Documentation sections

Rectangular Waveguide Cutoff Frequency Calculator

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

Slug waveguide-cutoff. Calculate rectangular waveguide cutoff frequencies for TE and TM modes, guide wavelength, and phase/group velocity. Enter dimensions and mode numbers. 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 waveguide-cutoff
Name	Unit	Range	Default	Description
widthnumber	mm	0.1 … 1000	22.86	Waveguide Width
heightnumber	mm	at least 0.1	10.16	Waveguide Height
frequencynumber	GHz	0.1 … 1000	10	Operating Frequency
modeMnumber	none	0 … 5	1	Mode Index m
modeNnumber	none	0 … 5	0	Mode Index n

Outputs

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

Outputs of waveguide-cutoff
Field	Unit	Description
cutoffFreqheadline	GHz	Cutoff Frequency
guideWavelength	mm	Guide Wavelength
phaseVelocity	×c	Phase Velocity
groupVelocity	×c	Group Velocity
betaPropagates	(1=yes)	Propagating

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": "waveguide-cutoff",
    "inputs": {
      "width": 22.86,
      "height": 10.16,
      "frequency": 10,
      "modeM": 1,
      "modeN": 0
    }
  }'

import rftools

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

result = client.calculate("waveguide-cutoff", {
    "width": 22.86,
    "height": 10.16,
    "frequency": 10,
    "modeM": 1,
    "modeN": 0,
})
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": "waveguide-cutoff",
    "inputs": {
      "width": 22.86,
      "height": 10.16,
      "frequency": 10,
      "modeM": 1,
      "modeN": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "waveguide-cutoff",
	  "inputs": {
	    "width": 22.86,
	    "height": 10.16,
	    "frequency": 10,
	    "modeM": 1,
	    "modeN": 0
	  }
	}`)
	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": "waveguide-cutoff",
  "values": {
    "cutoffFreq": 6.557140376202975,
    "guideWavelength": 39.70711921111211,
    "phaseVelocity": 1.324486929257977,
    "groupVelocity": 0.7550093382652211,
    "betaPropagates": 1
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:waveguide-cutoff",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Pozar, Microwave Engineering 4th Ed., Chapter 3",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "width": {
          "min": 0.1,
          "max": 1000,
          "unit": "mm"
        },
        "height": {
          "min": 0.1,
          "max": null,
          "unit": "mm"
        },
        "frequency": {
          "min": 0.1,
          "max": 1000,
          "unit": "GHz"
        },
        "modeM": {
          "min": 0,
          "max": 5,
          "unit": ""
        },
        "modeN": {
          "min": 0,
          "max": 5,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "width": 22.86,
      "height": 10.16,
      "frequency": 10,
      "modeM": 1,
      "modeN": 0
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "width"
      ],
      "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 pageRectangular Waveguide Cutoff Frequency Calculator, at these values