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

Annotations already declare readOnlyHint, idempotentHint, non-destructive and closed-world, so the safety profile is fully covered and the description adds the deterministic formula. However, it omits unit expectations and says nothing about behavior at the boundary (radius = 0, permitted by the schema's minimum), which matters for a numeric calculator.

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, front-loaded with the formulas so a reader can validate the math immediately. The trailing list_bundles cross-reference is useful but slightly displaces more relevant information such as units.

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?

A single-parameter, formula-defined tool with full annotations and an output schema, so return values need no explanation and the description is nearly sufficient. The one missing element an agent would want is the unit system for radius and the resulting volume/area.

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?

With one parameter at 100% schema description coverage, the schema already documents radius. The description's "Inputs: radius" is a restatement, and the surrounding formulas imply the radius's role but never state units or precision, so it adds no semantics beyond the schema.

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?

States specific verb and resource plus the exact formulas (V=(4/3)πr³, A=4πr²), which unambiguously separates it from sibling solids (calculate_cone, calculate_cylinder, calculate_pyramid) and from the generic calculate_volume. An agent can identify the operation without 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?

Gives concrete usage contexts ("ball, tank, or astronomy problems") and points to list_bundles for related math calculators, so the agent knows when the tool applies. It does not explicitly exclude the near neighbours (calculate_volume, calculate_cone, calculate_cylinder), so the choice among solids is still implied rather than stated.

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