{ "capability_id": "electrical.capacitance", "tool_id": "capacitance", "engine": "capacitance", "calculation_version": "1.1.0", "generated_at": "2026-09-16T22:03:43.728Z", "engine_build": "2026-09-11", "test_count": 17, "passed": 17, "failed": 0, "tests_summary": { "golden": { "total": 3, "passed": 3 }, "boundary": { "total": 8, "passed": 8 }, "property": { "total": 6, "passed": 6 } }, "engine_tested": true, "expert_reviewed": true, "internally_reviewed": false, "review_kind": "expert", "source_checked": true, "reviewed_by": "CalculatorX electrical review", "reviewer_role": "electrical-engineer", "last_reviewed": "2026-09-11", "expert_review": { "status": "approved", "reviewer": { "name": "CalculatorX electrical review", "role": "electrical-engineer" }, "reviewed_at": "2026-09-11", "scope": [ "formula", "input semantics", "assumptions", "limitations", "sources", "tests" ], "kind": "expert" }, "internal_review": { "status": "not_applicable", "reviewer": null }, "page": "https://www.calculatorx.com/calc/electric/capacitance", "api": "https://www.calculatorx.com/api/v1/calc/capacitance", "schema_input": "https://www.calculatorx.com/schemas/electrical.capacitance.input.json", "schema_output": "https://www.calculatorx.com/schemas/electrical.capacitance.output.json", "assumptions": [ "Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap", "Relative permittivity is a scalar constant (no frequency dependence or dielectric loss)", "Fringing, leakage, ESR/ESL and parasitic capacitance are neglected", "Scope is vacuum or conventional passive dielectric: εr ≥ 1" ], "limitations": [ "Ideal parallel plates; homogeneous isotropic dielectric fully filling the gap; fringing, frequency dependence, dielectric loss, leakage, ESR/ESL and parasitics neglected" ], "boundary_conditions": [ "A, d, Ci ≤ 0 → VALUE_MUST_BE_POSITIVE", "εr ≤ 0 → VALUE_MUST_BE_POSITIVE; 0 < εr < 1 → VALUE_OUT_OF_RANGE (εr ≥ 1 required)", "parallel/series with fewer than two capacitances → NEEDS_TWO_INPUTS", "unknown mode → INVALID_MODE" ], "sources": [ { "title": "IEC 60050-131 — International Electrotechnical Vocabulary", "section": "Capacitance (IEV 131-12-13)", "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-12-13", "supports": "Definition C = Q/U", "kind": "standard", "accessed": "2026-09-11", "clause": "IEV 131-12-13" }, { "title": "IEC 60050-121 — International Electrotechnical Vocabulary", "section": "Electric constant (IEV 121-11-03)", "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-03", "supports": "Vacuum electric permittivity ε0 used in C = ε0·εr·A/d", "kind": "standard", "accessed": "2026-09-11", "clause": "IEV 121-11-03" }, { "title": "IEC 60050-121 — International Electrotechnical Vocabulary", "section": "Relative permittivity (IEV 121-12-13)", "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-12-13", "supports": "εr as a scalar ratio; this page does not use complex permittivity", "kind": "standard", "accessed": "2026-09-11", "clause": "IEV 121-12-13" }, { "title": "NIST CODATA 2022", "section": "Vacuum electric permittivity ε0", "url": "https://physics.nist.gov/cgi-bin/cuu/Value?ep0", "supports": "Engine constant ε0 = 8.8541878188×10⁻¹² F/m", "kind": "reference", "accessed": "2026-09-11" }, { "title": "Horowitz & Hill — The Art of Electronics, 3rd ed.", "section": "Capacitor networks (series/parallel combinations)", "supports": "Parallel sum and series reciprocal sum", "kind": "reference" } ], "methods": [], "fingerprint": "sha256:517e5fb7d116021589bd6cca4b4fa9db355d18438b09c41d81d446cb2237f824", "tests": [ { "id": "plate", "ok": true, "kind": "golden", "inputs": { "mode": "plate", "A_m2": 0.01, "d_m": 0.001, "er": 4 }, "expect": { "C_F": 3.54167512752e-10 }, "expectWarning": null, "actual": { "mode": "plate", "A_m2": 0.01, "d_m": 0.001, "er": 4, "C_F": 3.54167512752e-10, "C_uF": 0.000354167512752, "C_nF": 0.35416751275200004, "C_pF": 354.167512752 }, "tol": 1e-20 }, { "id": "parallel", "ok": true, "kind": "golden", "inputs": { "mode": "parallel", "capacitors_F": [ 0.000001, 0.000002 ] }, "expect": { "C_F": 0.000003 }, "expectWarning": null, "actual": { "mode": "parallel", "n": 2, "C_F": 0.000003, "C_uF": 3, "capacitors_F": [ 0.000001, 0.000002 ] }, "tol": 1e-18 }, { "id": "series", "ok": true, "kind": "golden", "inputs": { "mode": "series", "capacitors_F": [ 0.000002, 0.000002 ] }, "expect": { "C_F": 0.000001 }, "expectWarning": null, "actual": { "mode": "series", "n": 2, "C_F": 0.000001, "C_uF": 1, "capacitors_F": [ 0.000002, 0.000002 ] }, "tol": 1e-18 }, { "id": "bad-d", "ok": true, "kind": "boundary", "inputs": { "mode": "plate", "A_m2": 0.01, "d_m": 0, "er": 4 }, "expectError": "VALUE_MUST_BE_POSITIVE", "code": "VALUE_MUST_BE_POSITIVE", "error": "d_m must be greater than zero" }, { "id": "boundary-cap-plate", "ok": true, "kind": "boundary", "inputs": { "mode": "plate", "A_m2": 0.01, "d_m": 0.001, "er": 1 }, "expect": { "C_F": 8.8541878188e-11 }, "expectWarning": null, "actual": { "mode": "plate", "A_m2": 0.01, "d_m": 0.001, "er": 1, "C_F": 8.8541878188e-11, "C_uF": 0.000088541878188, "C_nF": 0.08854187818800001, "C_pF": 88.541878188 }, "tol": 1e-20 }, { "id": "boundary-cap-series-three", "ok": true, "kind": "boundary", "inputs": { "mode": "series", "capacitors_F": [ 0.000003, 0.000003, 0.000003 ] }, "expect": { "C_F": 0.000001 }, "expectWarning": null, "actual": { "mode": "series", "n": 3, "C_F": 0.000001, "C_uF": 1, "capacitors_F": [ 0.000003, 0.000003, 0.000003 ] }, "tol": 1e-18 }, { "id": "boundary-cap-bad", "ok": true, "kind": "boundary", "inputs": { "mode": "plate", "A_m2": 0, "d_m": 0.001, "er": 1 }, "expectError": "VALUE_MUST_BE_POSITIVE", "code": "VALUE_MUST_BE_POSITIVE", "error": "A_m2 must be greater than zero" }, { "id": "boundary-cap-d-zero", "ok": true, "kind": "boundary", "inputs": { "mode": "plate", "A_m2": 0.01, "d_m": 0, "er": 1 }, "expectError": "VALUE_MUST_BE_POSITIVE", "code": "VALUE_MUST_BE_POSITIVE", "error": "d_m must be greater than zero" }, { "id": "boundary-cap-er-frac", "ok": true, "kind": "boundary", "inputs": { "mode": "plate", "A_m2": 0.01, "d_m": 0.001, "er": 0.5 }, "expectError": "VALUE_OUT_OF_RANGE", "code": "VALUE_OUT_OF_RANGE", "error": "er must be ≥ 1 (vacuum or conventional passive dielectric)" }, { "id": "boundary-cap-one", "ok": true, "kind": "boundary", "inputs": { "mode": "parallel", "capacitors_F": [ 0.000001 ] }, "expectError": "NEEDS_TWO_INPUTS", "code": "NEEDS_TWO_INPUTS", "error": "Provide at least two capacitances (capacitors_F, or C1 and C2)" }, { "id": "boundary-cap-mode", "ok": true, "kind": "boundary", "inputs": { "mode": "coax", "A_m2": 0.01, "d_m": 0.001, "er": 1 }, "expectError": "INVALID_MODE", "code": "INVALID_MODE", "error": "mode must be plate|parallel|series" }, { "id": "property-plate", "ok": true, "kind": "property", "detail": "ε0·A/d", "expect": 8.8541878188e-11, "actual": 8.8541878188e-11 }, { "id": "property-parallel", "ok": true, "kind": "property", "detail": "ΣC", "expect": 0.000003, "actual": 0.000003 }, { "id": "property-series", "ok": true, "kind": "property", "detail": "½", "expect": 5e-7, "actual": 5e-7 }, { "id": "property-parallel-commute", "ok": true, "kind": "property", "detail": "C(C1,C2)=C(C2,C1)", "expect": 0.000003, "actual": 0.000003 }, { "id": "property-parallel-gt-max", "ok": true, "kind": "property", "detail": "Ceq>max(Ci)", "expect": true, "actual": 0.000003 }, { "id": "property-series-lt-min", "ok": true, "kind": "property", "detail": "Ceq