{
  "capability_id": "electrical.battery.aging",
  "tool_id": "battery-aging",
  "engine": "battery-aging",
  "calculation_version": "1.0.2",
  "generated_at": "2026-09-16T22:03:43.746Z",
  "engine_build": "2026-09-10",
  "test_count": 14,
  "passed": 14,
  "failed": 0,
  "tests_summary": {
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      "total": 3,
      "passed": 3
    },
    "boundary": {
      "total": 6,
      "passed": 6
    },
    "property": {
      "total": 5,
      "passed": 5
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  "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": "2026-09-05",
  "expert_review": {
    "status": "approved",
    "reviewer": {
      "name": "CalculatorX electrical review",
      "role": "electrical-engineer"
    },
    "reviewed_at": "2026-09-05",
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "kind": "expert"
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  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/electric/battery-aging",
  "api": "https://www.calculatorx.com/api/v1/calc/battery-aging",
  "schema_input": "https://www.calculatorx.com/schemas/electrical.battery.aging.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/electrical.battery.aging.output.json",
  "assumptions": [
    "Independent linear cycle + calendar fade",
    "Default k_cycle=0.0002/cycle and k_cal=0.02/year are illustrative",
    "N should match the cycle definition used to calibrate k_cycle; EFC recommended",
    "Not temperature, SOC, DoD, C-rate, or chemistry aware"
  ],
  "limitations": [
    "Linear independent cycle+calendar fade — not temperature, SOC, DoD, C-rate, or chemistry aware",
    "Default k_cycle=0.0002/cycle and k_cal=0.02/year are illustrative",
    "fade_frac is unclamped exposure and may exceed 1; SOH and capacity_Ah are clamped at 0"
  ],
  "boundary_conditions": [
    "C0≤0 → VALUE_MUST_BE_POSITIVE",
    "N, years, k_cycle, k_cal < 0 → VALUE_MUST_BE_NON_NEGATIVE",
    "Unclamped fade > 1 → SOH=0 and C=0"
  ],
  "sources": [
    {
      "title": "Smith, K.; Neubauer, J.; Wood, E.; Jun, M.; Pesaran, A. — Models for Battery Reliability and Lifetime: Applications in Design and Health Management",
      "section": "NREL/PR-5400-58550",
      "url": "https://www.nrel.gov/docs/fy13osti/58550.pdf",
      "supports": "Institutional evidence that battery lifetime models combine cycle and calendar degradation, with coefficients that depend on temperature, DOD, voltage/SOC, and other stress factors — not a single universal linear law. CalculatorX uses a deliberately simplified linear approximation, not the NREL life model. (Distinct from NREL/CP-5400-57746, which has a different author list.)",
      "kind": "reference",
      "accessed": "2026-09-05",
      "publisher": "National Renewable Energy Laboratory",
      "published": "2013"
    },
    {
      "title": "Saldaña, G.; San Martín, J. I.; Zamora, I.; Asensio, F. J.; Oñederra, O.; González-Pérez, M. — Empirical calendar ageing model for electric vehicles and energy storage systems batteries",
      "section": "Calendar fade vs storage time, temperature, and SOC",
      "url": "https://doi.org/10.1016/j.est.2022.105676",
      "supports": "Shows calendar ageing is commonly modeled with a power of time (often near t^1/2) and is strongly sensitive to storage temperature and SOC. Documents why CalculatorX linear-in-years k_cal is an illustrative first-order stand-in, not the complete empirical model.",
      "kind": "reference",
      "accessed": "2026-09-05",
      "publisher": "Journal of Energy Storage",
      "published": "2022",
      "doi": "https://doi.org/10.1016/j.est.2022.105676"
    },
    {
      "title": "NREL — Battery lifespan modeling (BLAST / life-model overview)",
      "section": "Calendar and cycle aging, operating windows, and stress factors",
      "url": "https://www.nrel.gov/transportation/battery-lifespan.html",
      "supports": "Public institutional overview that lifetime prediction must consider temperature, operating windows, charge/discharge rates, storage environment, and cycling patterns. Used here to bound the scope of the linear model — not as a coefficient source.",
      "kind": "reference",
      "accessed": "2026-09-05",
      "publisher": "National Renewable Energy Laboratory"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:665eac2d2a81eb2215b2a1834aa96235cda400f92218f4362d905e8536c25471",
  "tests": [
    {
      "id": "golden-default",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "C0_Ah": 3,
        "N_cycles": 500,
        "years": 1
      },
      "expect": {
        "capacity_Ah": 2.64,
        "SOH": 0.88
      },
      "expectWarning": null,
      "actual": {
        "mode": "linear_fade",
        "C0_Ah": 3,
        "N_cycles": 500,
        "years": 1,
        "k_cycle": 0.0002,
        "k_cal": 0.02,
        "fade_frac": 0.12000000000000001,
        "SOH": 0.88,
        "capacity_Ah": 2.64
      },
      "tol": 1e-12
    },
    {
