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IBM

MCP Math Server

by IBM

vector_angle

Calculate the angle between two vectors in radians or degrees for linear algebra applications. Input two vectors to determine their angular relationship.

Instructions

Calculate the angle between two vectors in radians (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
degreesNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden. It states the output is in radians by default, with an optional 'degrees' parameter, which is useful. However, it lacks details on error handling (e.g., invalid vectors, dimension mismatches), performance, or mathematical assumptions (e.g., Euclidean space). For a tool with no annotations, this leaves significant behavioral gaps.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise—a single sentence that efficiently conveys the core purpose and key details (radians default, domain). There is no wasted text, and it is front-loaded with the essential action. Every word earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given no annotations, no output schema, and 0% schema description coverage for 3 parameters, the description is incomplete. It covers the basic purpose and output units but misses critical context: vector format, error conditions, mathematical context (e.g., dot product formula), and how results are returned. For a mathematical tool with multiple inputs, this leaves too much undefined.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the schema provides no parameter descriptions. The description adds minimal semantics: it implies 'vector_a' and 'vector_b' are the vectors to compare, and 'degrees' controls output units. However, it doesn't explain vector format (e.g., arrays of strings representing numbers), dimensionality requirements, or default behavior. With 3 parameters and 0% coverage, the description partially compensates but remains inadequate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Calculate the angle between two vectors in radians.' It specifies the verb ('calculate'), resource ('angle between two vectors'), and domain/context ('linear_algebra.vectors'). However, it doesn't explicitly differentiate from sibling tools like 'angle_difference' or 'convert_angle', which might handle similar angle-related operations.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides minimal usage guidance. It mentions the domain ('linear_algebra.vectors') and category ('general'), but offers no explicit advice on when to use this tool versus alternatives like 'angle_difference' or 'convert_angle'. There are no prerequisites, exclusions, or comparisons to sibling tools listed.

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

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