Documentation sections

Solve for a target

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

Finds the value of one calculator input that brings one of its outputs to a target (the trace width that gives 50 Ω, the gap that gives a target differential impedance) and returns it with the forward result at exactly that value. One metered call replaces the forward calls a client would otherwise spend searching by hand.

How the search runs

The search runs over solveFor's stated bounds, narrowed by range where one is given; an input with no stated bound needs range. Where grid is given, the returned value is rounded to the nearest grid multiple inside the range and unrounded carries the exact solution; without a grid, value and unrounded are the same number. Either way, result (exactly what /calculate returns for those inputs, provenance included) is the forward calculator run at exactly the returned value, so what a client displays is a real forward computation, never the solver's own estimate.

Request body

SolveRequest
Field	Description
slugrequiredstring	The calculator.
inputsrequiredobject of numbers	Every input except solveFor. A value given for solveFor is only the search's start point, used to break a tie between more than one solution.
solveForrequiredstring	A declared numeric input of the calculator.
target.outputrequiredstring	An output key the calculator returns.
target.valuerequirednumber	The value that output should reach.
gridnumber	A positive manufacturing grid; the returned value is rounded to its nearest multiple inside the range.
range[number, number]	Narrows solveFor's stated bounds; required when it states none.

Response

SolveResponse
Field	Description
valuenumber	The solved value, rounded to grid when one was given.
unroundednumber	The exact solution, before grid rounding.
reachedboolean	Whether the target was reached; false still carries the nearest value found, not a guess.
evaluationsinteger	How many forward evaluations the search used.
warningsstring[]	The solve's own findings: another solution in the range, or a target not reached.
resultobject	Exactly what /calculate returns for the inputs with solveFor set to value: values, warnings, errors and provenance.
slug, solveFor, target, gridecho	The request's fields, as given; grid is null when none was.

Cost and ties

Cost

One metered call, charged like /calculate after every check below, and given back if the service then fails. A target the search cannot reach still succeeds and is still charged, with reached: false and the nearest value found: the caller asked for something the service delivered.

Refusals

A request that cannot be solved is refused before anything is charged, and param names the field at fault:

Solve refusals
Status	When
404	The calculator slug does not exist.
400	solveFor is not one of the calculator's declared numeric inputs (param: solveFor, with allowed).
400	target.output is not one of the calculator's outputs (param: target.output, with allowed).
400	grid is given and is not a finite, positive number, or has no multiple in the range.
400	Any given value (an input, target.value or a range bound) is not finite.
400	solveFor has no stated bound and the body gives no range, or the given range lies outside the stated bounds or is empty.
400	A fixed input exceeds a limit the calculator enforces on its own running time, as for /calculate.

curl -X POST https://rftools.io/api/py/v1/calculate/solve \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "microstrip-impedance",
    "inputs": {
      "substrateHeight": 1.51,
      "dielectricConstant": 4.5,
      "copperThickness": 35
    },
    "solveFor": "traceWidth",
    "target": {
      "output": "impedance",
      "value": 50
    },
    "grid": 0.001
  }'

import rftools

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

result = client.solve(
    "microstrip-impedance",
    {
        "substrateHeight": 1.51,
        "dielectricConstant": 4.5,
        "copperThickness": 35,
    },
    "traceWidth", "impedance", 50,
    grid=0.001,
)
print(result.value, result.reached)
print(result.result.values)

const response = await fetch("https://rftools.io/api/py/v1/calculate/solve", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "microstrip-impedance",
    "inputs": {
      "substrateHeight": 1.51,
      "dielectricConstant": 4.5,
      "copperThickness": 35
    },
    "solveFor": "traceWidth",
    "target": {
      "output": "impedance",
      "value": 50
    },
    "grid": 0.001
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "microstrip-impedance",
	  "inputs": {
	    "substrateHeight": 1.51,
	    "dielectricConstant": 4.5,
	    "copperThickness": 35
	  },
	  "solveFor": "traceWidth",
	  "target": {
	    "output": "impedance",
	    "value": 50
	  },
	  "grid": 0.001
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate/solve", 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": "microstrip-impedance",
  "solveFor": "traceWidth",
  "target": {
    "output": "impedance",
    "value": 50
  },
  "grid": 0.001,
  "value": 2.781,
  "unrounded": 2.780720522734193,
  "reached": true,
  "evaluations": 68,
  "warnings": [],
  "result": {
    "slug": "microstrip-impedance",
    "values": {
      "impedance": 49.99705984469245,
      "effectiveDielectric": 3.3944336801230706,
      "propagationDelay": 6.145581196647901,
      "guidedWavelength": 67.79939168226058,
      "quarterWavelength": 16.949847920565144
    },
    "warnings": [],
    "errors": [],
    "provenance": {
      "method": "calculator:microstrip-impedance",
      "version": "api@3f2c1a9b04de",
      "formulaRef": "Hammerstad & Jensen (1980); Wadell, \"Transmission Line Design Handbook\" 1991",
      "assumptions": [
        {
          "code": "quasi-static",
          "text": "Quasi-static: Z₀ and εeff are the Hammerstad–Jensen static values, with no frequency dependence; dispersion is not modelled."
        },
        {
          "code": "bare-microstrip",
          "text": "Bare microstrip: air above the trace, with no soldermask or other cover layer."
        },
        {
          "code": "homogeneous-substrate",
          "text": "One homogeneous, isotropic, non-magnetic substrate of relative permittivity εr over a solid ground plane, both extending well beyond the trace."
        },
        {
          "code": "thickness-effective-width",
          "text": "Copper thickness t is modelled as an effective width increase Δw = (t/π)(1 + ln(2h/t)), applied to both Z₀ and εeff."
        },
        {
          "code": "lossless",
          "text": "Lossless: conductor and dielectric losses are neglected, so Z₀ is real and the propagation delay is √εeff/c."
        }
      ],
      "validRange": {
        "status": "inside",
        "bounds": {
          "traceWidth": {
            "min": 0.01,
            "max": 50,
            "unit": "mm"
          },
          "substrateHeight": {
            "min": 0.05,
            "max": 10,
            "unit": "mm"
          },
          "dielectricConstant": {
            "min": 1,
            "max": 100,
            "unit": ""
          },
          "copperThickness": {
            "min": 1,
            "max": 200,
            "unit": "μm"
          },
          "frequency": {
            "min": 0.001,
            "max": 300,
            "unit": "GHz"
          }
        },
        "outside": [],
        "model": null
      },
      "computedAt": "2026-09-24T14:05:11.004Z",
      "inputs": {
        "traceWidth": 2.781,
        "substrateHeight": 1.51,
        "dielectricConstant": 4.5,
        "copperThickness": 35,
        "frequency": 2.4
      },
      "seed": null,
      "elapsedSeconds": 0.004
    }
  }
}

The trace width that reaches 50 Ω on 1.51 mm FR-4, on a 0.001 mm grid.

{
  "detail": "'impedance' is not an input of 'microstrip-impedance', so it cannot be solved for. Its inputs: traceWidth, substrateHeight, dielectricConstant, copperThickness, frequency.",
  "errorKind": "invalid_request",
  "param": "solveFor",
  "allowed": [
    "traceWidth",
    "substrateHeight",
    "dielectricConstant",
    "copperThickness",
    "frequency"
  ]
}

An output named as solveFor. Nothing was charged.

{
  "detail": "Calculator 'microstrip' not found",
  "errorKind": "invalid_request"
}

A slug that does not exist.