Math & Numbers
Duct Size Calculator (Flow Rate × Velocity)
Size a duct cross-section from the air flow rate Q and the design mean velocity v: area A = Q/v. Circular duct diameter D = √(4A/π). Rectangular duct with aspect ratio r = a/b gives b = √(A/r) and a = r·b, plus the ASHRAE equivalent diameter D_eq = 1.30·(a·b)^0.625/(a+b)^0.25. Flow rate in m³/s/m³/h/CFM, velocity in m/s; dimensions reported in mm and inches.
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/duct-size-calculator' \
-H 'Content-Type: application/json' \
-d '{"shape":"rectangular","flowRate":1000,"flowUnit":"m3/h","velocity":4,"aspectRatio":2,"decimalPlaces":2}'API reference
Send a POST request with your inputs as JSON. File parameters require a separate upload first.
Endpoint
POST https://api.elysiatools.com/en/api/tools/duct-size-calculatorParameters
| Name | Type | Required | Description |
|---|---|---|---|
| shape | select | No | Duct cross-section shape: Rectangular or Circular. |
| flowRate | number | Yes | Volumetric air flow rate Q. Enter in the selected Flow Unit. |
| flowUnit | select | No | — |
| velocity | number | Yes | Design mean air velocity v in m/s. Typical: low-pressure 3–5 m/s, main 6–8 m/s. |
| aspectRatio | 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:
{
"mcpServers": {
"elysiatools-duct-size-calculator": {
"name": "duct-size-calculator",
"description": "Size a duct cross-section from the air flow rate Q and the design mean velocity v: area A = Q/v. Circular duct diameter D = √(4A/π). Rectangular duct with aspect ratio r = a/b gives b = √(A/r) and a = r·b, plus the ASHRAE equivalent diameter D_eq = 1.30·(a·b)^0.625/(a+b)^0.25. Flow rate in m³/s/m³/h/CFM, velocity in m/s; dimensions reported in mm and inches.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=duct-size-calculator",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}List available tools
After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "duct-size-calculator",
"arguments": {
"shape": "rectangular",
"flowRate": 1000,
"flowUnit": "m3/h",
"velocity": 4,
"aspectRatio": 2,
"decimalPlaces": 2
}
}
}