Math & Numbers

Moment of Inertia Calculator

Calculate the second moment of area (I) and section modulus (Z) for common cross-sections: solid circle, rectangle, hollow tube, and I-beam. Results in mm⁴ and cm⁴.

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/moment-of-inertia-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"shape":"circle","D":100,"b":0,"h":0,"Do":0,"Di":0,"B":0,"H":0,"tw":0,"tf":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/moment-of-inertia-calculator

Parameters

Name	Type	Required	Description
shape	select	No	—
D	number	No	Diameter. Required for Solid Circle.
b	number	No	Section width (horizontal). Required for Rectangle.
h	number	No	Section height (vertical). Required for Rectangle.
Do	number	No	Outer diameter. Required for Hollow Circle.

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-moment-of-inertia-calculator": {
      "name": "moment-of-inertia-calculator",
      "description": "Calculate the second moment of area (I) and section modulus (Z) for common cross-sections: solid circle, rectangle, hollow tube, and I-beam. Results in mm⁴ and cm⁴.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=moment-of-inertia-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": "moment-of-inertia-calculator",
    "arguments": {
  "shape": "circle",
  "D": 100,
  "b": 0,
  "h": 0,
  "Do": 0,
  "Di": 0,
  "B": 0,
  "H": 0,
  "tw": 0,
  "tf": 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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