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

There are no annotations, so the description carries the full burden of explaining behavior. It only says 'calculation,' which implies a read-only computation, but does not disclose what inputs are expected (mass, velocity, radius), what units are used, what output format is returned, or how the tool obtains values given an empty input schema.

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 description is extremely short and front-loaded, but this is under-specification rather than helpful conciseness. It is essentially a noun phrase that adds little beyond the tool name, similar to the 'Process' calibration example.

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 physics calculator with an empty input schema, no annotations, and no output schema, the description is far too sparse. An agent cannot determine what arguments to provide, what formula is used, what units to expect, or what the return value will be. This is seriously inadequate even for a simple calculator.

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?

With zero parameters, there is no input schema semantics to document, so the baseline of 4 applies. The description does not add parameter-level meaning, but none is needed for schema purposes. However, it also fails to explain how the tool gets the values needed for a centripetal force calculation.

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 essentially restates the tool name: 'Centripetal Force: centripetal force calculation.' It identifies the topic and operation, but does not explain what the calculation does, what inputs it needs, or what it returns. It also does not differentiate it from sibling physics calculators like x402-force, x402-gravitational-force, or x402-acceleration.

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?

No guidance is given on when to use this tool versus alternatives such as x402-force or x402-gravitational-force. The only implied usage is 'calculates centripetal force,' but there is no mention of prerequisites, contexts, or exclusions, so an agent cannot decide between this and similar physics tools.

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