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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false, and openWorldHint=false, so the safety profile is covered. The description adds only that it returns a minimum sample size and lists the inputs, but does not disclose calculation assumptions such as finite-population correction or handling of defaults. That is useful context, but not rich behavioral detail beyond annotations.

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?

The definition is short and front-loads the core purpose. The 'Inputs' and 'Returns' sentences are somewhat redundant given the input and output schemas, but the overall structure is efficient and easy to parse.

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 simple calculator with full schema coverage, complete annotations, and an output schema, the description is nearly sufficient: it states purpose, usage context, inputs, and return value. The only missing context is any note about calculation assumptions or defaults, though those are partly covered by schema defaults.

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 100%, so the schema already documents population, confidence, and margin_error_pct. The description lists the same parameters but adds no formatting, default, or interpretation details beyond what the schema provides, making the baseline 3 appropriate.

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?

The description states a specific verb and resource: 'Compute required sample size for a survey to hit a target margin of error.' It also identifies the domain (survey design, A/B testing), so an agent can immediately tell what the tool does and when it applies.

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?

It gives clear usage context: 'Use for survey design and A/B testing,' and points to list_bundles for related math calculators. However, it does not name a direct alternative or state any when-not-to-use conditions, so it stops short of explicit routing guidance.

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