Documentation sections

Coaxial Cable Impedance Calculator

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

Slug coax-impedance. Calculate coaxial cable characteristic impedance (Z0), capacitance, inductance per meter, and TE11 cutoff frequency from conductor dimensions. 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 coax-impedance
Name	Unit	Range	Default	Description
innerDiameternumber	mm	0.01 … 100	0.9	Outer diameter of the inner conductor
outerDiameternumber	mm	0.1 … 200	2.95	Inner diameter of the outer conductor (shield)
dielectricConstantnumber	none	1 … 20	2.2	Relative permittivity of the insulating dielectric between conductors
frequencynumber	GHz	0.001 … 300	2.4	Used only for the guided wavelength; the impedance does not depend on it in this model

Outputs

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

Outputs of coax-impedance
Field	Unit	Description
impedanceheadline	Ω	Characteristic impedance of the coaxial cable
capacitancePFm	pF/m	Distributed capacitance per meter of cable length
inductanceNHm	nH/m	Distributed inductance per meter of cable length
velocityFactor	none	Signal propagation speed as fraction of speed of light (1/sqrt(εᵣ))
cutoffFreqGHz	GHz	Frequency above which higher-order modes can propagate (TE11 mode)
guidedWavelength	mm	Guided Wavelength
quarterWavelength	mm	Quarter Wavelength

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": "coax-impedance",
    "inputs": {
      "innerDiameter": 0.9,
      "outerDiameter": 2.95,
      "dielectricConstant": 2.2,
      "frequency": 2.4
    }
  }'

import rftools

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

result = client.calculate("coax-impedance", {
    "innerDiameter": 0.9,
    "outerDiameter": 2.95,
    "dielectricConstant": 2.2,
    "frequency": 2.4,
})
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": "coax-impedance",
    "inputs": {
      "innerDiameter": 0.9,
      "outerDiameter": 2.95,
      "dielectricConstant": 2.2,
      "frequency": 2.4
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "coax-impedance",
	  "inputs": {
	    "innerDiameter": 0.9,
	    "outerDiameter": 2.95,
	    "dielectricConstant": 2.2,
	    "frequency": 2.4
	  }
	}`)
	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": "coax-impedance",
  "values": {
    "impedance": 47.98999377849511,
    "capacitancePFm": 103.09555569337834,
    "inductanceNHm": 237.43313733116378,
    "velocityFactor": 0.674199862463242,
    "cutoffFreqGHz": 33.42171688438652,
    "guidedWavelength": 84.21668081296554,
    "quarterWavelength": 21.054170203241384
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:coax-impedance",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Pozar, Microwave Engineering, 4th ed. (2011), §2.2 and §3.5; CODATA 2018; Wadell, \"Transmission Line Design Handbook\" 1991, Chapter 3",
    "assumptions": [
      {
        "code": "codata-2018-constants",
        "text": "Z₀, C′ and L′ use the CODATA 2018 µ₀ and ε₀ and the exact speed of light, so Z₀ = (η₀/2π)·ln(D/d)/√εr equals √(L′/C′); the line is a lossless TEM coaxial line."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "innerDiameter": {
          "min": 0.01,
          "max": 100,
          "unit": "mm"
        },
        "outerDiameter": {
          "min": 0.1,
          "max": 200,
          "unit": "mm"
        },
        "dielectricConstant": {
          "min": 1,
          "max": 20,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": 300,
          "unit": "GHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "innerDiameter": 0.9,
      "outerDiameter": 2.95,
      "dielectricConstant": 2.2,
      "frequency": 2.4
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "innerDiameter"
      ],
      "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 pageCoaxial Cable Impedance Calculator, at these values