Math & Numbers

Inverse Laplace Transform Calculator (Partial Fractions)

Partial-fraction inverse Laplace transform for proper rational functions: root factorization (real + conjugate pairs), exact coefficient system, term-by-term inversion.

text· Text resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/inverse-laplace-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"numCoeffs":"1","denCoeffs":"2,3,1","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/inverse-laplace-calculator

Parameters

Name	Type	Required	Description
numCoeffs	text	Yes	Comma-separated numerator coefficients, constant term first, e.g. 5,3 → 3s + 5.
denCoeffs	text	Yes	Comma-separated denominator coefficients, constant term first, degree ≤ 6, e.g. 2,3,1 → s² + 3s + 2.
decimalPlaces	number	No	—

Response format

Text result

JSON

{
  "result": "Processed text content",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

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-inverse-laplace-calculator": {
      "name": "inverse-laplace-calculator",
      "description": "Partial-fraction inverse Laplace transform for proper rational functions: root factorization (real + conjugate pairs), exact coefficient system, term-by-term inversion.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=inverse-laplace-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": "inverse-laplace-calculator",
    "arguments": {
  "numCoeffs": "1",
  "denCoeffs": "2,3,1",
  "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]

Browse tools Open tool

Name

Type

Required

Description

numCoeffs

text

Yes

Comma-separated numerator coefficients, constant term first, e.g. 5,3 → 3s + 5.

denCoeffs

text

Yes

Comma-separated denominator coefficients, constant term first, degree ≤ 6, e.g. 2,3,1 → s² + 3s + 2.

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-inverse-laplace-calculator": { "name": "inverse-laplace-calculator", "description": "Partial-fraction inverse Laplace transform for proper rational functions: root factorization (real + conjugate pairs), exact coefficient system, term-by-term inversion.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=inverse-laplace-calculator", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "inverse-laplace-calculator", "arguments": { "numCoeffs": "1", "denCoeffs": "2,3,1", "decimalPlaces": 4 } } }