Documentation sections

Nyquist Sampling Theorem Calculator

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

Slug sampling-nyquist. Calculate Nyquist sampling rate, oversampling ratio, and aliasing frequency. Verify your ADC sampling meets the Nyquist criterion and determine data rate. 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 sampling-nyquist
Name	Unit	Range	Default	Description
signalFreqnumber	Hz	1 … 1000000000	10000	Maximum frequency component in the signal (or signal bandwidth for baseband signals)
samplingRatenumber	Sa/s	1 … 1000000000000	44100	Number of samples taken per second
adcBitsnumber	bits	4 … 24	16	Number of bits in the ADC. Each additional bit adds ~6 dB of dynamic range.
channelsnumber	none	1 … 32	1	Number of parallel ADC channels (e.g., 2 for stereo, 1 for mono)
harmonicOrdernumber	none	1 … 50	5	The highest harmonic of a tone at the top of the band, as the converter's distortion makes it, that the frequency plan follows; 1 follows the tone alone

Outputs

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

Outputs of sampling-nyquist
Field	Unit	Description
nyquistRate_Hzheadline	Hz	Minimum sampling rate required to avoid aliasing (= 2 × signal bandwidth)
oversamplingRatio	none	Ratio of actual sampling rate to Nyquist rate. Values < 1 indicate aliasing.
aliasFreq_Hz	Hz	Where the signal appears once sampled below the Nyquist rate: \|f − k·f_s\| for the integer k nearest f/f_s. Zero if no aliasing.
dynamicRangeDB	dB	Theoretical dynamic range of the ADC: DR = 20·log₁₀(2)·N + 10·log₁₀(1.5) dB
snr_dB	dB	Signal-to-quantization-noise ratio for an ideal ADC at full scale
dataRateMbps	Mbps	Uncompressed raw data rate = sampling rate × ADC bits × channels
antiAliasingFC_Hz	Hz	Maximum anti-aliasing filter cutoff frequency (= fs / 2, the Nyquist frequency)
aliasesInBand	none	A tone at the top of the band that the sampling rate aliases back into the signal band: no filter after the converter can remove it
harmonicAliasesInBand	none	The harmonics of a tone at the top of the band, up to the highest harmonic, that fold back into the signal band after sampling: they matter as far as the converter's SFDR, which this page does not know
lowestAliasingInput	Hz	The lowest input frequency that folds into the signal band, f_s − f_sig (f_s/2 once the band reaches past it): the anti-alias filter must reject from here

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": "sampling-nyquist",
    "inputs": {
      "signalFreq": 10000,
      "samplingRate": 44100,
      "adcBits": 16,
      "channels": 1,
      "harmonicOrder": 5
    }
  }'

import rftools

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

result = client.calculate("sampling-nyquist", {
    "signalFreq": 10000,
    "samplingRate": 44100,
    "adcBits": 16,
    "channels": 1,
    "harmonicOrder": 5,
})
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": "sampling-nyquist",
    "inputs": {
      "signalFreq": 10000,
      "samplingRate": 44100,
      "adcBits": 16,
      "channels": 1,
      "harmonicOrder": 5
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "sampling-nyquist",
	  "inputs": {
	    "signalFreq": 10000,
	    "samplingRate": 44100,
	    "adcBits": 16,
	    "channels": 1,
	    "harmonicOrder": 5
	  }
	}`)
	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": "sampling-nyquist",
  "values": {
    "nyquistRate_Hz": 20000,
    "oversamplingRatio": 2.205,
    "aliasFreq_Hz": 0,
    "dynamicRangeDB": 98.0905112030308,
    "snr_dB": 98.0905112030308,
    "dataRateMbps": 0.7056,
    "antiAliasingFC_Hz": 22050,
    "aliasesInBand": 0,
    "harmonicAliasesInBand": 2,
    "lowestAliasingInput": 34100
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:sampling-nyquist",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Nyquist, H. (1928). \"Certain Topics in Telegraph Transmission Theory\". AIEE Transactions. Shannon-Nyquist sampling theorem.",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "signalFreq": {
          "min": 1,
          "max": 1000000000,
          "unit": "Hz"
        },
        "samplingRate": {
          "min": 1,
          "max": 1000000000000,
          "unit": "Sa/s"
        },
        "adcBits": {
          "min": 4,
          "max": 24,
          "unit": "bits"
        },
        "channels": {
          "min": 1,
          "max": 32,
          "unit": ""
        },
        "harmonicOrder": {
          "min": 1,
          "max": 50,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "signalFreq": 10000,
      "samplingRate": 44100,
      "adcBits": 16,
      "channels": 1,
      "harmonicOrder": 5
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "signalFreq"
      ],
      "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 pageNyquist Sampling Theorem Calculator, at these values