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

Annotations already declare readOnlyHint=true, idempotentHint=true and openWorldHint=false, so the safety profile is covered structurally. The description adds one genuinely useful behavioral note — that small-population correction is applied — but says nothing about the return format or what the result represents, leaving the mutation-free read behavior largely to the 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?

Front-loaded with a concrete numeric example, followed by the capability statement and a link. Three short sentences with no bloat, though the trailing web-page URL does not help an agent decide or invoke and could be dropped.

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 deterministic, side-effect-free calculator with a fully documented schema and read-only annotations, the description supplies what an agent needs: the output's meaning, the input concepts, and the population-correction behavior. No output schema exists, but the return value (a sample size) is self-evident from the description.

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% and the schema already documents p (with the 50%-if-unsure heuristic), conf enum, margin and population. The description's mention of 'confidence level, margin of error and proportion, with small-population correction' maps to all four parameters but adds no syntax, units, or constraints beyond the schema, so the baseline 3 applies.

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 ('Get the survey sample size') and pins it down with a concrete worked anchor ('385 responses give ±5% at 95% confidence'). This is clearly separable from near siblings like confidence_interval_calculator or z_score_calculator, which answer a different question.

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 names the inputs it accepts and the small-population correction, which implies when the tool is applicable, but never says when to prefer it over confidence_interval_calculator or what happens if the population is left blank (that detail lives only in the schema). Usage is inferred rather than stated.

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