Documentation sections

FM Modulation Index & Bandwidth Calculator

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

Slug fm-modulation-index. Calculate FM modulation index, Carson's rule bandwidth, and SNR improvement over AM. Determine Bessel bandwidth for FM transmitter design. Free, instant results.

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 fm-modulation-index
Name	Unit	Range	Default	Description
frequencyDeviationnumber	kHz	at least 0.001	75	Peak frequency deviation of the FM signal
messageFreqnumber	kHz	at least 0.001	15	Highest modulating signal frequency
channelLownumber	kHz	at least 0	98000	Where the channel the emission must fit begins; the carrier sits at its centre. FM broadcast channels are 200 kHz wide, 88.1 to 107.9 MHz (47 CFR 73.201)
channelHighnumber	kHz	at least 0	98200	Where the channel ends

Retired, still accepted and ignored with a warning: carrierFreq (Carrier Frequency, 2026-10-12).

Outputs

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

Outputs of fm-modulation-index
Field	Unit	Description
modulationIndexheadline	none	Modulation Index (β)
carsonBandwidth	kHz	Carson's Rule Bandwidth
besselBandwidth	kHz	The span of the sidebands above 1 % of the unmodulated carrier, 2·n·f_m with n the highest such order (Haykin, Communication Systems)
snrImprovement	dB	FM SNR improvement over AM: 10·log₁₀(3β²(β+1))
occupiedBandwidth	kHz	The narrowest span of sidebands, the same on each side, holding 99 % of the power, 0.5 % left on each side (ITU Radio Regulations No. 1.153)
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 above 1 % of the unmodulated carrier inside the channel
sidebandsOutside	none	Sidebands above 1 % of the unmodulated carrier outside the channel: check them against the emission mask that applies

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": "fm-modulation-index",
    "inputs": {
      "frequencyDeviation": 75,
      "messageFreq": 15,
      "channelLow": 98000,
      "channelHigh": 98200
    }
  }'

import rftools

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

result = client.calculate("fm-modulation-index", {
    "frequencyDeviation": 75,
    "messageFreq": 15,
    "channelLow": 98000,
    "channelHigh": 98200,
})
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": "fm-modulation-index",
    "inputs": {
      "frequencyDeviation": 75,
      "messageFreq": 15,
      "channelLow": 98000,
      "channelHigh": 98200
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "fm-modulation-index",
	  "inputs": {
	    "frequencyDeviation": 75,
	    "messageFreq": 15,
	    "channelLow": 98000,
	    "channelHigh": 98200
	  }
	}`)
	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": "fm-modulation-index",
  "values": {
    "modulationIndex": 5,
    "carsonBandwidth": 180,
    "besselBandwidth": 240,
    "snrImprovement": 26.532125137753436,
    "occupiedBandwidth": 180,
    "powerInChannel": 99.35588993208525,
    "sidebandsInChannel": 12,
    "sidebandsOutside": 4
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:fm-modulation-index",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequencyDeviation": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "messageFreq": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "channelLow": {
          "min": 0,
          "max": null,
          "unit": "kHz"
        },
        "channelHigh": {
          "min": 0,
          "max": null,
          "unit": "kHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequencyDeviation": 75,
      "messageFreq": 15,
      "channelLow": 98000,
      "channelHigh": 98200
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "frequencyDeviation"
      ],
      "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 pageFM Modulation Index & Bandwidth Calculator, at these values