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tresor4k

macalc

calculate_ellipse

Compute ellipse area and approximate perimeter using semi-major and semi-minor axes. Ideal for elliptical fields, tracks, or design calculations.

Instructions

Compute ellipse area A=π·a·b and approximate perimeter (Ramanujan). Use for elliptical fields, tracks, or design. Inputs: semi-major a, semi-minor b. Returns area and perimeter. See list_bundles for related 'math' calculators.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYesSemi-major axis
bYesSemi-minor axis

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultNoComputed result. Object whose fields depend on the tool (e.g. {tax, marginal_rate, brackets} for tax tools, {volume_l, gallons} for volume tools).
formulaNoHuman-readable formula or method used (e.g. "I=P·r·t", "Magnus formula").
sourceNoAuthoritative source for the rule or formula (e.g. "Article 197 CGI", "NF DTU 21").
reference_urlNoLink to a calcul2 page documenting the calculation in detail.
Behavior4/5

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

No annotations provided, but description discloses the computation (formulas), inputs, and returns. For a pure calculation tool, this is transparent. No side effects or destructive actions are expected.

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?

Three concise sentences front-load the purpose and formula, then provide usage and reference. Every sentence adds value; no fluff.

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

Completeness4/5

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

Covers purpose, usage, inputs, outputs, and links to related tools. Missing details on precision or approximation limitations, but output schema likely covers return structure.

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

Parameters4/5

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

Schema already describes parameters with 100% coverage, but description adds context: identifying a as semi-major and b as semi-minor axes and embedding them in the formulas, reinforcing mathematical meaning.

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

Purpose5/5

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

Clearly states the tool computes ellipse area and perimeter, naming the specific formulas (Ramanujan). Distinguishes from siblings like calculate_area or calculate_perimeter by explicitly being about ellipses.

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

Usage Guidelines4/5

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

Provides use cases: elliptical fields, tracks, or design. Points to list_bundles for related calculators. Lacks explicit comparison to shape-specific siblings but is sufficient for common scenarios.

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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