Math & Numbers

Gear Train Speed Ratio Calculator

Calculate the overall ratio and output speed of a multi-stage gear train. i_total = i₁·i₂·…·iₙ (each i = z₂/z₁). Enter tooth pairs per stage and the input speed to get the final output speed.

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-train-speed-ratio' \
  -H 'Content-Type: application/json' \
  -d '{"teethInput":"20,60\n15,45","inputSpeed":1800,"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-train-speed-ratio

Parameters

Name	Type	Required	Description
teethInput	textarea	Yes	Each line is one stage: driver teeth, then driven teeth, separated by a comma. Separate stages with new lines or semicolons.
inputSpeed	number	No	Optional. If provided, the final output speed is computed.
decimalPlaces	number	No	—

Response format

JSON result

JSON

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}

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-train-speed-ratio": {
      "name": "gear-train-speed-ratio",
      "description": "Calculate the overall ratio and output speed of a multi-stage gear train. i_total = i₁·i₂·…·iₙ (each i = z₂/z₁). Enter tooth pairs per stage and the input speed to get the final output speed.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=gear-train-speed-ratio",
      "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-train-speed-ratio",
    "arguments": {
  "teethInput": "20,60\n15,45",
  "inputSpeed": 1800,
  "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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Name

Type

Required

Description

teethInput

textarea

Yes

Each line is one stage: driver teeth, then driven teeth, separated by a comma. Separate stages with new lines or semicolons.

inputSpeed

number

Optional. If provided, the final output speed is computed.

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-gear-train-speed-ratio": { "name": "gear-train-speed-ratio", "description": "Calculate the overall ratio and output speed of a multi-stage gear train. i_total = i₁·i₂·…·iₙ (each i = z₂/z₁). Enter tooth pairs per stage and the input speed to get the final output speed.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=gear-train-speed-ratio", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "gear-train-speed-ratio", "arguments": { "teethInput": "20,60\n15,45", "inputSpeed": 1800, "decimalPlaces": 4 } } }