AM modulation index calculator
A 2 V message on a 5 V carrier gives a modulation index of 0.4, or 40 %. Enter both peak amplitudes in the same unit to see whether an AM signal is undermodulated, at 100 % or overmodulated. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Message amplitude
- 2
- Carrier amplitude
- 5
- Modulation index
- 0.4
- Modulation percent
- 40
- Kind
- under
- Expression
- m = 2 / 5 = 0.4
Amplitude modulation writes a low-frequency message onto a radio-frequency carrier by scaling the carrier envelope with the message waveform. The modulation index is the dimensionless ratio of those two peak amplitudes: m equals Am divided by Ac. Broadcast engineers, amateur-radio operators, and students of analog communications need that number because it decides whether the envelope stays undistorted (m at most one) or folds into overmodulation (m greater than one). This calculator accepts the message amplitude and the carrier amplitude in any consistent voltage or current unit, returns the index together with the equivalent percentage, and rejects a zero or negative carrier because division by a non-positive carrier is undefined.
What the AM modulation index means and how m = Am / Ac is defined
The amplitude-modulated wave written in every analog-communications textbook is the carrier peak Ac multiplied by one plus m times a normalised message, then multiplied by the carrier cosine. Rearranging the envelope shows that m is simply the ratio of the message peak Am to the carrier peak Ac: m equals Am over Ac.
That ratio is dimensionless because both amplitudes share the same physical unit — volts with volts, millivolts with millivolts — so a two-volt message on a five-volt carrier is the same index as a two-millivolt message on a five-millivolt carrier. When m is zero the carrier is unmodulated and the sidebands vanish. When m sits strictly between zero and one the envelope never reaches zero and an envelope detector recovers the message without folding.
When m equals one the envelope just touches zero at the troughs: that is one-hundred-percent or critical modulation, the largest index that still avoids overmodulation distortion. When m exceeds one the mathematical envelope would go negative, which a physical carrier cannot do, so the troughs clip, extra harmonics appear, and adjacent-channel splatter grows.
Oscilloscope users sometimes compute an equivalent index from the envelope maximum and minimum as (Amax minus Amin) over (Amax plus Amin); that identity matches Am over Ac only when Amax equals Ac plus Am and Amin equals Ac minus Am. This landing evaluates the two-amplitude form, not the envelope-extrema form, and it does not synthesise a time-domain waveform, estimate occupied bandwidth, or convert between power in watts and peak voltage.
Frequency modulation, phase modulation, and pulse-code modulation answer different search intents and belong on separate landings so this page stays focused on the AM index m equals Am over Ac.
The two amplitudes you enter and the result
Both magnitudes must use the same physical unit because the ratio is unitless only when the units match; the calculator does not convert millivolts to volts for you. Numeric values and numeric strings are both accepted so form widgets and spreadsheet paste stay convenient. A negative message amplitude is rejected because peak amplitude is a magnitude, not a signed instantaneous sample.
A message of zero is valid and returns modulation index zero, the unmodulated-carrier case. Classic classroom checks include two volts of message on five volts of carrier for an index of zero point four (forty percent), equal amplitudes for critical modulation of one, and a message larger than the carrier for overmodulation. Wire the free browser form for homework and quick sanity checks, then call the identical contract from scripts when you need bulk answer keys.
What you can do with it
Communications lab and oscilloscope drills
Convert measured message and carrier peaks into the dimensionless index m = Am/Ac so students complete AM tables and match envelope sketches to percent modulation.
Broadcast and amateur transmitter checks
Turn two probe amplitudes into a modulation index and percentage to flag overmodulation before adjacent-channel splatter or a licensed ceiling is breached.
FAQ
What formula does this modulation index calculator use?
m = Am / Ac, the dimensionless ratio of the message (modulating) peak amplitude to the carrier peak amplitude. The equivalent percentage is 100·m. Both amplitudes must use the same unit.
What does overmodulation mean for the returned index?
When Am is larger than Ac the index is greater than one.
Do message and carrier amplitudes need the same units?
Yes. The ratio is dimensionless only when both magnitudes share the same unit (V with V, mV with mV). Convert both sides first if your probes disagree.
What does the modulation index calculator cost?
The browser tool is free and runs locally.
What does a modulation index of exactly 1 mean?
It is 100 % or critical modulation: the envelope just touches zero at its troughs. It is the largest index that still avoids overmodulation distortion; anything above it makes the troughs clip.
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/modulation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"message_amplitude":2,"carrier_amplitude":5}'const res = await fetch("https://api.kit.forhosting.com/phys/modulation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"message_amplitude": 2,
"carrier_amplitude": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/modulation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"message_amplitude": 2,
"carrier_amplitude": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/modulation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"message_amplitude":2,"carrier_amplitude":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"message_amplitude":2,"carrier_amplitude":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/modulation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"message_amplitude": 2,
"carrier_amplitude": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.modulation",
"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
Input contract, response fields, units, and error behaviour
POST a JSON body with two required finite numbers: message_amplitude, the peak of the modulating signal Am, and carrier_amplitude, the peak of the unmodulated carrier Ac. Message amplitude is also accepted under the aliases am, Am, modulating_amplitude, or A_m, and carrier amplitude under ac, Ac, carrier, or A_c, but only one key may appear for each quantity. The carrier must be strictly greater than zero: a zero or negative carrier amplitude fails with invalid_input because m equals Am over Ac is undefined when the denominator is not positive, and those failures are not billed. Missing fields, conflicting aliases, NaN, and Infinity fail the same way. On success the response includes cleaned message_amplitude and carrier_amplitude, modulation_index as the dimensionless ratio, modulation_percent as one hundred times that ratio, kind as unmodulated, under, critical, or over, the boolean is_overmodulated, a short expression string showing the division with numbers, method am_modulation_index, and the formula string m equals Am over Ac. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where AM modulation-index calculations show up in real work
Introductory communications labs constantly assign envelope sketches so students can move between a pair of peak readings on an oscilloscope and the datasheet modulation index without mixing AM with frequency-modulation deviation. AM broadcast transmitters are licensed with a maximum modulation percentage; converting two probe amplitudes into m keeps the legal envelope honest and flags overmodulation before the adjacent channel fills with splatter. Amateur-radio operators tuning an AM or double-sideband transmitter watch the same ratio so the carrier is fully used without flattening the troughs. Incoming inspection of AM exciters and modulators uses the same closed form as a pass-fail gate against a licensed or contractual ceiling such as ninety-five or one hundred percent. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance. The browser tool is free for interactive use; scripted API traffic uses prepaid KIT balance at the published rate without hidden per-field surcharges.
Integration use cases
CI fixtures and homework answer keys
Script the same m = Am/Ac product used in the browser so automated graders share one ground truth for under, critical, and over-modulation cases.
Technical questions
What happens if the carrier amplitude is zero or negative?
The request fails with invalid_input. Division by a non-positive carrier is undefined, so carrier_amplitude must be strictly greater than zero. Those failures are not billed.