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physics-calculators

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Physics calculators that show their work, plus the CODATA 2022 constants. Educational use.

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Status
Healthy
Last Tested
Transport
Streamable HTTP · MCP 2025-11-25
URL
ChatGPT
–
Claude
–

TDQS

A3.9/5.0

Scored across 4 tools

Disambiguation5/5

The four tools split cleanly along two axes: listing vs. resolving, applied separately to calculators and constants. calculate is scoped by an id from list_calculators, while get_constant is a lookup producing a constant record; no two tools could be reasonably confused for one another.

Naming Consistency4/5

Three tools use a predictable verb_noun pattern (list_calculators, list_constants, get_constant), but the primary execution tool is a bare verb 'calculate' rather than something like 'run_calculator'. Minor deviation, still immediately readable.

Tool Count4/5

Four tools is on the lean side, but each maps to a distinct need: discover calculators, run one, discover constants, fetch one. Nothing is redundant, though the surface is small enough that it borders on thin.

Completeness4/5

This is a read-only reference/execution domain, and the discovery-plus-execution lifecycle is covered for both calculators and constants. Gaps are minor: no free-text search across calculators/constants, no unit-conversion or batch-calculation helper, and no way to validate input keys before calling calculate.

Available Tools

4 tools
calculateRun a calculatorA
Read-onlyIdempotent
Inspect

Run one calculator by id with numeric inputs (keys from list_calculators, in the listed units). Returns every result with its unit, the formula, the Given → Formula → Substitute → Result working when the engine can derive it, and the URL of the solved page.

NameRequiredDescriptionDefault
inputsYesInput values keyed by input key, in the listed units; a missing key takes the default
calculator_idYesThe calculator id (slug) from list_calculators, e.g. kinetic-energy

TDQS

A4.1/5.0
Behavior4/5

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

Annotations already declare readOnly, idempotent, non-destructive and closed-world, so safety is covered; the description adds real value by disclosing the response payload (result values with units, the formula, the worked Given → Formula → Substitute → Result when derivable, and a solved-page URL). With no output schema, that return-shape disclosure is genuinely load-bearing. It omits failure behavior for unknown calculator ids or unit mismatches.

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

Conciseness4/5

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

A single front-loaded sentence with no filler — the action and its inputs come first, return details after. It is dense, enumerating four return components in one clause, but every clause earns its place.

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 the two things an agent needs beyond the schema: where ids/keys come from and what comes back, which matters since there is no output schema. Annotations handle the safety profile. Only edge-case behavior (invalid id, unit mismatch, unknown key) is left unaddressed.

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 100%, so both parameters are already documented, including the defaults rule and the slug example. The description reinforces that input keys must come from list_calculators and must be in the listed units, adding a modest constraint but no syntax beyond what the schema states. Baseline 3 applies.

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?

States a specific verb and resource ('Run one calculator by id') and immediately scopes it to a single calculator with numeric inputs, which cleanly separates it from the sibling listing tools (list_calculators, list_constants) and get_constant. The parenthetical pointing at list_calculators as the source of ids tells an agent exactly where this tool sits in the workflow.

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?

Gives clear context: obtain the id from list_calculators, supply keys in the listed units, and missing keys fall back to defaults. It stops short of exclusions — it never says when NOT to use it or when to call get_constant instead of passing a constant as a numeric input, so no alternative routing is given beyond the id-sourcing prerequisite.

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

get_constantLook up a physical constantA
Read-onlyIdempotent
Inspect

One CODATA 2022 constant by id, symbol or name (e.g. 'c', 'speed of light', 'planck-constant'): value as NIST prints it, machine-readable value, standard uncertainty (null = exact), unit, note, page and NIST source.

NameRequiredDescriptionDefault
queryYesid, symbol or name, e.g. 'c', 'speed-of-light-in-vacuum', 'Planck constant'

TDQS

A4.3/5.0
Behavior4/5

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

Annotations already declare readOnly, idempotent, non-destructive and closed-world, so the safety profile is covered. The description goes further by enumerating the returned content (printed value, machine-readable value, uncertainty, unit, note, page, source) and, critically, disclosing that a null standard uncertainty means an exact constant — a genuinely useful interpretive detail annotations cannot supply.

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?

A single dense sentence with the resource and accepted key forms front-loaded, followed by the return payload. No filler and nothing redundant given the tool's simplicity.

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

Completeness5/5

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

For a one-parameter read with no output schema, the description covers both the input forms and the shape of the result, including the null-uncertainty convention. There is no obvious gap an agent would need filled before calling it.

