Documentation sections

Servo Motor Torque & Speed

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

Slug servo-motor. Calculate servo motor torque, speed, efficiency, and back-EMF from electrical and load parameters.

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 servo-motor
Name	Unit	Range	Default	Description
voltagenumber	V	at least 0	5	Supply Voltage
currentnumber	A	at least 0	0.5	Current measured at the operating point; sets the torque, speed and power outputs
speednumber	RPM	at least 1	500	Datasheet no-load speed at this supply voltage; with it, K_t = K_e = V/ω_nl
loadTorquenumber	N·m	at least 0	0.05	Torque the load demands; sets the current, speed and power at load torque
armResnumber	Ω	at least 0.1	2	Winding Resistance

Outputs

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

Outputs of servo-motor
Field	Unit	Description
torqueheadline	N·m	Operating Torque
operatingSpeed	RPM	Operating Speed
backEmf	V	Back-EMF
inputPower	W	Input Power
outputPower	W	Output Power
efficiency	%	Efficiency
torqueConstant	N·m/A	Torque Constant
stallTorque	N·m	Stall Torque
loadCurrent	A	Current at Load Torque
loadSpeed	RPM	Speed at Load Torque
loadPower	W	Output Power at Load Torque

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": "servo-motor",
    "inputs": {
      "voltage": 5,
      "current": 0.5,
      "speed": 500,
      "loadTorque": 0.05,
      "armRes": 2
    }
  }'

import rftools

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

result = client.calculate("servo-motor", {
    "voltage": 5,
    "current": 0.5,
    "speed": 500,
    "loadTorque": 0.05,
    "armRes": 2,
})
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": "servo-motor",
    "inputs": {
      "voltage": 5,
      "current": 0.5,
      "speed": 500,
      "loadTorque": 0.05,
      "armRes": 2
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "servo-motor",
	  "inputs": {
	    "voltage": 5,
	    "current": 0.5,
	    "speed": 500,
	    "loadTorque": 0.05,
	    "armRes": 2
	  }
	}`)
	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": "servo-motor",
  "values": {
    "torque": 0.047746482927568605,
    "operatingSpeed": 400,
    "backEmf": 4,
    "inputPower": 2.5,
    "outputPower": 2,
    "efficiency": 80,
    "torqueConstant": 0.09549296585513721,
    "stallTorque": 0.23873241463784303,
    "loadCurrent": 0.5235987755982988,
    "loadSpeed": 395.28024488034026,
    "loadPower": 2.069682522375419
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:servo-motor",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Hughes & Drury, Electric Motors and Drives, ch. 3 (d.c. motors); maxon, Key information on maxon DC motors",
    "assumptions": [
      {
        "code": "linear-dc-motor",
        "text": "The motor is a linear brushed DC machine: V = I·R_a + K_e·ω and T = K_t·I, with K_t = K_e in SI units and R_a constant."
      },
      {
        "code": "no-load-current-neglected",
        "text": "The no-load current is neglected, so K_e = V/ω_nl and the friction and iron-loss torque are not subtracted: the torque is the electromagnetic torque, and the shaft delivers slightly less."
      },
      {
        "code": "stall-without-back-drive",
        "text": "A load torque above the stall torque is reported as a stall at zero speed and stall current: the load is assumed not to drive the motor backwards."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "voltage": {
          "min": 0,
          "max": null,
          "unit": "V"
        },
        "current": {
          "min": 0,
          "max": null,
          "unit": "A"
        },
        "speed": {
          "min": 1,
          "max": null,
          "unit": "RPM"
        },
        "loadTorque": {
          "min": 0,
          "max": null,
          "unit": "N·m"
        },
        "armRes": {
          "min": 0.1,
          "max": null,
          "unit": "Ω"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "voltage": 5,
      "current": 0.5,
      "speed": 500,
      "loadTorque": 0.05,
      "armRes": 2
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "voltage"
      ],
      "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 pageServo Motor Torque & Speed, at these values