Documentation sections

Skin Depth Percentage Calculator

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

Slug skin-depth-percentage. Express skin depth as a percentage of trace thickness and get the AC/DC resistance ratio that follows, so you can tell whether a copper weight choice still matters at your frequency.

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-percentage
Name	Unit	Range	Default	Description
frequencynumber	MHz	at least 0.001	1000	Frequency
conductorThicknessnumber	μm	at least 0.1	35	Conductor Thickness
resistivityRationumber	none	at least 0.5	1	Electrodeposited PCB copper runs a few percent above annealed bulk copper; 1.0 is bulk
temperaturenumber	°C	at least −55	20	Temperature
targetPercentagenumber	%	1 … 1000	50	The skin depth, as a share of the conductor thickness, the design should reach so that most of the copper carries current. The status fails below 33 %.

Outputs

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

Outputs of skin-depth-percentage
Field	Unit	Description
skinDepthPercentageheadline	%	Skin Depth as % of Thickness
skinDepth	μm	Skin Depth
acDcRatio	none	Approaches 1 when the current fills the conductor
effectiveDepth	μm	Thickness of an equivalent uniformly-conducting layer
sheetResistanceDc	mΩ/□	DC Sheet Resistance
sheetResistanceAc	mΩ/□	AC Sheet Resistance

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-percentage",
    "inputs": {
      "frequency": 1000,
      "conductorThickness": 35,
      "resistivityRatio": 1,
      "temperature": 20,
      "targetPercentage": 50
    }
  }'

import rftools

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

result = client.calculate("skin-depth-percentage", {
    "frequency": 1000,
    "conductorThickness": 35,
    "resistivityRatio": 1,
    "temperature": 20,
    "targetPercentage": 50,
})
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-percentage",
    "inputs": {
      "frequency": 1000,
      "conductorThickness": 35,
      "resistivityRatio": 1,
      "temperature": 20,
      "targetPercentage": 50
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "skin-depth-percentage",
	  "inputs": {
	    "frequency": 1000,
	    "conductorThickness": 35,
	    "resistivityRatio": 1,
	    "temperature": 20,
	    "targetPercentage": 50
	  }
	}`)
	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-percentage",
  "values": {
    "skinDepth": 2.089806784938892,
    "skinDepthPercentage": 5.970876528396834,
    "acDcRatio": 8.375913014653381,
    "effectiveDepth": 4.178648935198904,
    "sheetResistanceDc": 0.4926108374384237,
    "sheetResistanceAc": 4.126065524459795
  },
  "warnings": [
    "Skin depth is under a third of the thickness — most of the copper is carrying little current, and adding more will not reduce AC resistance"
  ],
  "errors": [],
  "provenance": {
    "method": "calculator:skin-depth-percentage",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Standard skin-effect result; ρ₂₀(Cu) = 1.724×10⁻⁸ Ω·m, α = 0.00393/°C.",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.001,
          "max": null,
          "unit": "MHz"
        },
        "conductorThickness": {
          "min": 0.1,
          "max": null,
          "unit": "μm"
        },
        "resistivityRatio": {
          "min": 0.5,
          "max": null,
          "unit": ""
        },
        "temperature": {
          "min": -55,
          "max": null,
          "unit": "°C"
        },
        "targetPercentage": {
          "min": 1,
          "max": 1000,
          "unit": "%"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 1000,
      "conductorThickness": 35,
      "resistivityRatio": 1,
      "temperature": 20,
      "targetPercentage": 50
    },
    "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 Percentage Calculator, at these values