Math & Numbers

Gear Module Calculator

Calculate the gear module m. m = d/z = p/π. Solve the module from the pitch diameter d and tooth count z, or from the circular pitch p. Also returns the pitch diameter, circular pitch and addendum.

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/gear-module-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"mode":"fromDiameter","pitchDiameter":100,"teeth":20,"circularPitch":0,"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/gear-module-calculator

Parameters

Name	Type	Required	Description
mode	select	No	—
pitchDiameter	number	No	Used in 'Module from d and z' mode.
teeth	number	No	Used in 'Module from d and z' mode.
circularPitch	number	No	Used in 'Module from pitch p' mode.
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-gear-module-calculator": {
      "name": "gear-module-calculator",
      "description": "Calculate the gear module m. m = d/z = p/π. Solve the module from the pitch diameter d and tooth count z, or from the circular pitch p. Also returns the pitch diameter, circular pitch and addendum.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=gear-module-calculator",
      "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": "gear-module-calculator",
    "arguments": {
  "mode": "fromDiameter",
  "pitchDiameter": 100,
  "teeth": 20,
  "circularPitch": 0,
  "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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