Math & Numbers

Standard Normal Calculator

Calculate standard normal PDF, CDF, tail probability, two-tail probability, and central area from a z-score

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/standard-normal-calculator' \
  -H 'Content-Type: application/json' \
  -d '{"zScore":1.96,"probabilityMode":"left-tail","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/standard-normal-calculator

Parameters

Name	Type	Required	Description
zScore	number	Yes	—
probabilityMode	select	No	—
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-standard-normal-calculator": {
      "name": "standard-normal-calculator",
      "description": "Calculate standard normal PDF, CDF, tail probability, two-tail probability, and central area from a z-score",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=standard-normal-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": "standard-normal-calculator",
    "arguments": {
  "zScore": 1.96,
  "probabilityMode": "left-tail",
  "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

zScore

number

Yes

—

probabilityMode

select

—

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-standard-normal-calculator": { "name": "standard-normal-calculator", "description": "Calculate standard normal PDF, CDF, tail probability, two-tail probability, and central area from a z-score", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=standard-normal-calculator", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "standard-normal-calculator", "arguments": { "zScore": 1.96, "probabilityMode": "left-tail", "decimalPlaces": 4 } } }