Mathematical Calculator MCP Server

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vector_magnitude

Calculate the Euclidean length of a numeric vector and return its scalar magnitude for math, physics, or data analysis tasks.

Instructions

Computes the magnitude of a vector.

Args: vector: A vector as a list of numbers.

Returns: On success: {"result": } On error: {"error": }

Examples: >>> vector_magnitude([1, 2, 3]) {'result': 3.7416573867739413}

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "vector": "<vector>"
    },
    "name": "vector_magnitude"
  }
}

Input Schema

Name	Required	Description	Default
`vector`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv1.1.1Oct 20, 2026

TDQS

A3.7/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden, and it does disclose the result shape ('{result: <scalar magnitude>}') and the error contract ('{error: <error message>}') plus a worked example. It omits any note on edge cases like empty vectors or non-numeric input, so it is strong but not exhaustive.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loads the one-line purpose, then cleanly separates Args, Returns, and an example. The docstring convention is slightly verbose but every section carries information, with no filler sentences.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

There is no output schema, so the Returns section is genuinely needed and present, including the error path, and the example confirms the output form. Coverage is good for a one-parameter tool, though edge-case input behavior remains unspecified.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, but the single parameter's type (array of numbers) is already fully expressed in the schema. The description's 'A vector as a list of numbers' essentially restates that, adding no format, dimensionality, or validation detail beyond structured data.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Computes the magnitude of a vector'), making it unambiguous among siblings like vector_dot_product and vector_cross_product. It does not explicitly name or contrast those siblings, so it falls short of a 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no explicit when-to-use or when-not-to-use guidance, nor any named alternative. For a pure single-purpose math function the intended usage is implied by the definition itself, which matches a 3 rather than a 4 or 5.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.