{
  "id": "specific-gravity",
  "version": "bcaf71c7a350",
  "status": "published",
  "name": "Specific Gravity Calculator",
  "question": "What is the specific gravity?",
  "summary": "Computes specific gravity, the density of a substance divided by the density of water, from its density or by weighing an object in air and in water, with its density in g/cm³, kg/m³ and lb/ft³.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/specific-gravity-calculator",
  "markdown": "https://www.acalculator.org/physics/specific-gravity-calculator.md",
  "kind": "function",
  "method": "Specific gravity = ρ ÷ ρ_water. By weighing: specific gravity = m_air ÷ (m_air − m_water), since m_air − m_water is the mass of water displaced; density = specific gravity × ρ_water.",
  "assumptions": [
    "The reference is water at 4 °C, 1.000 g/cm³ (1,000 kg/m³), unless you type another reference density.",
    "When weighing, the object is fully under water, holds no air, and does not absorb water; the apparent mass in water is the scale reading then.",
    "Units convert exactly: 1 g/cm³ = 1,000 kg/m³; 1 lb = 0.45359237 kg; 1 ft³ = 0.028316846592 m³; 1 gal = 0.003785411784 m³."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "m": {
        "title": "Method",
        "description": "From a known density, or by weighing the object in air and then in water.",
        "type": "string",
        "enum": [
          "density",
          "weigh"
        ]
      },
      "rho": {
        "title": "Density of the substance",
        "description": "The density of the substance or object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "minimum": 0.000001,
        "maximum": 1000000
      },
      "ma": {
        "title": "Mass in air",
        "description": "The mass (or weight) of the object weighed in air.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "mw": {
        "title": "Apparent mass in water",
        "description": "The reading with the object hanging fully under water; it must be less than the mass in air.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 0,
        "maximum": 1000000
      },
      "ref": {
        "title": "Density of water (reference)",
        "description": "The density of the reference liquid: water at 4 °C is 1 g/cm³ (1,000 kg/m³).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "minimum": 0.001,
        "maximum": 1000000
      }
    }
  },
  "outputs": {
    "sg": {
      "label": "Specific gravity",
      "description": "The density of the substance ÷ the density of water; it has no unit.",
      "format": "number"
    },
    "gcc": {
      "label": "Density (g/cm³)",
      "description": "Specific gravity × the reference density, in grams per cubic centimeter.",
      "format": "number"
    },
    "kgm3": {
      "label": "Density (kg/m³)",
      "description": "The same density in kilograms per cubic meter.",
      "format": "number"
    },
    "lbft3": {
      "label": "Density (lb/ft³)",
      "description": "The same density in pounds per cubic foot.",
      "format": "number"
    },
    "displaced": {
      "label": "Mass of water displaced (g)",
      "description": "Mass in air − apparent mass in water.",
      "format": "number"
    },
    "volume": {
      "label": "Volume of the object (cm³)",
      "description": "Mass of water displaced ÷ the density of water.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "m": "density",
      "rho": "19.32 g/cm³",
      "ma": "8.630 g",
      "mw": "7.800 g",
      "ref": "1 g/cm³"
    },
    "outputs": {
      "sg": 19.32,
      "gcc": 19.32,
      "kgm3": 19320,
      "lbft3": 1206.108198331114
    },
    "text": "The specific gravity is 19.32, a density of 19.32 g/cm³."