      "id": "zero-aging",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "C0_Ah": 3,
        "N_cycles": 0,
        "years": 0
      },
      "expect": {
        "capacity_Ah": 3,
        "SOH": 1
      },
      "expectWarning": null,
      "actual": {
        "mode": "linear_fade",
        "C0_Ah": 3,
        "N_cycles": 0,
        "years": 0,
        "k_cycle": 0.0002,
        "k_cal": 0.02,
        "fade_frac": 0,
        "SOH": 1,
        "capacity_Ah": 3
      },
      "tol": 1e-12
    },
    {
      "id": "custom-coefficients",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "C0_Ah": 3,
        "N_cycles": 500,
        "years": 1,
        "k_cycle": 0.0001,
        "k_cal": 0.01
      },
      "expect": {
        "capacity_Ah": 2.82,
        "SOH": 0.94
      },
      "expectWarning": null,
      "actual": {
        "mode": "linear_fade",
        "C0_Ah": 3,
        "N_cycles": 500,
        "years": 1,
        "k_cycle": 0.0001,
        "k_cal": 0.01,
        "fade_frac": 0.060000000000000005,
        "SOH": 0.94,
        "capacity_Ah": 2.82
      },
      "tol": 1e-12
    },
    {
      "id": "bad-C0",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 0,
        "N_cycles": 1
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "C0_Ah must be greater than zero"
    },
    {
      "id": "negative-cycles",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 3,
        "N_cycles": -1
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "N_cycles must be ≥ 0"
    },
    {
      "id": "negative-years",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 3,
        "years": -1
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "years must be ≥ 0"
    },
    {
      "id": "negative-k-cycle",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 3,
        "k_cycle": -0.001
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "k_cycle must be ≥ 0"
    },
    {
      "id": "negative-k-calendar",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 3,
        "k_cal": -0.01
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "k_cal must be ≥ 0"
    },
    {
      "id": "boundary-clamp-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "C0_Ah": 3,
        "N_cycles": 10000,
        "years": 0
      },
      "expect": {
        "capacity_Ah": 0,
        "SOH": 0
      },
      "expectWarning": null,
      "actual": {
        "mode": "linear_fade",
        "C0_Ah": 3,
        "N_cycles": 10000,
        "years": 0,
        "k_cycle": 0.0002,
        "k_cal": 0.02,
        "fade_frac": 2,
        "SOH": 0,
        "capacity_Ah": 0
      },
      "tol": 1e-12
    },
    {
      "id": "property-capacity-bounded",
      "ok": true,
      "kind": "property",
      "detail": "0 ≤ C ≤ C0 and 0 ≤ SOH ≤ 1",
      "expect": true,
      "actual": [
        {
          "C": 3,
          "C0": 3,
          "SOH": 1
        },
        {
          "C": 2.64,
          "C0": 3,
          "SOH": 0.88
        },
        {
          "C": 0,
          "C0": 3,
          "SOH": 0
        },
        {
          "C": 4.1000000000000005,
          "C0": 5,
          "SOH": 0.8200000000000001
        }
      ]
    },
    {
      "id": "property-cycle-monotonic",
      "ok": true,
      "kind": "property",
      "detail": "N2>N1 ⇒ C(N2)≤C(N1)",
      "expect": true,
      "actual": [
        2.88,
        2.46
      ]
    },
    {
      "id": "property-calendar-monotonic",
      "ok": true,
      "kind": "property",
      "detail": "t2>t1 ⇒ C(t2)≤C(t1)",
      "expect": true,
      "actual": [
        2.91,
        2.7
      ]
    },
    {
      "id": "property-output-identity",
      "ok": true,
      "kind": "property",
      "detail": "fade_frac=kN+kt; SOH=max(0,1−fade); C=C0·SOH",
      "expect": true,
      "actual": [
        {
          "fade_frac": 0,
          "SOH": 1,
          "capacity_Ah": 3
        },
        {
          "fade_frac": 0.12000000000000001,
          "SOH": 0.88,
          "capacity_Ah": 2.64
        },
        {
          "fade_frac": 2,
          "SOH": 0,
          "capacity_Ah": 0
        },
        {
          "fade_frac": 0.18,
          "SOH": 0.8200000000000001,
          "capacity_Ah": 4.1000000000000005
        }
      ]
    },
    {
      "id": "property-default-equivalence",
      "ok": true,
      "kind": "property",
      "detail": "omit k ≡ explicit k_cycle=0.0002, k_cal=0.02 (numeric)",
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        "omitted": {
          "C": 2.64,
          "SOH": 0.88,
          "fade": 0.12000000000000001
        },
        "explicit": {
          "C": 2.64,
          "SOH": 0.88,
          "fade": 0.12000000000000001
        }
      }
    }
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  "tier": "expert_verified",
  "verification": {
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      "passed": 14,
      "total": 14,
      "golden": 3,
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  "evidence_core_generated_at": "2026-09-05T10:20:02.590Z",
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