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  "failed": 0,
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      "passed": 7
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    "boundary": {
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      "sources",
      "tests"
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  "schema_output": "https://www.calculatorx.com/schemas/electrical.volts_to_kw.output.json",
  "assumptions": [
    "Balanced three-phase when √3 mode is selected",
    "Voltage is RMS for AC",
    "PF = 1 for DC / resistive"
  ],
  "limitations": [
    "PF ∈ (0,1] hard — FRACTION_OUT_OF_RANGE",
    "V>0 on forward; I>0 on reverse"
  ],
  "boundary_conditions": [
    "power_factor must be in (0, 1] — PF≤0 → FRACTION_OUT_OF_RANGE (engine volts-kw)",
    "Voltage must be > 0 on Volts→kW — VOLTAGE_MUST_BE_POSITIVE",
    "Current must be > 0 on kW→Volts — VALUE_MUST_BE_POSITIVE",
    "Zero current on forward yields 0 kW — soft boundary"
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    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Active power (IEV 131-11-42)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-42",
      "supports": "P is active power; unit watt (W). Under sinusoidal conditions P = Re S.",
      "kind": "standard",
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      "clause": "IEV 131-11-42"
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      "section": "Power factor (IEV 131-11-46)",
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      "supports": "λ = |P| / S; AC real-power formulas multiply V·I (and √3 for 3φ L-L) by λ",
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      "accessed": "2026-09-05",
      "clause": "IEV 131-11-46"
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    {
      "title": "IEEE Std 1459-2025",
      "section": "Real power from voltage, current, and power factor",
      "url": "https://standards.ieee.org/ieee/1459/7578/",
      "supports": "1φ P = PF·V·I/1000; 3φ L-L P = √3·PF·V·I/1000; DC P = V·I/1000",
      "kind": "standard",
      "accessed": "2026-09-05",
      "publisher": "IEEE",
      "published": "2025-05-16",
      "errata_checked": true
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    {
      "title": "BIPM SI Brochure (9th edition, version 4.01)",
      "section": "SI units for ampere, volt, and watt",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "DC P = V·I; kW = 1000 W unit scaling",
      "kind": "reference",
      "accessed": "2026-09-05",
      "published": "2026-06",
      "doi": "https://doi.org/10.59161/AUEZ1291"
    },
    {
      "title": "NIST Guide to the SI (SP 811)",
      "section": "Volt, ampere, and watt",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "supports": "SI unit relationships in power calculations",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:46d20f463d78f11ad829119706429c19f5fb104b29bbe184c7c42f8ba0487675",
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      "ok": true,
      "kind": "golden",
      "inputs": {
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        "a": 240,
        "b": 10,
        "phase": "single",
        "pf": 1
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      "expectWarning": null,
      "actual": 2.4,
      "tol": 0.001
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      "ok": true,
      "kind": "golden",
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        "a": 120,
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      "tol": 0.01
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      "id": "kw-to-v",
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      "inputs": {
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        "a": 2.4,
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        "phase": "single",
        "pf": 1
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      "expect": 240,
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      "actual": 240,
      "tol": 0.1
    },
    {
      "id": "soft-zero-I",
      "ok": true,
      "kind": "golden",
      "inputs": {
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        "a": 230,
        "b": 0,
        "phase": "single",
        "pf": 1
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      "expect": 0,
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      "actual": 0,
      "tol": 1e-12
    },
    {
      "id": "pf-zero",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "v-kw",
        "a": 230,
        "b": 10,
        "phase": "single",
        "pf": 0
      },
      "expectError": "FRACTION_OUT_OF_RANGE",
      "code": "FRACTION_OUT_OF_RANGE",
      "error": "pf must be in (0, 1]"
    },
    {
      "id": "zero-volts",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "v-kw",
        "a": 0,
        "b": 10,
        "phase": "single",
        "pf": 1
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      "expectError": "VOLTAGE_MUST_BE_POSITIVE",
      "code": "VOLTAGE_MUST_BE_POSITIVE",
      "error": "V must be greater than zero"
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      "id": "kw-v-zero-I",
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      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
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      "inputs": {
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        "a": 12.471,
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        "phase": "three",
        "pf": 0.9
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      "tol": 0.5
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        "phase": "three",
        "pf": 0.45
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