Documentation sections

Loop Antenna Calculator

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

Slug loop-antenna. Calculate loop antenna radiation resistance, Q factor, bandwidth, and gain. Design magnetic loop antennas for HF and VHF bands. 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 loop-antenna
Name	Unit	Range	Default	Description
frequencynumber	MHz	at least 0.1	7	Operating frequency in MHz
diameternumber	m	0.01 … 20	1	Diameter of the loop structure in meters
conductorDiamnumber	mm	at least 0.1	10	Diameter of the conductor tube or wire in mm

Outputs

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

Outputs of loop-antenna
Field	Unit	Description
circumference	m	Loop Circumference
radiation_resistanceheadline	Ω	Radiation Resistance
loss_resistance	Ω	Loss Resistance
gain	dBi	The small loop's directivity, 3/2 (1.76 dBi), times its radiation efficiency: G = 10·log₁₀(1.5·e)
bandwidth	kHz	-3 dB Bandwidth
radiationEfficiency	%	Share of the input power radiated: e = R_rad/(R_rad + R_loss)

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": "loop-antenna",
    "inputs": {
      "frequency": 7,
      "diameter": 1,
      "conductorDiam": 10
    }
  }'

import rftools

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

result = client.calculate("loop-antenna", {"frequency": 7, "diameter": 1, "conductorDiam": 10})
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": "loop-antenna",
    "inputs": {
      "frequency": 7,
      "diameter": 1,
      "conductorDiam": 10
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "loop-antenna",
	  "inputs": {
	    "frequency": 7,
	    "diameter": 1,
	    "conductorDiam": 10
	  }
	}`)
	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": "loop-antenna",
  "values": {
    "circumference": 3.141592653589793,
    "radiation_resistance": 0.005715294057365037,
    "loss_resistance": 0.06902634719744663,
    "gain": -9.40432791079153,
    "bandwidth": 4.041376318650862,
    "radiationEfficiency": 7.646733415821401
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:loop-antenna",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Balanis, Antenna Theory, 4th ed.: Chapter 2 (gain = radiation efficiency × directivity); §5.2 (small circular loop, directivity 3/2, R_rad = 320π⁴(A/λ²)²)",
    "assumptions": [
      {
        "code": "small-loop-efficiency",
        "text": "A small loop (circumference well below a tenth of a wavelength): directivity 3/2 and R_rad = 320π⁴(A/λ²)². The gain is that directivity times e = R_rad/(R_rad + R_loss), with the copper skin-effect loss only; a tuning capacitor's loss and nearby ground lower it further."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.1,
          "max": null,
          "unit": "MHz"
        },
        "diameter": {
          "min": 0.01,
          "max": 20,
          "unit": "m"
        },
        "conductorDiam": {
          "min": 0.1,
          "max": null,
          "unit": "mm"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 7,
      "diameter": 1,
      "conductorDiam": 10
    },
    "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 pageLoop Antenna Calculator, at these values