  },
  "examples": [
    {
      "given": {
        "m": "density",
        "rho": 19320,
        "ref": 1000
      },
      "expect": {
        "sg": 19.32,
        "gcc": 19.32,
        "kgm3": 19320,
        "lbft3": 1206.108198331114
      },
      "source": "OpenStax, College Physics 2e, §11.2 Density, Table 11.1 (water at 4 °C 1.000, gold 19.32, mercury 13.6, in 10³ kg/m³), https://openstax.org/books/college-physics-2e/pages/11-2-density (retrieved 2026-10-18); OpenStax, College Physics 2e, §11.7 Archimedes’ Principle (specific gravity = ρ̄ ÷ ρw, the density of water at 4.00 °C; apparent mass loss = mass of fluid displaced; Example 11.10: 8.630 g in air, 7.800 g in water, 0.830 cm³, 10.4 g/cm³), https://openstax.org/books/college-physics-2e/pages/11-7-archimedes-principle (retrieved 2026-10-18); hand calculation in content.mdx: 19.32 ÷ 1.000 = 19.32"
    },
    {
      "given": {
        "m": "weigh",
        "ma": 0.00863,
        "mw": 0.0078,
        "ref": 1000
      },
      "expect": {
        "sg": 10.397590361445783,
        "kgm3": 10397.590361445784,
        "displaced": 0.83,
        "volume": 0.83
      },
      "source": "OpenStax, College Physics 2e, §11.7 Archimedes’ Principle (specific gravity = ρ̄ ÷ ρw, the density of water at 4.00 °C; apparent mass loss = mass of fluid displaced; Example 11.10: 8.630 g in air, 7.800 g in water, 0.830 cm³, 10.4 g/cm³), https://openstax.org/books/college-physics-2e/pages/11-7-archimedes-principle (retrieved 2026-10-18); hand calculation in content.mdx: 8.630 ÷ (8.630 − 7.800) = 10.3976 (the book: 10.4 g/cm³)"
    },
    {
      "given": {
        "m": "density",
        "rho": 999.5521145351128,
        "ref": 1000
      },
      "expect": {
        "sg": 0.9995521145351127,
        "lbft3": 62.4
      },
      "source": "OpenStax, College Physics 2e, §11.7 Archimedes’ Principle (specific gravity = ρ̄ ÷ ρw, the density of water at 4.00 °C; apparent mass loss = mass of fluid displaced; Example 11.10: 8.630 g in air, 7.800 g in water, 0.830 cm³, 10.4 g/cm³), https://openstax.org/books/college-physics-2e/pages/11-7-archimedes-principle (retrieved 2026-10-18); NIST SP 811, Appendix B.8 (1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³); hand calculation in content.mdx: 62.4 × 16.0184634 ÷ 1,000"
    },
    {
      "given": {
        "m": "density",
        "rho": 13600,
        "ref": 1000
      },
      "expect": {
        "sg": 13.6,
        "gcc": 13.6
      },
      "source": "OpenStax, College Physics 2e, §11.2 Density, Table 11.1 (water at 4 °C 1.000, gold 19.32, mercury 13.6, in 10³ kg/m³), https://openstax.org/books/college-physics-2e/pages/11-2-density (retrieved 2026-10-18); hand calculation in content.mdx: 13.6 ÷ 1.000 = 13.6"
    }
  ],
  "sources": [
    "OpenStax, College Physics 2e, §11.7 Archimedes’ Principle: specific gravity is the ratio of the density of an object to a fluid (usually water), specific gravity = ρ̄ ÷ ρw with ρw the density of water at 4.00 °C (Eq. 11.40); apparent mass loss = mass of fluid displaced (Eq. 11.45); Example 11.10, Is the Coin Authentic? (8.630 g in air, 7.800 g in water, 0.830 cm³, 10.4 g/cm³). https://openstax.org/books/college-physics-2e/pages/11-7-archimedes-principle (retrieved 2026-10-18)",
    "OpenStax, College Physics 2e, §11.2 Density, Table 11.1 Densities of Various Substances: water (4 °C) 1.000, gold 19.32, aluminum 2.7, mercury 13.6, in 10³ kg/m³ or g/mL. https://openstax.org/books/college-physics-2e/pages/11-2-density (retrieved 2026-10-18)"
  ],
  "related": [
    "density",
    "mass",
    "pressure",
    "ppm"
  ],
  "changelog": []
}