{ "capability_id": "math.percent_error", "tool_id": "percent-error", "engine": "percent-error", "calculation_version": "1.1.4", "generated_at": "2026-10-22T01:03:27.742Z", "engine_build": "2026-10-14", "test_count": 14, "passed": 14, "failed": 0, "tests_summary": { "golden": { "passed": 10, "total": 10 }, "boundary": { "passed": 4, "total": 4 }, "property": { "passed": 0, "total": 0 } }, "engine_tested": true, "expert_reviewed": false, "internally_reviewed": false, "review_kind": null, "source_checked": true, "reviewed_by": null, "reviewer_role": null, "last_reviewed": null, "expert_review": { "status": "optional_not_performed", "reviewer": null, "scope": [ "formula", "input semantics", "assumptions", "limitations", "sources", "tests" ], "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance." }, "internal_review": { "status": "not_applicable", "reviewer": null }, "page": "https://www.calculatorx.com/calc/math/percent-error", "api": "https://www.calculatorx.com/api/v1/calc/percent-error", "schema_input": "https://www.calculatorx.com/schemas/math.percent_error.input.json", "schema_output": "https://www.calculatorx.com/schemas/math.percent_error.output.json", "assumptions": [ "Interactive evaluation runs locally in the browser. Shared URLs and REST may evaluate the same versioned engine on the server (query SSR).", "Accepted value T ≠ 0.", "Default formula uses absolute value so % error ≥ 0.", "Exactly two fields are inputs. Explicit solve_for selects the output. If all three are supplied without solve_for, they are checked for consistency rather than overwritten." ], "limitations": [ "T = 0 → TRUE_VALUE_ZERO", "Inconsistent triples may return status inconsistent", "Reverse solve edge cases → NO_REAL_SOLUTION / INFINITELY_MANY" ], "boundary_conditions": [ "T = 0 → TRUE_VALUE_ZERO (undefined)", "Fewer than two inputs → MISSING_REQUIRED_INPUT", "Invalid solve_for → INVALID_SOLVE_FOR", "Negative P in absolute mode → INVALID_PERCENT", "O = 0, P = 100%, absolute, solve T → INFINITELY_MANY (any T ≠ 0)", "O = 0, P ≠ 100%, absolute, solve T → NO_REAL_SOLUTION", "O ≠ 0, P = 100%, absolute, solve T → T = O/2; the 1 − P/100 branch is omitted (not a full calculation error)", "O = 0, P = −100%, signed, solve T → INFINITELY_MANY (any T ≠ 0)", "O = 0, P ≠ −100%, signed, solve T → NO_REAL_SOLUTION", "O ≠ 0, P = −100%, signed, solve T → NO_REAL_SOLUTION", "Solving from P may yield two candidates (±) when absolute mode is on", "All three values filled without solve_for and not matching the formula → INCONSISTENT_INPUTS" ], "sources": [ { "title": "JCGM 200:2012 — International vocabulary of metrology (VIM)", "section": "§2.16 measurement error", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "Defines measurement error as measured quantity value minus a reference quantity value (ε = O − T). Does not define relative error — VIM §2.18 is measurement bias, not relative error. Does not prescribe a percent-error ×100% laboratory convention.", "kind": "reference", "accessed": "2026-08-28" }, { "title": "NIST Dataplot PERCERR", "section": "Percent error of a true/accepted value vs an observed value", "url": "https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/percerr.htm", "supports": "Documents percent error from an accepted (true) value and an observed value, and notes that some conventions take the absolute value. Instantly readable page — not the frameset handbook root.", "kind": "reference", "accessed": "2026-08-28", "publisher": "National Institute of Standards and Technology" }, { "title": "NIST Dataplot RELERR", "section": "Relative error of a true/accepted value vs an observed value", "url": "https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/relerr.htm", "supports": "Documents relative error (Xt − Xo)/Xt. Notes that some sources take the absolute value, and some reverse numerator order — those change sign, not magnitude.", "kind": "reference", "accessed": "2026-08-28" }, { "title": "CalculatorX laboratory convention", "section": "Absolute-value percent error, signed opt-in, and reverse-solve states", "supports": "Default % error = |O−T|/|T|×100% so the result is ≥ 0; signed (O−T)/T×100% is opt-in. Displayed absolute error is |ε|, the magnitude of VIM measurement error — not a separate VIM term. Absolute reverse-solves publish both ± candidates, omit a zero-denominator branch, and publish INFINITELY_MANY when every T ≠ 0 works. Signed P = −100% with O ≠ 0 is NO_REAL_SOLUTION.", "kind": "definition" } ], "methods": [], "fingerprint": "sha256:783cd14e12cb9811044d6bc3fce9d6c1f6fd3cf96201ae81a3916d8ad4aad9f1", "tier": "engine_tested", "verification": { "tests": { "passed": 14, "total": 14, "golden": 10, "boundary": 4, "property": 0 }, "contract_checks": { "passed": 5, "total": 5 } }, "evidence_core_generated_at": "2026-10-14T02:50:33.742Z", "rendered_at": "2026-10-22T01:03:27.742Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.1.4", "artifacts": { "engine": "1.1.4", "page": "1.1.4", "capability": "1.1.4", "evidence": "1.1.4", "input_schema": "1.1.4", "output_schema": "1.1.4", "mcp_contract": "1.1.4" }, "digests": { "input_schema_sha256": "9e03727ba37a3e2ed408e1b5848d278926befd7c7560784f476b13b239ba0ac9", "output_schema_sha256": "1ffdaff2555960cc04fef346c1146c38f6a8feb12995a9fdb488e220d00a439c", "evidence_sha256": "5f08d089bf833245e1b0b09eb66bc1384a5b33087aed01edff241c86be657f48", "evidence_core_sha256": "5f08d089bf833245e1b0b09eb66bc1384a5b33087aed01edff241c86be657f48", "capability_sha256": "7ac7de746bc902956c88290a5ebc9e5487953995e917a9b89101eaa21e18621a", "engine_sha256": "6ef38e64f6a7018cce0538e78ba57c8e2a141f11e8779e9e3f91408a668b7b71", "mcp_contract_sha256": "e089bba4051e861e09f14334f5cdf32bb35aec100ef05a24d2c91957c8f7c7b9" }, "contract_checks": { "total": 5, "passed": 5, "failed": 0, "items": [ { "id": "release-artifacts-aligned", "status": "pass", "detail": "1.1.4" }, { "id": "schema-output-required-declared", "status": "pass" }, { "id": "schema-valid-input-executes", "status": "pass" }, { "id": "engine-success-output-validates-schema", "status": "pass" }, { "id": "rest-success-payload-validates-schema", "status": "pass" } ] }, "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json" }, "tests": [], "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }