Documentation sections

Helical Antenna Calculator (Axial Mode)

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

Slug helical-antenna. Design an axial-mode helical antenna: enter frequency, turns, helix diameter, turn spacing and wire size to get directivity, half-power and first-null beamwidths, axial ratio, input resistance and pitch angle by Kraus's formulas, with warnings outside their valid range.

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 helical-antenna
Name	Unit	Range	Default	Description
frequencynumber	MHz	1 … 100000	2400	Design (centre) frequency
turnsnumber	none	1 … 100	10	Whole turns; a fraction is rounded to the nearest turn
diameternumber	mm	0.1 … 10000	40	Diameter of the helix measured to the wire centre; circumference C = πD
spacingnumber	mm	0.1 … 10000	30	Axial distance between successive turns (the pitch)
conductorDiameternumber	mm	at least 0.01	2	Wire or tube diameter. It does not enter Kraus's formulas; it is carried to the antenna simulator

Outputs

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

Outputs of helical-antenna
Field	Unit	Description
directivityDbiheadline	dBi	Kraus's axial-mode approximation; measured gain is typically lower
directivity	none	Directivity (linear)
hpbw	°	Half-Power Beamwidth
fnbw	°	First-Null Beamwidth
axialRatio	none	Axial Ratio
inputResistance	Ω	Input Resistance (axial feed)
circumferenceWavelengths	none	Circumference in Wavelengths
spacingWavelengths	none	Spacing in Wavelengths
pitchAngle	°	Pitch Angle
axialLength	mm	Axial Length
wavelength	mm	Free-Space 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": "helical-antenna",
    "inputs": {
      "frequency": 2400,
      "turns": 10,
      "diameter": 40,
      "spacing": 30,
      "conductorDiameter": 2
    }
  }'

import rftools

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

result = client.calculate("helical-antenna", {
    "frequency": 2400,
    "turns": 10,
    "diameter": 40,
    "spacing": 30,
    "conductorDiameter": 2,
})
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": "helical-antenna",
    "inputs": {
      "frequency": 2400,
      "turns": 10,
      "diameter": 40,
      "spacing": 30,
      "conductorDiameter": 2
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "helical-antenna",
	  "inputs": {
	    "frequency": 2400,
	    "turns": 10,
	    "diameter": 40,
	    "spacing": 30,
	    "conductorDiameter": 2
	  }
	}`)
	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": "helical-antenna",
  "values": {
    "directivityDbi": 15.618038581705719,
    "directivity": 36.45892491084807,
    "hpbw": 33.35393238921151,
    "fnbw": 73.7635043222947,
    "axialRatio": 1.05,
    "inputResistance": 140.84078547515304,
    "circumferenceWavelengths": 1.0060056105368074,
    "spacingWavelengths": 0.2401661485426695,
    "pitchAngle": 13.42704175848521,
    "axialLength": 300,
    "wavelength": 124.91352416666666
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:helical-antenna",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Kraus & Marhefka, Antennas for All Applications, 3rd ed. (2002), ch. 8; Balanis, Antenna Theory, 4th ed. (2016), §10.3.1",
    "assumptions": [
      {
        "code": "kraus-empirical",
        "text": "Directivity, beamwidths, axial ratio and input resistance are Kraus's empirical axial-mode formulas; Kraus's directivity is known to overestimate measured gain (King & Wong, 1980)."
      },
      {
        "code": "axial-feed-ground-plane",
        "text": "The helix is fed axially over a ground plane; the ground plane size and the conductor diameter do not enter the formulas."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 1,
          "max": 100000,
          "unit": "MHz"
        },
        "turns": {
          "min": 1,
          "max": 100,
          "unit": ""
        },
        "diameter": {
          "min": 0.1,
          "max": 10000,
          "unit": "mm"
        },
        "spacing": {
          "min": 0.1,
          "max": 10000,
          "unit": "mm"
        },
        "conductorDiameter": {
          "min": 0.01,
          "max": null,
          "unit": "mm"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 2400,
      "turns": 10,
      "diameter": 40,
      "spacing": 30,
      "conductorDiameter": 2
    },
    "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 pageHelical Antenna Calculator (Axial Mode), at these values