mutual inductance magnitude cannot exceed the geometric mean of the two self inductances. A larger result usually indicates inconsistent units or measurements.

Is coupling coefficient the same as efficiency?

No. Coupling measures magnetic linkage, while efficiency also depends on winding resistance, core loss, frequency, load matching, and other circuit losses.

What does the API request cost?

Each API request costs $0.002. The calculation is also available through the browser experience.

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

POSThttps://api.kit.forhosting.com/elec/coupling-coefficient

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/coupling-coefficient \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"mutual_inductance":0.006,"self_inductance_1":0.01,"self_inductance_2":0.04}'

const res = await fetch("https://api.kit.forhosting.com/elec/coupling-coefficient", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "mutual_inductance": 0.006,
    "self_inductance_1": 0.01,
    "self_inductance_2": 0.04
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/elec/coupling-coefficient",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "mutual_inductance": 0.006,
    "self_inductance_1": 0.01,
    "self_inductance_2": 0.04
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/coupling-coefficient", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"mutual_inductance":0.006,"self_inductance_1":0.01,"self_inductance_2":0.04}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"mutual_inductance":0.006,"self_inductance_1":0.01,"self_inductance_2":0.04}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/coupling-coefficient", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "mutual_inductance": 0.006,
  "self_inductance_1": 0.01,
  "self_inductance_2": 0.04
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "elec.coupling_coefficient",
  "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

Per request$0.002

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.

Read the full KIT documentation →