Math & Numbers

DC Motor Back-EMF & Torque Calculator (E=kω, T=kI)

Compute the back-EMF and electromagnetic torque of a DC motor from its machine constant: E=k·ω, T=k·I. In SI units the back-EMF constant equals the torque constant (k_e=k_t=k, V·s/rad=N·m/A). Also returns the mechanical (air-gap) power P=T·ω=E·I. Speed accepted in rad/s or RPM.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/dc-motor-back-emf' \
  -H 'Content-Type: application/json' \
  -d '{"k":0.1,"speed":100,"speedUnit":"rad_s","current":5,"decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/dc-motor-back-emf

Parameters

Name	Type	Required	Description
k	number	Yes	Machine constant k. In SI units k_e (V·s/rad) = k_t (N·m/A) = k.
speed	number	Yes	Rotor angular speed in the selected unit (rad/s or RPM).
speedUnit	select	No	—
current	number	Yes	Armature current I (A). May be 0 (then torque and power are 0).
decimalPlaces	number	No

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-dc-motor-back-emf": {
      "name": "dc-motor-back-emf",
      "description": "Compute the back-EMF and electromagnetic torque of a DC motor from its machine constant: E=k·ω, T=k·I. In SI units the back-EMF constant equals the torque constant (k_e=k_t=k, V·s/rad=N·m/A). Also returns the mechanical (air-gap) power P=T·ω=E·I. Speed accepted in rad/s or RPM.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=dc-motor-back-emf",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "dc-motor-back-emf",
    "arguments": {
  "k": 0.1,
  "speed": 100,
  "speedUnit": "rad_s",
  "current": 5,
  "decimalPlaces": 4
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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