{
  "capability_id": "electrical.voltage_drop",
  "tool_id": "voltage-drop",
  "engine": "voltage-drop",
  "calculation_version": "1.5.2",
  "generated_at": "2026-09-16T22:03:43.700Z",
  "engine_build": "2026-09-12",
  "test_count": 38,
  "passed": 38,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 12,
      "passed": 12
    },
    "boundary": {
      "total": 12,
      "passed": 12
    },
    "property": {
      "total": 14,
      "passed": 14
    }
  },
  "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/wire/voltage-drop",
  "api": "https://www.calculatorx.com/api/v1/calc/voltage-drop",
  "schema_input": "https://www.calculatorx.com/schemas/electrical.voltage_drop.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/electrical.voltage_drop.output.json",
  "assumptions": [
    "Constant resistance; temperature neglected.",
    "AC estimate assumes PF ≈ 1 and neglects conductor reactance.",
    "DC / resistive 1φ uses round-trip path; 3φ assumes balanced line-to-line drop.",
    "V_system for 3φ is line-to-line; V_load = V_system − V_drop on that same basis.",
    "User supplies an appropriate Ω/km for the conductor and conditions.",
    "When u_* are set, first-order GUM sensitivity with independent inputs (no ρ on this page)."
  ],
  "limitations": [
    "Resistance-only estimate — AC reactance neglected; AC modes assume PF ≈ 1",
    "Not a substitute for code-compliant cable sizing or ampacity",
    "3φ V_system is line-to-line; percent_drop and V_load use that same basis",
    "Zero I/length/R → 0 V (valid); negatives → VALUE_MUST_BE_NON_NEGATIVE",
    "mode must be dc or three (INVALID_MODE otherwise); REST/UI default dc if omitted",
    "V_system if set must be > 0 (VALUE_MUST_BE_POSITIVE); omit it to return volts only",
    "Optional u_* use GUM sensitivity only; empty u_* still returns { V_drop, R_one_way, P_loss, … } without uncertainty",
    "Engine tested, source checked, evidence published (L1). Named expert review is a higher assurance tier (L3), not required for engine-tested status. Not a code-compliance certification."
  ],
  "boundary_conditions": [
    "Missing I/length_m/R_ohm_per_km → MISSING_REQUIRED_INPUT",
    "Non-finite inputs → INVALID_NUMBER",
    "Negative I/length/R → VALUE_MUST_BE_NON_NEGATIVE",
    "Unknown mode → INVALID_MODE (only dc|three)",
    "V_system ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Zero I, length, or R → 0 V and 0 W (valid soft result)",
    "uncertainty_k without any u_* → INVALID_INPUT",
    "uncertainty_k XOR confidence",
    "Not a substitute for code-compliant cable sizing"
  ],
  "sources": [
    {
      "title": "IEC 60364-5-52:2009+AMD1:2024",
      "section": "Clause 525 / Annex G — Voltage drop in consumers' installations",
      "url": "https://webstore.iec.ch/en/publication/103734",
      "supports": "CalculatorX implements a resistance-only / PF≈1 approximation, not the complete impedance-aware Annex G model. DC/1φ ≈ 2·I·R; balanced 3φ ≈ √3·I·R (reactance and PF neglected on this page).",
      "kind": "standard",
      "accessed": "2026-09-10",
      "clause": "525 / Annex G"
    },
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Voltage drop (IEV 151-15-08)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=151-15-08",
      "supports": "Voltage between the terminals of a resistive element due to the current through that element",
      "kind": "standard",
      "accessed": "2026-09-05",
      "clause": "IEV 151-15-08"
    },
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Resistance (IEV 131-12-04)",
      "url": "https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-12-04",
      "supports": "R = u/I; this page’s resistance-only drop uses V ≈ I·R (reactance neglected)",
      "kind": "standard",
      "accessed": "2026-09-05",
      "clause": "IEV 131-12-04"
    },
    {
      "title": "NFPA 70 — National Electrical Code (NEC)",
      "section": "Informational notes on voltage-drop limits for feeders and branch circuits",
      "url": "https://www.nfpa.org/codes-and-standards/all-codes-and-standards/list-of-codes-and-standards/detail?code=70",
      "supports": "Design estimate for conductor voltage drop (not a code substitute)",
      "kind": "standard"
    },
    {
