{
  "id": "free-water-deficit",
  "version": "79dc5d8407b3",
  "status": "published",
  "name": "Free Water Deficit Calculator",
  "question": "How much is the free water deficit?",
  "summary": "Estimates the free water deficit in hypernatremia from body weight, sex and age group, and serum sodium: total body water × (sodium ÷ 140 − 1).",
  "category": "health",
  "subcategory": "clinical",
  "url": "https://www.acalculator.org/health/free-water-deficit-calculator",
  "markdown": "https://www.acalculator.org/health/free-water-deficit-calculator.md",
  "kind": "function",
  "method": "Total body water (L) = weight (kg) × fraction (0.6 men, 0.5 women, 0.55 older men, 0.45 older women). Free water deficit (L) = total body water × (serum sodium ÷ 140 − 1).",
  "assumptions": [
    "The target sodium is 140 mmol/L, as in the source equation.",
    "The deficit is worked from the exact typed values and rounded once to 1 decimal, halves up.",
    "The estimate does not include ongoing water losses (urine, stool, sweat, breathing)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "group": {
        "title": "Patient",
        "description": "Sets total body water as a share of body weight: 60% men, 50% women, 5 points less for older adults.",
        "type": "string",
        "enum": [
          "man",
          "woman",
          "olderMan",
          "olderWoman"
        ]
      },
      "weight": {
        "title": "Weight",
        "description": "Body weight, from 20 to 300 kg.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 20,
        "maximum": 300
      },
      "na": {
        "title": "Serum sodium (mmol/L)",
        "description": "Serum sodium in mmol/L (the same as mEq/L), above 140 and up to 200.",
        "type": "number",
        "exclusiveMinimum": 140,
        "maximum": 200
      }
    }
  },
  "outputs": {
    "deficit": {
      "label": "Free water deficit (L)",
      "description": "Total body water × (sodium ÷ 140 − 1), in liters, to 1 decimal.",
      "format": "number"
    },
    "tbw": {
      "label": "Total body water (L)",
      "description": "Body weight in kg × the fraction for the patient group, in liters, to 1 decimal.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "group": "man",
      "weight": "70 kg",
      "na": 150
    },
    "outputs": {
      "deficit": 3,
      "tbw": 42
    },
    "text": "The estimated free water deficit is 3 L (total body water 42 L)."
  },
  "examples": [
    {
      "given": {
        "group": "man",
        "weight": 70,
        "na": 150
      },
      "expect": {
        "deficit": 3,
        "tbw": 42
      },
      "source": "0.6 × 70 = 42 L; 42 × (150 ÷ 140 − 1) = 3.0 L (hand calculation in content.mdx)"
    },
    {
      "given": {
        "group": "woman",
        "weight": 60,
        "na": 166
      },
      "expect": {
        "deficit": 5.6,
        "tbw": 30
      },
      "source": "Yun, Baek and Kim 2023, worked example after Eq. 5: 0.5 × 60 × (166 ÷ 140 − 1) = 5.6 L"
    },
    {
      "given": {
        "group": "olderWoman",
        "weight": 50,
        "na": 160
      },
      "expect": {
        "deficit": 3.2,
        "tbw": 22.5
      },
      "source": "0.45 × 50 = 22.5 L; 22.5 × 20 ÷ 140 = 3.21 L (hand calculation in content.mdx)"
    },
    {
      "given": {
        "group": "olderMan",
        "weight": 80,
        "na": 155
      },
      "expect": {
        "deficit": 4.7,
        "tbw": 44
      },
      "source": "0.55 × 80 = 44 L; 44 × 15 ÷ 140 = 4.71 L (hand calculation in content.mdx)"
    },
    {
      "given": {
        "group": "man",
        "weight": 69.85322498000001,
        "na": 145
      },
      "expect": {
        "deficit": 1.5,
        "tbw": 41.9
      },
      "source": "0.6 × 69.853 = 41.912 L; 41.912 × 5 ÷ 140 = 1.497 L (hand calculation in content.mdx)"
    }
  ],
  "sources": [
    "Yun G, Baek SH, Kim S. Evaluation and management of hypernatremia in adults: clinical perspectives. Korean J Intern Med. 2023;38(3):290-302. https://doi.org/10.3904/kjim.2022.346 (open at https://pmc.ncbi.nlm.nih.gov/articles/PMC10175862/, retrieved 2026-10-05)"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-10-05",
      "note": "Published after this site's editorial review against the cited sources (no clinician review); the page notices say so."
    }
  ]
}