Verified calculation capability

Area moment Calculation Capability

Second moment of composite plane areas about the composite centroid. Centroid reuses plane centroid. Parallel-axis shift of supplied centroidal Ix and Iy. Radius of gyration is sqrt(I/A). Not a section modulus and not a beam.

Mechanical · Statics Capability ID mechanical.statics.area_moment version 1.0.0 UNPUBLISHED

Model

Parallel axis

Parallel axis: Ix = Σ(Īx + A (y − ȳ)²)
Radius of gyration: kx = √(Ix / A), ky = √(Iy / A)

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`parts`	Rows Ix,Iy,A,x,y separated by semicolons	—	input
`area`	—	—	output
`x`	—	bar	output
`y`	—	bar	output
`Ix`	—	—	output
`Iy`	—	—	output
`kx`	—	—	output
`ky`	—	—	output
`n`	—	—	output
`model`	—	—	output
`solver`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Ix and Iy are supplied about each part centroid
Axes stay parallel to x and y
Negative area is a hole
Total area must not be zero
Not product of inertia, principal axes, section modulus, or beam deflection

Example

One numerical check. The calculator page holds worked steps and FAQ.

1,0,1,0,0; 1,0,1,0,2 → Ix = 4, ȳ = 1

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 6/6 calculation tests · golden 2/2 · boundary 4/4 · property 0/0
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (3 capabilities; 189 remain CURRENT) @ 2026-09-23T10:40:38.140Z
Semantic contract: PASS
Evidence attested at: 2026-09-23T02:27:54.588Z
Last production check: 2026-09-23T02:27:54.588Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/area-moment' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"parts":"1,0,1,0,0; 1,0,1,0,2"},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "parts": "1,0,1,0,0; 1,0,1,0,2"
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/area-moment. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: area-moment
Engine: area-moment
REST: POST /api/v1/calc/area-moment
MCP: execute_calculation with capability_id: "mechanical.statics.area_moment"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Hibbeler, Engineering Mechanics: Statics — Moments of inertia

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"mechanical.statics.area_moment"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"mechanical.statics.area_moment","inputs":{"parts":"1,0,1,0,0; 1,0,1,0,2"},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.