      "title": "NIST Guide to the SI (SP 811)",
      "section": "Volt, ampere, ohm, and metre",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "supports": "SI units for the resistance-based drop model",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:706e4bbf603a233a4f99d57b83a663ff4374263e7271a2bf3db58c58842133d3",
  "tests": [
    {
      "id": "dc-20A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expect": 10,
      "expectWarning": null,
      "actual": {
        "V_drop": 10,
        "R_one_way": 0.25,
        "P_loss": 200,
        "R_loop": 0.5
      },
      "tol": 0.01
    },
    {
      "id": "1phi-15A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 15,
        "length_m": 30,
        "R_ohm_per_km": 2.23
      },
      "expect": 2.007,
      "expectWarning": null,
      "actual": {
        "V_drop": 2.007,
        "R_one_way": 0.0669,
        "P_loss": 30.105,
        "R_loop": 0.1338
      },
      "tol": 0.02
    },
    {
      "id": "dc-1A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 1,
        "length_m": 30,
        "R_ohm_per_km": 5.61
      },
      "expect": 0.3366,
      "expectWarning": null,
      "actual": {
        "V_drop": 0.3366,
        "R_one_way": 0.1683,
        "P_loss": 0.3366,
        "R_loop": 0.3366
      },
      "tol": 0.01
    },
    {
      "id": "3phi-36A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "three",
        "I": 36.92,
        "length_m": 100,
        "R_ohm_per_km": 1.403
      },
      "expect": 8.976,
      "expectWarning": null,
      "actual": {
        "V_drop": 8.971808408906647,
        "R_one_way": 0.1403,
        "P_loss": 573.72306576
      },
      "tol": 0.05
    },
    {
      "id": "linear-2x-I",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 40,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expect": 20,
      "expectWarning": null,
      "actual": {
        "V_drop": 20,
        "R_one_way": 0.25,
        "P_loss": 800,
        "R_loop": 0.5
      },
      "tol": 0.01
    },
    {
      "id": "linear-2x-L",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 100,
        "R_ohm_per_km": 5
      },
      "expect": 20,
      "expectWarning": null,
      "actual": {
        "V_drop": 20,
        "R_one_way": 0.5,
        "P_loss": 400,
        "R_loop": 1
      },
      "tol": 0.01
    },
    {
      "id": "soft-zero-I",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 0,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expect": 0,
      "expectWarning": null,
      "actual": {
        "V_drop": 0,
        "R_one_way": 0.25,
        "P_loss": 0,
        "R_loop": 0.5
      },
      "tol": 1e-12
    },
    {
      "id": "soft-zero-L",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 0,
        "R_ohm_per_km": 5
      },
      "expect": 0,
      "expectWarning": null,
      "actual": {
        "V_drop": 0,
        "R_one_way": 0,
        "P_loss": 0,
        "R_loop": 0
      },
      "tol": 1e-12
    },
    {
      "id": "soft-zero-Rkm",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 0
      },
      "expect": 0,
      "expectWarning": null,
      "actual": {
        "V_drop": 0,
        "R_one_way": 0,
        "P_loss": 0,
        "R_loop": 0
      },
      "tol": 1e-12
    },
    {
      "id": "error-neg-Rkm",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": -5
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "R_ohm_per_km must be greater than or equal to 0"
    },
    {
      "id": "error-neg-I",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": -10,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "I must be greater than or equal to 0"
    },
    {
      "id": "error-missing-length",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "R_ohm_per_km": 5
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "length_m is required"
    },
    {
      "id": "error-invalid-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "single",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be \"dc\" or \"three\""
    },
    {
      "id": "3phi-50A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "three",
        "I": 50,
        "length_m": 200,
        "R_ohm_per_km": 2
      },
      "expect": 34.641,
      "expectWarning": null,
