Documentation sections

Skin Depth Calculator

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

Slug skin-depth. Calculate skin depth and surface resistance for copper, aluminum, and other conductors at any frequency. Essential for RF shielding and PCB design. 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 skin-depth
Name	Unit	Range	Default	Description
frequencynumber	MHz	0.001 … 1000000	1000	Operating frequency
conductivitynumber	S/m	1000 … 100000000	58000000	Electrical conductivity of the conductor material
relativePermeabilitynumber	none	1 … 100000	1	Relative magnetic permeability of the conductor (1 for non-magnetic materials)

Outputs

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

Outputs of skin-depth
Field	Unit	Description
skinDepthUmheadline	μm	Skin depth (1/e penetration depth) in micrometers
skinDepthNm	nm	Skin depth in nanometers
surfaceResistance	mΩ/□	Sheet resistance of the conductor surface (Rs = 1/(σ·δ))

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": "skin-depth",
    "inputs": {
      "frequency": 1000,
      "conductivity": 58000000,
      "relativePermeability": 1
    }
  }'

import rftools

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

result = client.calculate("skin-depth", {"frequency": 1000, "conductivity": 58000000, "relativePermeability": 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": "skin-depth",
    "inputs": {
      "frequency": 1000,
      "conductivity": 58000000,
      "relativePermeability": 1
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "skin-depth",
	  "inputs": {
	    "frequency": 1000,
	    "conductivity": 58000000,
	    "relativePermeability": 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": "skin-depth",
  "values": {
    "skinDepthUm": 2.089806784938892,
    "skinDepthNm": 2089.8067849388917,
    "surfaceResistance": 8.250226496823716
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:skin-depth",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Griffiths, \"Introduction to Electrodynamics\" 4th ed., Chapter 9",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.001,
          "max": 1000000,
          "unit": "MHz"
        },
        "conductivity": {
          "min": 1000,
          "max": 100000000,
          "unit": "S/m"
        },
        "relativePermeability": {
          "min": 1,
          "max": 100000,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 1000,
      "conductivity": 58000000,
      "relativePermeability": 1
    },
    "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 pageSkin Depth Calculator, at these values