Documentation sections

BLDC Thermal Derating Calculator

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

Slug bldc-thermal. Calculate BLDC motor winding temperature, thermal margin, derated current, and time to thermal limit. Supports insulation classes B, F, and H.

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 bldc-thermal
Name	Unit	Range	Default	Description
phaseResistancenumber	mΩ	at least 0.1	45	Cold resistance at 25°C, measured between two motor leads; the supply current flows through it under block commutation
continuousCurrentnumber	A	at least 0.1	20	Manufacturer rated continuous current
peakCurrentnumber	A	at least 0.1	40	Short-duration maximum current
thermalResWCnumber	°C/W	at least 0.01	2.5	From motor datasheet or measurement
thermalResCAnumber	°C/W	at least 0.01	8	Depends on mounting, airflow, heatsinking
ambientTempnumber	°C	−40 … 85	25	Ambient Temperature
maxWindingTempnumber	°C	80 … 250	155	Maximum allowable winding temperature — depends on insulation class
operatingCurrentnumber	A	at least 0.01	15	Current you intend to run continuously

Outputs

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

Outputs of bldc-thermal
Field	Unit	Description
tempRise	°C	Rθ·I²·R(T) at the steady state, with the resistance at that temperature; absent where the winding runs away
steadyStateTempheadline	°C	Absent where α·Rθ·R₂₅·I² ≥ 1: no steady state exists (thermal runaway)
thermalMargin	°C	Remaining temperature headroom before insulation limit
deratedCurrent	A	Max continuous current for this ambient + thermal path, with the resistance at the maximum winding temperature
timeToLimit	s	Estimated time from ambient at peak current until the winding reaches max temp, with the resistance rising as it heats (one 10 J/°C thermal mass)
hotResistance	mΩ	Winding resistance at steady-state temperature (α = 0.00393/°C for copper)
ratedCurrentShare	%	The operating current as a share of the rated continuous current; above 100 % the motor runs past its datasheet rating. The derated current is what this thermal path allows

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": "bldc-thermal",
    "inputs": {
      "phaseResistance": 45,
      "continuousCurrent": 20,
      "peakCurrent": 40,
      "thermalResWC": 2.5,
      "thermalResCA": 8,
      "ambientTemp": 25,
      "maxWindingTemp": 155,
      "operatingCurrent": 15
    }
  }'

import rftools

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

result = client.calculate("bldc-thermal", {
    "phaseResistance": 45,
    "continuousCurrent": 20,
    "peakCurrent": 40,
    "thermalResWC": 2.5,
    "thermalResCA": 8,
    "ambientTemp": 25,
    "maxWindingTemp": 155,
    "operatingCurrent": 15,
})
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": "bldc-thermal",
    "inputs": {
      "phaseResistance": 45,
      "continuousCurrent": 20,
      "peakCurrent": 40,
      "thermalResWC": 2.5,
      "thermalResCA": 8,
      "ambientTemp": 25,
      "maxWindingTemp": 155,
      "operatingCurrent": 15
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "bldc-thermal",
	  "inputs": {
	    "phaseResistance": 45,
	    "continuousCurrent": 20,
	    "peakCurrent": 40,
	    "thermalResWC": 2.5,
	    "thermalResCA": 8,
	    "ambientTemp": 25,
	    "maxWindingTemp": 155,
	    "operatingCurrent": 15
	  }
	}`)
	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": "bldc-thermal",
  "values": {
    "tempRise": 182.60732340175647,
    "steadyStateTemp": 207.60732340175647,
    "thermalMargin": -52.607323401756474,
    "deratedCurrent": 13.49437917545837,
    "timeToLimit": 15.548531495821049,
    "hotResistance": 77.29410514360063,
    "ratedCurrentShare": 75
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:bldc-thermal",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "maxon, Formulae Handbook (J. Braun, maxon academy, 2012), §9.2, p. 49; maxon, Key information (2009), p. 40; Drela, First-Order DC Electric Motor Model (MIT, 2007); IEC 60034-1 — Rotating electrical machines; NEMA MG-1",
    "assumptions": [
      {
        "code": "block-commutation-terminal-resistance",
        "text": "The supply current flows through the terminal resistance measured between two leads (block commutation), so the copper loss is I²·R (Drela 2007; maxon Formulae Handbook 2012, p. 37)."
      },
      {
        "code": "resistance-rises-with-temperature",
        "text": "The winding resistance rises as R₂₅·(1 + 0.00393·(T − 25 °C)) and the steady state, the derated current and the time to the limit use the resistance at the temperature they reach (maxon Formulae Handbook 2012, §9.2). Where α·Rθ·R₂₅·I² ≥ 1 there is no steady state and its values are absent."
      },
      {
        "code": "copper-loss-only",
        "text": "Copper loss is the only heat source: iron and friction losses do not heat the winding."
      },
      {
        "code": "single-thermal-mass",
        "text": "The time to the limit treats the winding as one thermal mass of 10 J/°C, a rough figure for a small motor, starting from ambient temperature."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "phaseResistance": {
          "min": 0.1,
          "max": null,
          "unit": "mΩ"
        },
        "continuousCurrent": {
          "min": 0.1,
          "max": null,
          "unit": "A"
        },
        "peakCurrent": {
          "min": 0.1,
          "max": null,
          "unit": "A"
        },
        "thermalResWC": {
          "min": 0.01,
          "max": null,
          "unit": "°C/W"
        },
        "thermalResCA": {
          "min": 0.01,
          "max": null,
          "unit": "°C/W"
        },
        "ambientTemp": {
          "min": -40,
          "max": 85,
          "unit": "°C"
        },
        "maxWindingTemp": {
          "min": 80,
          "max": 250,
          "unit": "°C"
        },
        "operatingCurrent": {
          "min": 0.01,
          "max": null,
          "unit": "A"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "phaseResistance": 45,
      "continuousCurrent": 20,
      "peakCurrent": 40,
      "thermalResWC": 2.5,
      "thermalResCA": 8,
      "ambientTemp": 25,
      "maxWindingTemp": 155,
      "operatingCurrent": 15
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "phaseResistance"
      ],
      "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 pageBLDC Thermal Derating Calculator, at these values