      "actual": {
        "V_drop": 34.64101615137755,
        "R_one_way": 0.4,
        "P_loss": 3000
      },
      "tol": 0.05
    },
    {
      "id": "dc-sys-230",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "V_system": 230
      },
      "expect": {
        "V_drop": 10,
        "percent_drop": 4.3478260869565215,
        "V_load": 220,
        "P_loss": 200
      },
      "expectWarning": null,
      "actual": {
        "V_drop": 10,
        "R_one_way": 0.25,
        "P_loss": 200,
        "R_loop": 0.5,
        "percent_drop": 4.3478260869565215,
        "V_load": 220
      },
      "tol": 0.01
    },
    {
      "id": "3phi-loss-10A",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "three",
        "I": 10,
        "length_m": 100,
        "R_ohm_per_km": 5
      },
      "expect": {
        "V_drop": 8.660254037844386,
        "P_loss": 150
      },
      "expectWarning": null,
      "actual": {
        "V_drop": 8.660254037844386,
        "R_one_way": 0.5,
        "P_loss": 150
      },
      "tol": 0.000001
    },
    {
      "id": "boundary-neg-I",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": -20,
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "I must be greater than or equal to 0"
    },
    {
      "id": "boundary-neg-length",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "three",
        "I": 20,
        "length_m": -50,
        "R_ohm_per_km": 5
      },
      "expectError": "VALUE_MUST_BE_NON_NEGATIVE",
      "code": "VALUE_MUST_BE_NON_NEGATIVE",
      "error": "length_m must be greater than or equal to 0"
    },
    {
      "id": "boundary-missing-I",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "length_m": 50,
        "R_ohm_per_km": 5
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "I is required"
    },
    {
      "id": "boundary-unc-I-length",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "u_I": 1,
        "u_length_m": 2
      },
      "expect": {
        "V_drop": 10
      },
      "expectWarning": null,
      "actual": {
        "V_drop": 10,
        "R_one_way": 0.25,
        "P_loss": 200,
        "R_loop": 0.5,
        "uncertainty": {
          "y": 10,
          "u_c": 0.6403124237432849,
          "U": 1.2806248474865698,
          "k": 2,
          "k_source": "user",
          "unit": "V",
          "u_rel": 0.06403124237432849,
          "mode": "sensitivity",
          "contributions": [
            {
              "i": 0,
              "label": "I",
              "c": 0.5,
              "u": 1,
              "variance": 0.25,
              "percent": 60.975609756097555,
              "type": null,
              "nu": null
            },
            {
              "i": 1,
              "label": "length_m",
              "c": 0.2,
              "u": 2,
              "variance": 0.16000000000000003,
              "percent": 39.024390243902445,
              "type": null,
              "nu": null
            }
          ],
          "largest": {
            "i": 0,
            "label": "I",
            "percent": 60.975609756097555
          },
          "reported": {
            "u_c": 0.64,
            "y": 10,
            "significant_digits": 2,
            "decimal_places": 2,
            "formatted_u_c": "0.64",
            "formatted_y": "10.00",
            "k": 2,
            "U": 1.3,
            "formatted_U": "1.30"
          },
          "capability_id": "engineering.uncertainty.propagate"
        }
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-unc-k-without-u",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "uncertainty_k": 2
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "uncertainty_k requires at least one u_* input"
    },
    {
      "id": "boundary-zero-Vsys",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "V_system": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "V_system must be > 0"
    },
    {
      "id": "boundary-neg-Vsys",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "V_system": -230
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "V_system must be > 0"
    },
    {
      "id": "boundary-sys-230",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "V_system": 230
      },
      "expect": {
        "V_drop": 10,
