Wave Power Transmittance Calculator from Impedances
See how much wave power gets through an impedance mismatch: going from 50 to 75 gives a transmittance of 0.96, so nearly all the power continues. Equal impedances give exactly one. Free in your browser.
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Worked example
- Impedance 1
- 50
- Impedance 2
- 75
- Power transmittance
- 0.96
The wave power transmittance calculator finds the fraction of incident wave power that crosses a boundary between two media. Enter the positive real wave impedance on the incident side and the positive real wave impedance on the transmission side. The result is a dimensionless value from zero to one, where one represents complete power transmission. It is useful for quick checks in acoustics, transmission lines, and other lossless normal-incidence models where impedance mismatch controls reflection and transmission.
What the transmittance value means
Power transmittance describes how much of the incident wave power continues into the second medium at an ideal interface. A result of one means that all incident power is transmitted by this model, while a value near zero means that very little crosses the boundary. The result is a fraction, not a percentage: for example, a transmittance of 0.8 corresponds to 80 percent of incident power.
Equal impedances produce a value of one because the interface is matched and causes no reflected power in the assumed model. As the impedance mismatch grows, the transmitted fraction decreases. This calculator concerns power, so its result should not be confused with an amplitude transmission coefficient.
Amplitude and power coefficients have different meanings and may require additional impedance factors. The calculation applies to positive real impedances and an ideal, lossless boundary under the assumptions behind the standard normal-incidence formula. If your media are lossy, dispersive, anisotropic, or described by complex impedances, a more complete field or circuit analysis is required.
How the calculator uses the impedances
Both values must be finite and greater than zero. They may be expressed in ohms or in another appropriate impedance unit, but they must use the same unit because the formula depends on their ratio. The calculator evaluates four times the product of the two impedances divided by the square of their sum.
Internally, it forms an impedance ratio first, which avoids an unnecessary overflow risk when both supplied impedances are extremely large but still finite. Swapping the two impedance values gives the same power transmittance, as expected for this ideal reciprocal interface model. No rounding is imposed, so automated users receive the deterministic JavaScript numeric result rather than a display-limited approximation.
For a matched pair, use identical positive values; for a mismatch study, keep one value fixed and compare results while varying the other.
Assumptions and practical interpretation
Use this result when the interface can be represented by two positive real characteristic or wave impedances and when the familiar lossless power-balance relation is appropriate. Typical examples include a first-pass comparison of transmission-line sections, normal-incidence acoustic boundaries, and simplified electromagnetic media. The calculator does not infer impedance from density, wave speed, permittivity, permeability, geometry, or frequency; those quantities must already have been reduced to the two relevant impedances.
It also does not include propagation loss after the wave enters the second medium. Therefore, the returned fraction describes transmission at the boundary only, not the power that will remain after traveling through a lossy path. A useful consistency check is that the value must stay between zero and one for valid positive real inputs.
In the ideal lossless model, the complementary reflected power fraction is one minus the returned transmittance. The calculation is also deterministic and runs without network access, external data, stored state, random values, or time-dependent inputs.
What you can do with it
Check a transmission-line mismatch
Compare two positive real characteristic impedances to estimate the ideal fraction of power crossing their junction.
Estimate acoustic boundary transmission
Use two real acoustic impedances for a quick normal-incidence, lossless interface calculation.
Validate an engineering worksheet
Recalculate a known impedance pair with a deterministic formula and compare the dimensionless result.
FAQ
What units should I use for impedance?
Use any appropriate impedance unit, commonly ohms, as long as both values use the same unit. The returned transmittance is dimensionless.
Why is transmittance equal to one when the impedances match?
In the ideal lossless model, equal impedances eliminate the mismatch that produces reflection, so all incident power crosses the interface.
Can I enter complex impedance values?
No. This calculator accepts positive real impedances only. Complex or lossy media require a calculation that includes phase and the appropriate real power terms.
Is this an amplitude transmission coefficient?
No. It returns a power fraction. An amplitude coefficient is defined differently and should not be substituted directly for this result.
Does it matter which impedance I enter first?
No. Swapping the two values gives the same power transmittance, because this ideal boundary behaves the same in both directions. Just keep both impedances in the same unit, since only their ratio counts.
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/optics/wave-power-transmittance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"impedance_1":50,"impedance_2":75}'const res = await fetch("https://api.kit.forhosting.com/optics/wave-power-transmittance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"impedance_1": 50,
"impedance_2": 75
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/wave-power-transmittance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"impedance_1": 50,
"impedance_2": 75
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/wave-power-transmittance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"impedance_1":50,"impedance_2":75}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"impedance_1":50,"impedance_2":75}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/wave-power-transmittance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"impedance_1": 50,
"impedance_2": 75
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.wave_power_transmittance",
"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
How the calculator uses the impedances
Enter the wave impedance of the incident medium as impedance_1 and the wave impedance of the receiving medium as impedance_2. The output is returned as power_transmittance with no unit.
Assumptions and practical interpretation
For API automation, each request costs $0.002.
Technical questions
What formula does the calculator use?
It uses power_transmittance = 4 × impedance_1 × impedance_2 ÷ (impedance_1 + impedance_2)² for positive real impedances.
How much does an API calculation cost?
Each API request costs $0.002. The browser calculation is available without network-dependent computation.