Documentation sections

Ground Plane Impedance vs Frequency

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

Slug ground-plane-impedance. Calculate PCB ground plane AC impedance, skin depth, and inductive reactance vs frequency. Analyze ground return paths for EMC compliance.

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 ground-plane-impedance
Name	Unit	Range	Default	Description
lengthnumber	mm	at least 1	100	Plane Length
widthnumber	mm	at least 0.1	50	Plane Width
thicknessnumber	μm	at least 1	35	Copper Thickness
frequencynumber	MHz	at least 0.001	10	Frequency
conductivitynumber	MS/m	at least 0.1	58	Copper: 58 MS/m, Aluminium: 37 MS/m
separationnumber	mm	at least 0.01	1	Distance from the plane to the plane or conductor carrying the return current; the inductance is µ₀·h·l/w

Outputs

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

Outputs of ground-plane-impedance
Field	Unit	Description
dcResistance	mΩ	DC Resistance
skinDepth	μm	Skin Depth
acResistance	mΩ	AC Resistance
inductance	nH	Plane Inductance
totalImpedanceheadline	mΩ	Total Impedance \|Z\|

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": "ground-plane-impedance",
    "inputs": {
      "length": 100,
      "width": 50,
      "thickness": 35,
      "frequency": 10,
      "conductivity": 58,
      "separation": 1
    }
  }'

import rftools

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

result = client.calculate("ground-plane-impedance", {
    "length": 100,
    "width": 50,
    "thickness": 35,
    "frequency": 10,
    "conductivity": 58,
    "separation": 1,
})
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": "ground-plane-impedance",
    "inputs": {
      "length": 100,
      "width": 50,
      "thickness": 35,
      "frequency": 10,
      "conductivity": 58,
      "separation": 1
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "ground-plane-impedance",
	  "inputs": {
	    "length": 100,
	    "width": 50,
	    "thickness": 35,
	    "frequency": 10,
	    "conductivity": 58,
	    "separation": 1
	  }
	}`)
	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": "ground-plane-impedance",
  "values": {
    "dcResistance": 0.9852216748768474,
    "skinDepth": 20.89806784938892,
    "acResistance": 1.5179633408858995,
    "inductance": 2.5132741228718345,
    "totalImpedance": 157.9209660476053
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:ground-plane-impedance",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Bogatin, Signal and Power Integrity — Simplified (plane-pair inductance per square); Ott, Electromagnetic Compatibility Engineering (2009) §10.6",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "length": {
          "min": 1,
          "max": null,
          "unit": "mm"
        },
        "width": {
          "min": 0.1,
          "max": null,
          "unit": "mm"
        },
        "thickness": {
          "min": 1,
          "max": null,
          "unit": "μm"
        },
        "frequency": {
          "min": 0.001,
          "max": null,
          "unit": "MHz"
        },
        "conductivity": {
          "min": 0.1,
          "max": null,
          "unit": "MS/m"
        },
        "separation": {
          "min": 0.01,
          "max": null,
          "unit": "mm"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "length": 100,
      "width": 50,
      "thickness": 35,
      "frequency": 10,
      "conductivity": 58,
      "separation": 1
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "length"
      ],
      "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 pageGround Plane Impedance vs Frequency, at these values