        "percent_drop": 4.3478260869565215,
        "V_load": 220,
        "R_one_way": 0.25,
        "R_loop": 0.5,
        "P_loss": 200
      },
      "expectWarning": null,
      "actual": {
        "V_drop": 10,
        "R_one_way": 0.25,
        "P_loss": 200,
        "R_loop": 0.5,
        "percent_drop": 4.3478260869565215,
        "V_load": 220
      },
      "tol": 1e-9
    },
    {
      "id": "property-dc-drop",
      "ok": true,
      "kind": "property",
      "detail": "DC: ΔV = 2·I·R",
      "expect": 10,
      "actual": 10
    },
    {
      "id": "property-linear-current",
      "ok": true,
      "kind": "property",
      "detail": "ΔV(2I)=2ΔV(I)",
      "expect": 20,
      "actual": 20
    },
    {
      "id": "property-linear-length",
      "ok": true,
      "kind": "property",
      "detail": "ΔV(2L)=2ΔV(L)",
      "expect": 20,
      "actual": 20
    },
    {
      "id": "property-3phi-drop",
      "ok": true,
      "kind": "property",
      "detail": "3φ: ΔV = √3·I·R",
      "expect": 8.660254037844386,
      "actual": 8.660254037844386
    },
    {
      "id": "property-linear-Rkm",
      "ok": true,
      "kind": "property",
      "detail": "ΔV(2R)=2ΔV(R)",
      "expect": 20,
      "actual": 20
    },
    {
      "id": "property-dc-vs-3phi-factor",
      "ok": true,
      "kind": "property",
      "detail": "ΔV_dc/ΔV_3φ = 2/√3",
      "expect": 1.1547005383792517,
      "actual": 1.1547005383792517
    },
    {
      "id": "property-linear-grid-IL",
      "ok": true,
      "kind": "property",
      "detail": "I×L grid 9/9",
      "expect": 9,
      "actual": 9
    },
    {
      "id": "property-uncertainty-compose",
      "ok": true,
      "kind": "property",
      "detail": "u_* → sensitivity U=k·u_c on V_drop",
      "expect": {
        "V_drop": 10,
        "u_c": 0.6403124237432849,
        "U": 1.2806248474865698
      },
      "actual": {
        "y": 10,
        "u_c": 0.6403124237432849,
        "U": 1.2806248474865698,
        "k": 2,
        "k_source": "user",
        "unit": "V",
        "u_rel": 0.06403124237432849,
        "mode": "sensitivity",
        "contributions": [
          {
            "i": 0,
            "label": "I",
            "c": 0.5,
            "u": 1,
            "variance": 0.25,
            "percent": 60.975609756097555,
            "type": null,
            "nu": null
          },
          {
            "i": 1,
            "label": "length_m",
            "c": 0.2,
            "u": 2,
            "variance": 0.16000000000000003,
            "percent": 39.024390243902445,
            "type": null,
            "nu": null
          }
        ],
        "largest": {
          "i": 0,
          "label": "I",
          "percent": 60.975609756097555
        },
        "reported": {
          "u_c": 0.64,
          "y": 10,
          "significant_digits": 2,
          "decimal_places": 2,
          "formatted_u_c": "0.64",
          "formatted_y": "10.00",
          "k": 2,
          "U": 1.3,
          "formatted_U": "1.30"
        },
        "capability_id": "engineering.uncertainty.propagate"
      },
      "inputs": {
        "mode": "dc",
        "I": 20,
        "length_m": 50,
        "R_ohm_per_km": 5,
        "u_I": 1,
        "u_length_m": 2
      }
    },
    {
      "id": "property-no-unc-omit",
      "ok": true,
      "kind": "property",
      "detail": "no u_* and no V_system → V_drop without uncertainty or %drop",
      "expect": 10,
      "actual": 10
    },
    {
      "id": "property-percent-drop",
      "ok": true,
      "kind": "property",
      "detail": "%drop = 100·V_drop/V_system",
      "expect": 4.3478260869565215,
      "actual": 4.3478260869565215
    },
    {
      "id": "property-load-voltage",
      "ok": true,
      "kind": "property",
      "detail": "V_load = V_system − V_drop",
      "expect": 220,
      "actual": 220
    },
    {
      "id": "property-3phi-ll-percent",
      "ok": true,
      "kind": "property",
      "detail": "3φ %drop uses line-to-line V_system; no R_loop",
      "expect": 2.1650635094610964,
      "actual": 2.1650635094610964
    },
    {
      "id": "property-dc-loss",
      "ok": true,
      "kind": "property",
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}