Documentation sections

Planar Spiral Inductor Calculator

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

Slug planar-spiral-inductor. Calculate PCB planar spiral inductance using Mohan current-sheet and modified Wheeler methods for square, hexagonal, octagonal, and circular geometries.

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 planar-spiral-inductor
Name	Unit	Range	Default	Description
outerDiameternumber	mm	1 … 100	10	Outer Diameter
innerDiameternumber	mm	0.5 … 99	4	Inner Diameter
turnsnumber	none	1 … 50	5	Number of Turns
traceWidthnumber	mm	0.05 … 5	0.3	Trace Width
traceSpacingnumber	mm	0.05 … 5	0.2	Trace Spacing
shapenumber	none	0 … 3	0	ShapeOne of: 0 Square · 1 Hexagonal · 2 Octagonal · 3 Circular
frequencynumber	MHz	0.01 … 100000	100	The frequency at which Q is evaluated. It changes no other output. Q is not reported at or above the self-resonant frequency.

Outputs

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

Outputs of planar-spiral-inductor
Field	Unit	Description
inductanceheadline	nH	Inductance (Mohan)
inductanceWheeler	nH	Inductance (Wheeler)
fillRatio	none	Fill Ratio (ρ)
dAvg	mm	Average Diameter
totalTraceLength	mm	n turns, each the shape's perimeter at the average diameter: 4·d_avg for a square, 2√3·d_avg for a hexagon, 8·tan(π/8)·d_avg for an octagon and π·d_avg for a circle.
dcResistance	Ω	DC Resistance (1 oz Cu)
qFactor	none	Jow & Ghovanloo's Q, [ωL − ω(R_s² + ω²L²)·C_p]/R_s, with the skin-effect resistance R_s and the inter-turn capacitance C_p. Proximity effect and substrate loss are not included, so a measured Q is lower. It is not reported at or above the self-resonant frequency, where the spiral is capacitive.
srf	GHz	1/(2π√(L·C_p)), with Jow & Ghovanloo's inter-turn capacitance for an uncoated spiral on FR-4. A ground plane below or a solder-mask coating adds capacitance and lowers it.

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": "planar-spiral-inductor",
    "inputs": {
      "outerDiameter": 10,
      "innerDiameter": 4,
      "turns": 5,
      "traceWidth": 0.3,
      "traceSpacing": 0.2,
      "shape": 0,
      "frequency": 100
    }
  }'

import rftools

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

result = client.calculate("planar-spiral-inductor", {
    "outerDiameter": 10,
    "innerDiameter": 4,
    "turns": 5,
    "traceWidth": 0.3,
    "traceSpacing": 0.2,
    "shape": 0,
    "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": "planar-spiral-inductor",
    "inputs": {
      "outerDiameter": 10,
      "innerDiameter": 4,
      "turns": 5,
      "traceWidth": 0.3,
      "traceSpacing": 0.2,
      "shape": 0,
      "frequency": 100
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "planar-spiral-inductor",
	  "inputs": {
	    "outerDiameter": 10,
	    "innerDiameter": 4,
	    "turns": 5,
	    "traceWidth": 0.3,
	    "traceSpacing": 0.2,
	    "shape": 0,
	    "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": "planar-spiral-inductor",
  "values": {
    "inductance": 234.02440786124947,
    "inductanceWheeler": 236.20656633482332,
    "fillRatio": 0.42857142857142855,
    "dAvg": 7,
    "totalTraceLength": 140,
    "dcResistance": 0.22988505747126436,
    "qFactor": 116.84778020944951,
    "srf": 0.6016757660809017
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:planar-spiral-inductor",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Mohan et al., \"Simple Accurate Expressions for Planar Spiral Inductances\", IEEE JSSC, vol. 34, no. 10, Oct 1999; Jow & Ghovanloo, \"Design and Optimization of Printed Spiral Coils for Efficient Transcutaneous Inductive Power Transmission\", IEEE TBCAS, vol. 1, no. 3, pp. 193–202, 2007, as restated in Ashoori et al., IEEE EMBC 2011, eqs. 6–12",
    "assumptions": [
      {
        "code": "uncoated-fr4",
        "text": "The parasitic capacitance is Jow & Ghovanloo’s inter-turn model for a spiral with no coating (εr 1 above the traces) on FR-4 (εr 4.4 below), with no ground plane beneath; a plane or a solder-mask coating raises it and lowers the self-resonance."
      },
      {
        "code": "copper-1oz",
        "text": "The traces are 1 oz copper, 35 µm thick, with ρ = 1/58 Ω·mm²/m (IEC 60028) at 20 °C."
      },
      {
        "code": "skin-effect-only",
        "text": "Q includes the skin effect in one skin depth of the trace width and the inter-turn capacitance; proximity effect, substrate loss and radiation are not modelled."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "outerDiameter": {
          "min": 1,
          "max": 100,
          "unit": "mm"
        },
        "innerDiameter": {
          "min": 0.5,
          "max": 99,
          "unit": "mm"
        },
        "turns": {
          "min": 1,
          "max": 50,
          "unit": ""
        },
        "traceWidth": {
          "min": 0.05,
          "max": 5,
          "unit": "mm"
        },
        "traceSpacing": {
          "min": 0.05,
          "max": 5,
          "unit": "mm"
        },
        "shape": {
          "min": 0,
          "max": 3,
          "unit": ""
        },
        "frequency": {
          "min": 0.01,
          "max": 100000,
          "unit": "MHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "outerDiameter": 10,
      "innerDiameter": 4,
      "turns": 5,
      "traceWidth": 0.3,
      "traceSpacing": 0.2,
      "shape": 0,
      "frequency": 100
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "outerDiameter"
      ],
      "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 pagePlanar Spiral Inductor Calculator, at these values