{
  "id": "transformer",
  "version": "5da527535838",
  "status": "published",
  "name": "Transformer Calculator",
  "question": "What are the transformer amps?",
  "summary": "Works out a transformer’s turns ratio from its primary and secondary voltages, the full-load current on each side from its kVA rating (single or three-phase), and the secondary turns from the primary turns.",
  "category": "physics",
  "subcategory": "electricity",
  "url": "https://www.acalculator.org/physics/transformer-calculator",
  "markdown": "https://www.acalculator.org/physics/transformer-calculator.md",
  "kind": "function",
  "method": "a = Vp ÷ Vs = Np ÷ Ns. Full-load current: I = kVA × 1,000 ÷ V (single-phase) or ÷ (√3 × V) (three-phase) on each side. Ns = Np × Vs ÷ Vp. Impedance ratio = a².",
  "assumptions": [
    "An ideal transformer: no losses, so the kVA in equals the kVA out, and the voltages are in the turns ratio.",
    "Three-phase voltages are line-to-line and the load is balanced.",
    "Full-load current is the current at the full kVA rating; real loads may draw less."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "ph": {
        "title": "Supply",
        "description": "Single-phase, or three-phase with line-to-line voltages.",
        "type": "string",
        "enum": [
          "single",
          "three"
        ]
      },
      "kva": {
        "title": "Rating (kVA)",
        "description": "The transformer’s rated apparent power in kilovolt-amperes, from its nameplate.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 10000000
      },
      "vp": {
        "title": "Primary voltage",
        "description": "The voltage on the supply side (line-to-line for three-phase).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "minimum": 0.001,
        "maximum": 10000000
      },
      "vs": {
        "title": "Secondary voltage",
        "description": "The voltage on the load side (line-to-line for three-phase).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "minimum": 0.001,
        "maximum": 10000000
      },
      "np": {
        "title": "Primary turns",
        "description": "The number of turns on the primary winding, if you know it. Leave empty to skip.",
        "type": "integer",
        "minimum": 1,
        "maximum": 10000000
      }
    }
  },
  "outputs": {
    "ratio": {
      "label": "Turns ratio (primary ÷ secondary)",
      "description": "Vp ÷ Vs, which equals Np ÷ Ns for an ideal transformer.",
      "format": "number"
    },
    "ip": {
      "label": "Primary full-load current (A)",
      "description": "The current on the primary side at the full kVA rating.",
      "format": "number"
    },
    "is": {
      "label": "Secondary full-load current (A)",
      "description": "The current on the secondary side at the full kVA rating.",
      "format": "number"
    },
    "ns": {
      "label": "Secondary turns",
      "description": "Np × Vs ÷ Vp.",
      "format": "number"
    },
    "zRatio": {
      "label": "Impedance ratio",
      "description": "a²: a load impedance on the secondary looks a² times as large from the primary.",
      "format": "number"
    },
    "kind": {
      "label": "Type",
      "description": "Step-down, step-up, or 1:1 (isolation).",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "ph": "single",
      "kva": 25,
      "vp": "480 V",
      "vs": "240 V"
    },
    "outputs": {
      "ratio": 2,
      "ip": 52.083333333333336,
      "is": 104.16666666666667,
      "zRatio": 4,
      "kind": "Step-down"
    },
    "text": "The turns ratio is 2:1 (Step-down); at full load the primary carries 52.0833 A and the secondary 104.167 A."
  },
  "examples": [
    {
      "given": {
        "ph": "single",
        "kva": 25,
        "vp": 480,
        "vs": 240,
        "np": 400
      },
      "expect": {
        "ratio": 2,
        "ip": 52.083333333333336,
        "is": 104.16666666666667,
        "ns": 200,
        "zRatio": 4,
        "kind": "Step-down"
      },
      "source": "OpenStax, University Physics Volume 2, §15.6 Transformers (V_S ÷ V_P = N_S ÷ N_P; I_P V_P = I_S V_S for an ideal transformer), https://openstax.org/books/university-physics-volume-2/pages/15-6-transformers (retrieved 2026-10-05); hand calculation in content.mdx: 480 ÷ 240 = 2; 25,000 ÷ 480 = 52.08 A; 25,000 ÷ 240 = 104.17 A; 400 ÷ 2 = 200"
    },
    {
      "given": {
        "ph": "three",
        "kva": 75,
        "vp": 480,
        "vs": 208
      },
      "expect": {
        "ratio": 2.3076923076923075,
        "ip": 90.21097956087904,
        "is": 208.17918360202853
      },
      "source": "OpenStax, University Physics Volume 2, §15.6 Transformers (V_S ÷ V_P = N_S ÷ N_P; I_P V_P = I_S V_S for an ideal transformer), https://openstax.org/books/university-physics-volume-2/pages/15-6-transformers (retrieved 2026-10-05); Wikipedia, \"Three-phase electric power\" (balanced load: S = √3 × line voltage × line current), https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05); hand calculation in content.mdx: 75,000 ÷ (√3 × 480) = 90.21 A; 75,000 ÷ (√3 × 208) = 208.18 A",
      "tolerance": 1e-12
    },
    {
      "given": {
        "ph": "single",
        "kva": 1,
        "vp": 120,
        "vs": 12000
      },
      "expect": {
        "ratio": 0.01,
        "ip": 8.333333333333334,
        "is": 0.08333333333333333,
        "kind": "Step-up"
      },
      "source": "OpenStax, University Physics Volume 2, §15.6 Transformers (V_S ÷ V_P = N_S ÷ N_P; I_P V_P = I_S V_S for an ideal transformer), https://openstax.org/books/university-physics-volume-2/pages/15-6-transformers (retrieved 2026-10-05); hand calculation in content.mdx: 120 ÷ 12,000 = 0.01; 1,000 ÷ 120 = 8.33 A; 1,000 ÷ 12,000 = 0.0833 A"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 2, §15.6 Transformers: V_S ÷ V_P = N_S ÷ N_P, and I_P V_P = I_S V_S for an ideal transformer. https://openstax.org/books/university-physics-volume-2/pages/15-6-transformers (retrieved 2026-10-05)",
    "Wikipedia, \"Three-phase electric power\": for a balanced load, S = √3 × line voltage × line current. https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05)"
  ],
  "related": [
    "kva",
    "amp",
    "ohms-law"
  ],
  "changelog": []
}