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  "page": "https://www.calculatorx.com/calc/electric/battery-runtime",
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  "schema_output": "https://www.calculatorx.com/schemas/electrical.battery_runtime.output.json",
  "assumptions": [
    "Constant load; ideal flat voltage until capacity is exhausted.",
    "DoD and η are independent planning knobs, not chemistry models.",
    "Amps mode I_A is battery-side discharge current; η does not enter t_h.",
    "When u_* are set, first-order GUM sensitivity with independent inputs (no ρ on this page)."
  ],
  "limitations": [
    "Constant-load idealization only — not Peukert, temperature, or BMS cutoffs",
    "Not a substitute for manufacturer runtime curves or pack design",
    "Amps mode = battery-side discharge current; η does not enter runtime",
    "capacity_Ah XOR capacity_mAh; both → INVALID_INPUT",
    "Missing capacity → MISSING_REQUIRED_INPUT; P_W/I_A ≤ 0 → LOAD_MUST_BE_POSITIVE",
    "dod/eta outside (0,1] → FRACTION_OUT_OF_RANGE",
    "mode=watts requires P_W; mode=amps requires I_A",
    "Optional u_* use GUM sensitivity only (no MC/ρ/νeff UI); empty u_* preserves nominal-only result",
    "Response inputs[] is mode-canonical (capacity_Ah only; amps omits eta)",
    "Basic frozen at calculation_version 1.2.1 — Agent schema requires u_* when uncertainty_k/confidence is set; do not stack Peukert/temperature/duty-cycle into this capability"
  ],
  "boundary_conditions": [
    "Missing capacity → MISSING_REQUIRED_INPUT",
    "Both capacity_Ah and capacity_mAh → INVALID_INPUT",
    "V ≤ 0 → VOLTAGE_MUST_BE_POSITIVE",
    "P_W/I_A ≤ 0 → LOAD_MUST_BE_POSITIVE",
    "dod/eta outside (0,1] → FRACTION_OUT_OF_RANGE",
    "Unknown mode → INVALID_MODE",
    "uncertainty_k without any u_* → INVALID_INPUT",
    "uncertainty_k and confidence together → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Electric battery capacity and related quantities",
      "supports": "Ah capacity and Wh energy relationship E ≈ Q·V for nominal estimates",
      "kind": "standard"
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    {
      "title": "IEC 61960 series (portable secondary lithium)",
      "section": "Capacity / performance concepts for portable Li cells and batteries",
      "supports": "Nameplate capacity language for portable secondary lithium; not a lead-acid Peukert model",
      "kind": "standard"
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    {
      "title": "Victron Energy — Battery capacity and Peukert exponent",
      "section": "Battery monitor documentation (BMV)",
      "url": "https://www.victronenergy.com/media/pg/BMV-700H/en/battery-capacity-and-peukert-exponent.html",
      "supports": "Why usable Ah falls with discharge rate; Peukert as reason simple Ah×V estimates differ from field runtime",
      "kind": "reference"
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    {
      "title": "NIST Guide to the SI (SP 811)",
      "section": "Coherent derived units for energy and time",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "supports": "Wh and hour as energy/time units in estimates",
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