calculator

ellipse_calculation

ellipse_calculation

Calculate the area and approximate perimeter of an ellipse using semi-major and semi-minor axes values.

Instructions

计算椭圆的面积和周长（近似）

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": {
      "semi_major_axis": "<semi_major_axis>",
      "semi_minor_axis": "<semi_minor_axis>"
    },
    "name": "ellipse_calculation"
  }
}

Input Schema

Name	Required	Description	Default
`semi_major_axis`	Yes
`semi_minor_axis`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv1.0.0Jan 5, 2026

TDQS

C2.9/5.0

Behavior2/5

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

No annotations are provided, so the description carries full burden. It states the tool calculates area and perimeter (approximate), but does not disclose behavioral traits such as the mathematical formulas used, precision of approximations, error handling for invalid inputs (e.g., negative axes), or output format. This leaves significant gaps for an agent to understand the tool's behavior.

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

Conciseness5/5

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

The description is a single, efficient sentence in Chinese: '计算椭圆的面积和周长（近似）'. It is front-loaded with the core purpose, has zero wasted words, and is appropriately sized for a straightforward calculation tool.

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

Completeness2/5

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

Given no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on behavior, parameter meanings, output format, and usage context. For a mathematical tool with two parameters, this minimal description does not provide enough information for an agent to use it effectively beyond basic inference.

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%, so the description must compensate. It implies parameters for ellipse dimensions but does not name or explain 'semi_major_axis' and 'semi_minor_axis' from the schema. The description adds minimal value beyond the schema's parameter names, resulting in a baseline score of 3 due to the simple nature of the tool.

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?

The description clearly states the tool's purpose: '计算椭圆的面积和周长（近似）' (calculates the area and perimeter/approximate circumference of an ellipse). It specifies the verb (calculate) and resource (ellipse), but does not differentiate from sibling tools like 'circle_calculation' or 'rectangle_calculation' beyond the resource name.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It does not mention sibling tools like 'circle_calculation' for circular calculations or 'regular_polygon' for other shapes, nor does it specify prerequisites or exclusions for ellipse-specific calculations.

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

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