Documentation sections

AM Modulation Index Calculator

POSThttps://rftools.io/api/py/v1/calculate

Slug am-modulation-index. Calculate AM modulation index: m = (Amax − Amin) / (Amax + Amin). Computes sideband amplitudes, bandwidth (2 × fm), power efficiency, and flags overmodulation (m > 1).

Inputs

Send every one of these in inputs, in the units shown. Most are required: a call without one is refused (400) and costs nothing; one the calculator can do without takes the default shown. An input outside its range is still computed and flagged in the provenance.

Inputs of am-modulation-index
Name	Unit	Range	Default	Description
carrierAmplitudenumber	V	at least 0.001	1	Peak amplitude of the carrier signal
messageAmplitudenumber	V	at least 0	0.5	Peak amplitude of the modulating signal
carrierFreqnumber	kHz	at least 0.001	1000	Carrier signal frequency (e.g. 1000 kHz = 1 MHz AM band)
messageFreqnumber	kHz	at least 0.001	1	Modulating signal (audio) frequency
channelWidthnumber	kHz	at least 0.001	10	The channel the emission must fit, centred on the carrier: 10 kHz on the 47 CFR 73.14 raster (540 to 1700 kHz in 10 kHz steps), 9 kHz where the GE75 plan puts carriers on multiples of 9 kHz

Outputs

Returned in values, by key. A value that is unbounded or undefined is null.

Outputs of am-modulation-index
Field	Unit	Description
modulationIndexheadline	%	100% = full modulation; >100% causes overmodulation distortion
upperSideband	kHz	Upper Sideband (USB)
lowerSideband	kHz	Lower Sideband (LSB)
bandwidth	kHz	Bandwidth
powerEfficiency	%	Power Efficiency
sidebandsToCarrier	dB	Sideband / Carrier Ratio
powerInChannel	%	The share of the emission's power inside the channel. The occupied bandwidth leaves 0.5 % on each side (ITU Radio Regulations No. 1.153), so below 99 % it does not fit the channel
sidebandsInChannel	none	Sidebands inside the channel, where they belong
sidebandsOutside	none	Sidebands outside the channel, in the adjacent one: the message is wider than half the channel

Calling it

Calculate: one call, the request and response in full, and its errors.
Batch: this calculator with others, or a sweep, in one request.
Solve for a target: the value of one input that brings an output to a target.

curl -X POST https://rftools.io/api/py/v1/calculate \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "am-modulation-index",
    "inputs": {
      "carrierAmplitude": 1,
      "messageAmplitude": 0.5,
      "carrierFreq": 1000,
      "messageFreq": 1,
      "channelWidth": 10
    }
  }'

import rftools

client = rftools.Client()  # reads RFTOOLS_API_KEY, or the key `rftools login` saved

result = client.calculate("am-modulation-index", {
    "carrierAmplitude": 1,
    "messageAmplitude": 0.5,
    "carrierFreq": 1000,
    "messageFreq": 1,
    "channelWidth": 10,
})
print(result.values)
print(result.warnings, result.provenance.formula_ref)

const response = await fetch("https://rftools.io/api/py/v1/calculate", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "am-modulation-index",
    "inputs": {
      "carrierAmplitude": 1,
      "messageAmplitude": 0.5,
      "carrierFreq": 1000,
      "messageFreq": 1,
      "channelWidth": 10
    }
  }),
});
console.log(response.status, await response.json());

package main

import (
	"bytes"
	"fmt"
	"io"
	"net/http"
	"os"
)

func main() {
	body := []byte(`{
	  "slug": "am-modulation-index",
	  "inputs": {
	    "carrierAmplitude": 1,
	    "messageAmplitude": 0.5,
	    "carrierFreq": 1000,
	    "messageFreq": 1,
	    "channelWidth": 10
	  }
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate", bytes.NewReader(body))
	if err != nil {
		panic(err)
	}
	req.Header.Set("X-API-Key", os.Getenv("RFTOOLS_API_KEY"))
	req.Header.Set("Content-Type", "application/json")
	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()
	out, _ := io.ReadAll(res.Body)
	fmt.Println(res.Status, string(out))
}

application/json

{
  "slug": "am-modulation-index",
  "values": {
    "modulationIndex": 50,
    "upperSideband": 1001,
    "lowerSideband": 999,
    "bandwidth": 2,
    "powerEfficiency": 11.11111111111111,
    "sidebandsToCarrier": -12.041199826559248,
    "powerInChannel": 100,
    "sidebandsInChannel": 2,
    "sidebandsOutside": 0
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:am-modulation-index",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "carrierAmplitude": {
          "min": 0.001,
          "max": null,
          "unit": "V"
        },
        "messageAmplitude": {
          "min": 0,
          "max": null,
          "unit": "V"
        },
        "carrierFreq": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "messageFreq": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "channelWidth": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "carrierAmplitude": 1,
      "messageAmplitude": 0.5,
      "carrierFreq": 1000,
      "messageFreq": 1,
      "channelWidth": 10
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "carrierAmplitude"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

An input sent as text. Nothing was counted.

{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

Too many requests in a minute, with Retry-After.

Same inputs on the calculator pageAM Modulation Index Calculator, at these values