Documentation sections

Rectangular ↔ Polar Complex Number Converter

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

Slug rectangular-polar. Convert complex numbers between rectangular (a + jb) and polar (r∠θ) form. Quadrant-correct via atan2, with degrees, radians, and 0–360° wrapped angle. For impedance, S-parameters, and phasor arithmetic.

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 rectangular-polar
Name	Unit	Range	Default	Description
realnumber	none	any	3	Real component of a + jb. For impedance this is resistance R.
imaginarynumber	none	any	4	Imaginary component of a + jb. For impedance this is reactance X.
magnitudenumber	none	any	5	Vector length r of r∠θ.
angleDegnumber	°	−360 … 360	53.13010235415598	Phase angle in degrees, measured counter-clockwise from the +real axis.

Outputs

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

Outputs of rectangular-polar
Field	Unit	Description
magnitudeOutheadline	none	Magnitude \|a + jb\|
angleDegOut	°	Angle (−180…180°)
angleRadOut	rad	Angle (radians)
angleDeg360	°	Angle (0…360°)
realOut	none	Real Part from r∠θ
imagOut	none	Imaginary Part from r∠θ

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": "rectangular-polar",
    "inputs": {
      "real": 3,
      "imaginary": 4,
      "magnitude": 5,
      "angleDeg": 53.13010235415598
    }
  }'

import rftools

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

result = client.calculate("rectangular-polar", {
    "real": 3,
    "imaginary": 4,
    "magnitude": 5,
    "angleDeg": 53.13010235415598,
})
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": "rectangular-polar",
    "inputs": {
      "real": 3,
      "imaginary": 4,
      "magnitude": 5,
      "angleDeg": 53.13010235415598
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "rectangular-polar",
	  "inputs": {
	    "real": 3,
	    "imaginary": 4,
	    "magnitude": 5,
	    "angleDeg": 53.13010235415598
	  }
	}`)
	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": "rectangular-polar",
  "values": {
    "magnitudeOut": 5,
    "angleDegOut": 53.13010235415598,
    "angleRadOut": 0.9272952180016122,
    "angleDeg360": 53.13010235415598,
    "realOut": 3.0000000000000004,
    "imagOut": 3.9999999999999996
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:rectangular-polar",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Standard complex-plane identities; Touchstone MA/RI conventions",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "real": {
          "min": null,
          "max": null,
          "unit": ""
        },
        "imaginary": {
          "min": null,
          "max": null,
          "unit": ""
        },
        "magnitude": {
          "min": null,
          "max": null,
          "unit": ""
        },
        "angleDeg": {
          "min": -360,
          "max": 360,
          "unit": "°"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "real": 3,
      "imaginary": 4,
      "magnitude": 5,
      "angleDeg": 53.13010235415598
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "real"
      ],
      "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 pageRectangular ↔ Polar Complex Number Converter, at these values