Documentation sections

PCB Power Plane Impedance Calculator

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

Slug power-plane-impedance. Calculate PCB power plane impedance, capacitance, inductance, and resonant frequency for PDN design. Optimize your power delivery network. 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 power-plane-impedance
Name	Unit	Range	Default	Description
lengthnumber	mm	1 … 1000	100	Length of the power plane area
widthnumber	mm	1 … 1000	80	Width of the power plane area
dielectricnumber	mm	0.01 … 5	0.1	Distance between power and ground planes (core/prepreg thickness)
ernumber	none	1 … 20	4.4	PCB dielectric constant (FR4 = 4.3–4.8 at 1 MHz)
frequencynumber	MHz	0.001 … 10000	100	Frequency at which to evaluate the reactance ωL of the plane inductance

Outputs

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

Outputs of power-plane-impedance
Field	Unit	Description
capacitanceheadline	nF	Distributed capacitance of the power-ground plane pair
impedance	mΩ	ωL = 2πf·L of the edge-to-edge plane inductance at the given frequency. It is not the impedance a device sees at a point on the plane, which also depends on the plane capacitance, the feed, the decoupling capacitors and the cavity resonances.
firstCavityResonance	MHz	The lowest resonance of the plane pair: the lower of TM₁₀ and TM₀₁, a half wavelength in the dielectric along the longer side of the plane.
cavityResonanceTM10	MHz	TM₁₀ cavity mode, c/(2·l·√εr): one half wavelength along the plane length, open edges.
cavityResonanceTM01	MHz	TM₀₁ cavity mode, c/(2·w·√εr): one half wavelength across the plane width, open edges.
inductance	nH	Plane-pair inductance μ0·d·(length/width): the sheet inductance μ0·d per square times the length/width squares, for current flowing uniformly along the length from edge to edge

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": "power-plane-impedance",
    "inputs": {
      "length": 100,
      "width": 80,
      "dielectric": 0.1,
      "er": 4.4,
      "frequency": 100
    }
  }'

import rftools

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

result = client.calculate("power-plane-impedance", {
    "length": 100,
    "width": 80,
    "dielectric": 0.1,
    "er": 4.4,
    "frequency": 100,
})
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": "power-plane-impedance",
    "inputs": {
      "length": 100,
      "width": 80,
      "dielectric": 0.1,
      "er": 4.4,
      "frequency": 100
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "power-plane-impedance",
	  "inputs": {
	    "length": 100,
	    "width": 80,
	    "dielectric": 0.1,
	    "er": 4.4,
	    "frequency": 100
	  }
	}`)
	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": "power-plane-impedance",
  "values": {
    "capacitance": 3.1166741101056004,
    "impedance": 98.69604406462132,
    "firstCavityResonance": 714.6022331024511,
    "cavityResonanceTM10": 714.6022331024511,
    "cavityResonanceTM01": 893.2527913780639,
    "inductance": 0.15707963276499998
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:power-plane-impedance",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Swaminathan & Engin, Power Integrity Modeling and Design for Semiconductors and Systems (cavity resonances of a rectangular plane pair); Novak & Miller, Frequency-Domain Characterization of Power Distribution Networks; Bogatin, Signal and Power Integrity — Simplified (sheet inductance of a plane pair, μ0·h per square)",
    "assumptions": [
      {
        "code": "parallel-plate",
        "text": "The plane pair is an ideal parallel-plate structure: C = ε0·εr·A/d with no fringing, and L = μ0·d·(l/w) for current spreading uniformly across the width and flowing along the length."
      },
      {
        "code": "open-edge-cavity",
        "text": "The cavity resonances are those of an ideal rectangular plane pair with open (magnetic-wall) edges, f_mn = c/(2√εr)·√((m/l)² + (n/w)²): fringing, vias, cut-outs, decoupling capacitors and losses are not included, and εr does not vary with frequency."
      },
      {
        "code": "lowest-two-modes",
        "text": "Only TM₁₀ and TM₀₁ are reported; the lower of the two is always the first resonance, but higher modes follow, and when one side is more than twice the other, the second half-wave mode along the longer side (TM₂₀ or TM₀₂) falls below the half-wave across the shorter side."
      },
      {
        "code": "inductive-reactance-only",
        "text": "The reactance at frequency is ωL of the plane inductance alone: the plane capacitance, spreading from a point feed, vias, decoupling capacitors and the cavity resonances are not included, so it describes the plane only well below the first cavity resonance."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "length": {
          "min": 1,
          "max": 1000,
          "unit": "mm"
        },
        "width": {
          "min": 1,
          "max": 1000,
          "unit": "mm"
        },
        "dielectric": {
          "min": 0.01,
          "max": 5,
          "unit": "mm"
        },
        "er": {
          "min": 1,
          "max": 20,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": 10000,
          "unit": "MHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "length": 100,
      "width": 80,
      "dielectric": 0.1,
      "er": 4.4,
      "frequency": 100
    },
    "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 pagePCB Power Plane Impedance Calculator, at these values