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-emfParameters
| 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]