Documentation sections

LC Resonance Calculator

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

Slug lc-resonance. Calculate the resonant frequency, characteristic impedance, Q factor, and bandwidth of a series or parallel LC tank circuit. Enter inductance, capacitance, and optional series resistance.

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 lc-resonance
Name	Unit	Range	Default	Description
inductancenumber	μH	0.001 … 1000000	10	Inductance
capacitancenumber	pF	0.01 … 1000000000	100	Capacitance
resistancenumber	Ω	0 … 10000	0	Series resistance for Q and bandwidth. Set 0 for ideal LC.
circuitTypenumber	none	0 … 1	0	Circuit TypeOne of: 0 Series LC · 1 Parallel LC (tank)

Outputs

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

Outputs of lc-resonance
Field	Unit	Description
f0_MHzheadline	MHz	Resonant Frequency
characteristicImpedance_ohm	Ω	Z₀ = √(L/C)
qFactor	none	Q Factor
bandwidth_kHz	kHz	−3 dB Bandwidth
wavelength_m	m	Free-space wavelength at the resonant frequency: λ = c / f₀
impedanceAtResonance_ohm	Ω	Series: the minimum, equal to R. Parallel tank with R in series with the inductor: the dynamic resistance L/(C·R), the maximum, where the impedance is purely resistive. Unbounded when R is 0.

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": "lc-resonance",
    "inputs": {
      "inductance": 10,
      "capacitance": 100,
      "resistance": 0,
      "circuitType": 0
    }
  }'

import rftools

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

result = client.calculate("lc-resonance", {
    "inductance": 10,
    "capacitance": 100,
    "resistance": 0,
    "circuitType": 0,
})
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": "lc-resonance",
    "inputs": {
      "inductance": 10,
      "capacitance": 100,
      "resistance": 0,
      "circuitType": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "lc-resonance",
	  "inputs": {
	    "inductance": 10,
	    "capacitance": 100,
	    "resistance": 0,
	    "circuitType": 0
	  }
	}`)
	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": "lc-resonance",
  "values": {
    "f0_MHz": 5.032921210448704,
    "characteristicImpedance_ohm": 316.2277660168379,
    "qFactor": null,
    "bandwidth_kHz": 0,
    "wavelength_m": 59.56629270841941,
    "impedanceAtResonance_ohm": 0
  },
  "warnings": [
    "With no resistance the circuit is lossless, so its Q is unbounded and its bandwidth zero. Enter the series resistance, such as the inductor’s ESR at f₀, for a real Q."
  ],
  "errors": [],
  "provenance": {
    "method": "calculator:lc-resonance",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Terman, Radio Engineers' Handbook, McGraw-Hill, 1943",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "inductance": {
          "min": 0.001,
          "max": 1000000,
          "unit": "μH"
        },
        "capacitance": {
          "min": 0.01,
          "max": 1000000000,
          "unit": "pF"
        },
        "resistance": {
          "min": 0,
          "max": 10000,
          "unit": "Ω"
        },
        "circuitType": {
          "min": 0,
          "max": 1,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "inductance": 10,
      "capacitance": 100,
      "resistance": 0,
      "circuitType": 0
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "inductance"
      ],
      "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 pageLC Resonance Calculator, at these values