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

Annotations already declare readOnly, idempotent, non-destructive and closed-world, so the safety profile is covered. The description adds real behavioral detail beyond that: unpaginated full listing of id/modes/fields, plus the fact that a calculator=<id> query enriches the response with field hints and an example input. It doesn't discuss size limits or ordering, but the useful extras are there.

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?

Three short sentences, front-loaded with the core listing behavior and then the optional enrichment, then the workflow tip. Nothing is redundant with the title and no sentence could be cut without losing information.

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?

There is no output schema, so the description must carry the return-value burden, and it does: it names the exact fields returned both in the base and calculator-filtered cases. For a two-parameter, all-optional, read-only discovery tool this is sufficient to call correctly.

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 coverage is 100%, so baseline is 3, but the description genuinely adds meaning beyond the schema's terse "Optional: only show this calculator id" by explaining the payoff of that parameter (field hints and an example input). The language parameter is left to the schema, which is acceptable given its enum and default are self-explanatory.

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 a specific verb and resource ("List every calculator") and immediately enumerates the surface it exposes: id, modes, input fields. The variant behavior with calculator=<id> and the routing sentence toward run_calculator make it unambiguous against the nearest sibling.

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?

"Call this before run_calculator" gives an explicit prerequisite and ordering, which is strong when-to-use guidance. It stops short of covering the other sibling (solve_math_question) or any when-not condition, so it isn't a full 5.

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