Documentation sections

Differential Pair Impedance Calculator

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

Slug differential-pair. Calculate Zdiff and Zcommon for edge-coupled microstrip pairs. Design USB, HDMI, and Ethernet differential pairs with odd/even mode impedance. 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 differential-pair
Name	Unit	Range	Default	Description
traceWidthnumber	mm	0.05 … 5	0.15	Width of each individual trace in the differential pair
traceSpacingnumber	mm	0.05 … 5	0.15	Edge-to-edge gap between the two traces
substrateHeightnumber	mm	0.05 … 5	0.1	Dielectric thickness between trace and ground plane
dielectricConstantnumber	none	1 … 20	4.2	Relative permittivity of the substrate material
copperThicknessnumber	μm	5 … 200	17.5	Thickness of the copper trace (plating + base)
frequencynumber	GHz	0.001 … 300	2.4	Used only for the guided wavelength of the differential (odd) mode; the impedances do not depend on it in this model

Outputs

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

Outputs of differential-pair
Field	Unit	Description
zdiffheadline	Ω	Differential impedance (2 × Zodd)
zcom	Ω	Common-mode impedance (Zeven / 2)
z0single	Ω	Uncoupled single-ended impedance (Hammerstad-Jensen)
zodd	Ω	Odd-mode impedance (Zdiff / 2)
zeven	Ω	Even-mode impedance (2 × Zcom)
erEffOdd	none	Effective permittivity seen by the odd (differential) mode
erEffEven	none	Effective permittivity seen by the even (common) mode — higher, because the odd mode routes field through the air gap
inValidatedRange	none	1 when the geometry lies inside the range the model was checked against a field solver
guidedWavelength	mm	Wavelength of the differential (odd) mode on the pair at the frequency, c/(f·√εeff,odd)
quarterWavelength	mm	Quarter Wavelength (odd mode)

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": "differential-pair",
    "inputs": {
      "traceWidth": 0.15,
      "traceSpacing": 0.15,
      "substrateHeight": 0.1,
      "dielectricConstant": 4.2,
      "copperThickness": 17.5,
      "frequency": 2.4
    }
  }'

import rftools

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

result = client.calculate("differential-pair", {
    "traceWidth": 0.15,
    "traceSpacing": 0.15,
    "substrateHeight": 0.1,
    "dielectricConstant": 4.2,
    "copperThickness": 17.5,
    "frequency": 2.4,
})
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": "differential-pair",
    "inputs": {
      "traceWidth": 0.15,
      "traceSpacing": 0.15,
      "substrateHeight": 0.1,
      "dielectricConstant": 4.2,
      "copperThickness": 17.5,
      "frequency": 2.4
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "differential-pair",
	  "inputs": {
	    "traceWidth": 0.15,
	    "traceSpacing": 0.15,
	    "substrateHeight": 0.1,
	    "dielectricConstant": 4.2,
	    "copperThickness": 17.5,
	    "frequency": 2.4
	  }
	}`)
	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": "differential-pair",
  "values": {
    "zdiff": 99.91396531405557,
    "zcom": 29.82840260591584,
    "z0single": 54.90377067499788,
    "zodd": 49.95698265702779,
    "zeven": 59.65680521183168,
    "erEffOdd": 2.9313216677405416,
    "erEffEven": 3.362873577002329,
    "inValidatedRange": 1,
    "guidedWavelength": 72.95880669275142,
    "quarterWavelength": 18.239701673187856
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:differential-pair",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "E. Hammerstad and Ø. Jensen, “Accurate Models for Microstrip Computer-Aided Design”, IEEE MTT-S International Microwave Symposium Digest, 1980 (single line); coupling fitted to rftools.io’s 2-D method-of-moments solver (src/lib/pcb/__tests__/solver), within 2% on a mode impedance over W/H 0.2–4 and S/H 0.1–3.",
    "assumptions": [
      {
        "code": "quasi-static",
        "text": "Quasi-static: the mode impedances and effective permittivities are the low-frequency values; dispersion is not modelled."
      },
      {
        "code": "bare-microstrip",
        "text": "Bare surface pair: air above the traces, with no soldermask or cover layer, on one homogeneous substrate over a solid ground plane."
      },
      {
        "code": "symmetric-pair",
        "text": "Two identical traces of the same width and thickness; Zdiff = 2·Zodd and Zcommon = Zeven/2."
      },
      {
        "code": "fitted-coupling",
        "text": "Coupling is fitted, as ratios to the Hammerstad–Jensen single line, to a 2-D method-of-moments solver over trace width 0.2–4× and spacing 0.1–3× the substrate height (published bound 2% on a mode impedance); outside that range the result is extrapolated and inValidatedRange reads 0."
      },
      {
        "code": "thickness-single-line-only",
        "text": "Copper thickness enters only through the single line’s effective-width correction; the added sidewall coupling across the gap is not modelled."
      },
      {
        "code": "lossless",
        "text": "Lossless: conductor and dielectric losses are neglected."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "traceWidth": {
          "min": 0.05,
          "max": 5,
          "unit": "mm"
        },
        "traceSpacing": {
          "min": 0.05,
          "max": 5,
          "unit": "mm"
        },
        "substrateHeight": {
          "min": 0.05,
          "max": 5,
          "unit": "mm"
        },
        "dielectricConstant": {
          "min": 1,
          "max": 20,
          "unit": ""
        },
        "copperThickness": {
          "min": 5,
          "max": 200,
          "unit": "μm"
        },
        "frequency": {
          "min": 0.001,
          "max": 300,
          "unit": "GHz"
        }
      },
      "outside": [],
      "model": {
        "description": "trace width 0.2–4× and spacing 0.1–3× the substrate height",
        "worstCaseError": 0.02,
        "inside": true
      }
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "traceWidth": 0.15,
      "traceSpacing": 0.15,
      "substrateHeight": 0.1,
      "dielectricConstant": 4.2,
      "copperThickness": 17.5,
      "frequency": 2.4
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "traceWidth"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

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{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

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Same inputs on the calculator pageDifferential Pair Impedance Calculator, at these values