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

No annotations are supplied, so the description carries the full burden. It does disclose one genuinely behavioral fact — the tool requires a signed wallet and offers 5 free trial calls — which is real context, but it says nothing about unit expectations, numeric handling, or the return value for a three-parameter computation.

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?

It is short and front-loaded with the tool name, with no filler sentences. However, the brevity comes from under-specification rather than efficiency — the first clause duplicates the name and title and the second clause is unrelated to invocation.

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 three-parameter physics calculator with no annotations, no output schema, and zero parameter documentation, the description supplies essentially none of what an agent needs to call it correctly. Units, formula variant, output format, and tie-breaking against similar physics siblings are all absent.

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 all three parameters are typed only as generic strings. The description never mentions mass, radius, or velocity, so an agent gets no unit conventions (kg vs g, m vs cm) and cannot tell whether the inputs are numbers-as-strings or symbolic expressions.

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?

"Centripetal Force: Centripetal force calculation" restates the tool name and title without adding a verb+resource distinction. It does not say what the output is (force in newtons?) or how it differs from nearby siblings such as x402-force, x402-gravitational-force, or x402-momentum, leaving the name to do all the work.

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, no mention of the formula (F = mv²/r), no exclusions, and no pointer to an alternative tool. The only extra sentence is a payment/free-tier note, not usage guidance.

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