geometry.area_circle

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

Annotations already guarantee readOnly, idempotent, closed-world behavior, so the safety profile is covered. The description adds real behavioral context beyond them: input must be a non-negative Decimal string, units are free-form and the output is in squared units, π is computed at 50-digit mpmath precision and returned as a 30-significant-digit string. It does not say what happens on a negative or malformed radius, which keeps it below 5.

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

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

Four short sentences, each earning its place: formula and purpose first, then input semantics, then numeric precision and return format, then the diameter pitfall. Front-loaded and free of filler.

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

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

For a one-parameter geometry tool with an output schema already covering return shape, this description covers purpose, input format, precision, and the principal error mode. An agent could call it correctly without any additional information.

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

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

Schema description coverage is 0%, so the description carries the full burden and does: it specifies the type (Decimal string), the constraint (>= 0), the unit semantics (free choice, result squared), and the most likely misuse (passing a diameter). That is a complete semantic specification for the single parameter.

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

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

Names a specific verb (계산한다) and resource (원의 넓이) and states the exact formula π * r², so it is instantly distinguishable from siblings such as geometry.area_rectangle, geometry.area_polygon, and geometry.volume_cylinder. Nothing about the intent requires opening the schema.

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

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

The description clarifies the key input decision (pass the radius, not the diameter) and warns that a diameter yields a 4x-too-large result, which is genuinely useful usage guidance. It does not, however, position the tool against alternatives such as geometry.volume_sphere or geometry.area_polygon, so scope routing is only implied by the tool's own math.

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