Documentation sections

Monopole / Whip Antenna Calculator

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

Slug monopole-antenna. Input impedance, radiation resistance and directivity of a monopole or whip over a ground plane at any height, from the induced-EMF model by image theory, plus the quarter-wave length and the base-loading inductance a short whip needs.

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 monopole-antenna
Name	Unit	Range	Default	Description
frequencynumber	MHz	0.1 … 30000	146	Operating frequency
heightnumber	mm	0.1 … 1000000	500	Height of the vertical element above the ground plane
conductorDiameternumber	mm	at least 0.01	2	Diameter of the whip; it sets the reactance away from resonance
velocityFactornumber	none	0.5 … 1	0.95	Shortens the quarter-wave cutting length only; the impedance model uses free space

Outputs

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

Outputs of monopole-antenna
Field	Unit	Description
inputResistanceheadline	Ω	Input Resistance
inputReactance	Ω	Input Reactance
radiationResistance	Ω	Radiation Resistance (current maximum)
directivityDbi	dBi	Directivity
loadingInductance	µH	Base-Loading Inductance
quarterWaveLength	mm	Quarter-Wave Length
electricalHeight	none	Electrical Height

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": "monopole-antenna",
    "inputs": {
      "frequency": 146,
      "height": 500,
      "conductorDiameter": 2,
      "velocityFactor": 0.95
    }
  }'

import rftools

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

result = client.calculate("monopole-antenna", {
    "frequency": 146,
    "height": 500,
    "conductorDiameter": 2,
    "velocityFactor": 0.95,
})
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": "monopole-antenna",
    "inputs": {
      "frequency": 146,
      "height": 500,
      "conductorDiameter": 2,
      "velocityFactor": 0.95
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "monopole-antenna",
	  "inputs": {
	    "frequency": 146,
	    "height": 500,
	    "conductorDiameter": 2,
	    "velocityFactor": 0.95
	  }
	}`)
	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": "monopole-antenna",
  "values": {
    "inputResistance": 33.84234991550575,
    "inputReactance": 7.140373716590908,
    "radiationResistance": 33.78596454256399,
    "directivityDbi": 5.139463064343217,
    "loadingInductance": 0,
    "quarterWaveLength": 487.6760875,
    "electricalHeight": 0.24350178949465098
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:monopole-antenna",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Balanis, Antenna Theory, 4th ed. (2016), §4.5, §4.7 and §8.5; Stutzman & Thiele, Antenna Theory and Design, 3rd ed. (2012)",
    "assumptions": [
      {
        "code": "perfect-infinite-ground",
        "text": "The ground plane is perfectly conducting and infinite; radials, finite ground planes and lossy earth are not modelled."
      },
      {
        "code": "sinusoidal-current",
        "text": "Induced-EMF model with a sinusoidal current on a thin, lossless wire; the feed gap is not modelled."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.1,
          "max": 30000,
          "unit": "MHz"
        },
        "height": {
          "min": 0.1,
          "max": 1000000,
          "unit": "mm"
        },
        "conductorDiameter": {
          "min": 0.01,
          "max": null,
          "unit": "mm"
        },
        "velocityFactor": {
          "min": 0.5,
          "max": 1,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 146,
      "height": 500,
      "conductorDiameter": 2,
      "velocityFactor": 0.95
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "frequency"
      ],
      "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 pageMonopole / Whip Antenna Calculator, at these values