Documentation sections

Microstrip Patch Antenna Calculator

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

Slug patch-antenna. Calculate rectangular microstrip patch antenna dimensions (width, length) using the Transmission Line Model. Outputs effective dielectric constant, edge-feed impedance, and nominal gain for common substrates like FR4 and Rogers.

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 patch-antenna
Name	Unit	Range	Default	Description
frequencynumber	GHz	0.1 … 100	2.45	Operating frequency in GHz
dielectricConstantnumber	none	1 … 30	4.4	FR4 ≈ 4.4; Rogers RO4003C ≈ 3.55; Air = 1
substrateHeightnumber	mm	0.1 … 10	1.6	Dielectric substrate thickness
feedOffsetnumber	mm	0 … 50	0	0 = edge feed; adjust for 50Ω match (inset feed position)

Outputs

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

Outputs of patch-antenna
Field	Unit	Description
patchWidth_mm	mm	Resonant patch width (determines polarisation direction)
patchLength_mmheadline	mm	Resonant patch length (determines resonant frequency)
effectiveDielectric	none	Effective dielectric constant accounting for fringing fields
edgeFeedImpedance_ohm	Ω	Input resistance at the radiating edge, 1/(2(G₁ + G₁₂)) from Balanis' slot conductances; not clamped
gainDbi	dBi	Typical single-element patch gain (6–8 dBi)
feedResistance_ohm	Ω	Input resistance at the entered feed offset, R_edge·cos²(π·y₀/L); equals the edge resistance at 0
insetFeedPosition_mm	mm	Inset from the radiating edge at which the feed resistance is 50 Ω

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": "patch-antenna",
    "inputs": {
      "frequency": 2.45,
      "dielectricConstant": 4.4,
      "substrateHeight": 1.6,
      "feedOffset": 0
    }
  }'

import rftools

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

result = client.calculate("patch-antenna", {
    "frequency": 2.45,
    "dielectricConstant": 4.4,
    "substrateHeight": 1.6,
    "feedOffset": 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": "patch-antenna",
    "inputs": {
      "frequency": 2.45,
      "dielectricConstant": 4.4,
      "substrateHeight": 1.6,
      "feedOffset": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "patch-antenna",
	  "inputs": {
	    "frequency": 2.45,
	    "dielectricConstant": 4.4,
	    "substrateHeight": 1.6,
	    "feedOffset": 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": "patch-antenna",
  "values": {
    "patchWidth_mm": 37.23426118288438,
    "patchLength_mm": 28.809290261854397,
    "effectiveDielectric": 4.080857521554887,
    "edgeFeedImpedance_ohm": 321.2209554654481,
    "gainDbi": 7,
    "feedResistance_ohm": 321.2209554654481,
    "insetFeedPosition_mm": 10.685551977674832
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:patch-antenna",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Balanis, \"Antenna Theory: Analysis and Design\", 4th ed., Chapter 14: slot conductances §14.2, Eqs. (14-12), (14-17) and (14-18a), Examples 14.1–14.3; inset feed §14.2.1, Eq. (14-20a)",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.1,
          "max": 100,
          "unit": "GHz"
        },
        "dielectricConstant": {
          "min": 1,
          "max": 30,
          "unit": ""
        },
        "substrateHeight": {
          "min": 0.1,
          "max": 10,
          "unit": "mm"
        },
        "feedOffset": {
          "min": 0,
          "max": 50,
          "unit": "mm"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 2.45,
      "dielectricConstant": 4.4,
      "substrateHeight": 1.6,
      "feedOffset": 0
    },
    "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 pageMicrostrip Patch Antenna Calculator, at these values