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 100%, so the single query parameter is already documented with the same example forms. The description restates that id, symbol or name are accepted but adds no format or disambiguation rules beyond the schema; baseline 3 applies.

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?

States a specific verb+resource (one CODATA 2022 constant) with an explicit input space (id, symbol or name) and concrete examples. The singular "one" implicitly distinguishes it from the sibling list_constants, which returns multiple.

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?

The context is clear: this is the single-record lookup path, and the examples ('c', 'speed of light', 'planck-constant') show the accepted identifier forms. It never explicitly names list_constants as the browse alternative or states when not to use it, so it stops short of full routing guidance.

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

list_calculatorsList the calculatorsA
Read-onlyIdempotent
Inspect

Every UsePhysics calculator: id (slug), name, category, formula, inputs (key, unit, default) and page URL. Optional category filter.

NameRequiredDescriptionDefault
categoryNoe.g. Mechanics, Energy, Electricity & Waves, Everyday Life

TDQS

A3.5/5.0
Behavior3/5

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

Annotations already declare readOnlyHint=true, idempotentHint=true, openWorldHint=false and destructiveHint=false, so the safety profile is fully covered without the description's help. The description adds the shape of the payload by enumerating returned fields, which is genuinely useful given there is no output schema. It says nothing about ordering, pagination, or result size for what is presumably the full catalogue.

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

Conciseness4/5

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

A single front-loaded sentence that covers the resource, returned fields, and the one option; nothing is padded. It is written as a fragment rather than a sentence with an explicit verb, which costs a little clarity.

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?

With no output schema and only one optional parameter, the description carries its weight by listing the exact fields returned, so an agent knows what it gets without calling. Missing ordering and pagination details keep it from being fully complete.

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 100%, so the schema with its example category values already does the work and baseline 3 applies. The description's 'Optional category filter' restates rather than extends the schema by confirming it is not required and that omitting it returns everything, which is a small but real addition.

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 states this returns every UsePhysics calculator and enumerates the returned fields (id slug, name, category, formula, inputs, page URL), which clearly separates it from calculate, get_constant and list_constants. The verb 'list' only appears in the title, and no sibling is named explicitly, so it stops short of a 5.

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

Usage Guidelines3/5

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

'Optional category filter' implies that filtering is available but never states when to filter versus fetching all. There is no guidance on choosing list_calculators over calculate, or on what to do when a category returns nothing. Usage is inferable but not taught.

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

list_constantsList the physical constantsA
Read-onlyIdempotent
Inspect

The CODATA 2022 constants UsePhysics keeps, grouped; optional group id filter. Values are NIST's.

NameRequiredDescriptionDefault
groupNoA group id from a previous answer, e.g. si-defining-constants

TDQS

A3.5/5.0
Behavior3/5

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

Annotations already cover the safety profile fully (readOnly, idempotent, closed-world, non-destructive), so the bar is lower. The description adds genuine context the annotations cannot: data provenance (CODATA 2022, NIST values) and the fact that results are grouped. It does not describe the return envelope, which matters somewhat since no output schema is declared.

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

Conciseness4/5

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

Two short clauses, front-loaded with the resource and provenance before the filter detail. No filler, though the phrasing 'the constants UsePhysics keeps' is slightly informal relative to the otherwise technical register.

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?

For a zero-required-parameter read tool with rich annotations, the description covers provenance, grouping, and filtering, which is what an agent needs to select and call it. The main residual gap is the shape of the returned grouping, which cannot be inferred without an output schema.

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 coverage is 100% and the schema already documents the group parameter, including the example id. The description only restates that the filter is optional over a grouped result, adding no format or validation detail beyond the schema, so the baseline applies.

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?

States the specific resource (CODATA 2022 physical constants) and the organizing shape (grouped, with an optional group filter), which is enough to separate it from get_constant and list_calculators. It never names those siblings explicitly, so the differentiation is inferred rather than stated.

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

Usage Guidelines3/5

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

The phrase 'optional group id filter' implies the two usage modes (list everything vs. narrow to one group), but there is no explicit guidance on when to prefer this over get_constant for a single value, nor any prerequisite or exclusion. Usage is implied rather than prescribed.

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

Tool Schema Changelog

Recent tool additions, removals, and schema changes observed during successful MCP inspections.

  1. 4 tool updates
    • First observedcalculate
    • First observedget_constant
    • First observedlist_calculators
    • First observedlist_constants

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