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

With no annotations, the description carries the full burden and discloses almost nothing: no statement of units, output format, precision, or error behavior for non-numeric input. The free-trial/payment note is the sole behavioral detail and is orthogonal to how the computation behaves.

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?

Two short fragments, front-loaded with the resource and the computed quantity; no padding. It is terse to the point of under-specification, but nothing is wasted.

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 math tool with two unit-ambiguous string parameters, no output schema, and no annotations, the description should at minimum pin down input units and the returned quantity. As written, an agent knows the concept but not how to call it correctly or interpret the result.

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% and both parameters are untyped-meaning strings, so the description should explain what majorRadius/minorRadius mean and in what units. It says nothing about them, leaving an agent to guess whether values are numbers, strings, or which unit system is expected.

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 restates the name and adds one clarifying word, 'Surface area', which does distinguish it from the sibling x402-torus-volume. However, it does not name that sibling or state the formula/scope, so the agent gets only a marginally clearer picture than the tool name alone.

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?

There is no when-to-use guidance and no mention of the closely related x402-torus-volume tool, which is the obvious alternative an agent must choose between. The only extra clause concerns billing, not invocation context.

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