{
  "id": "buoyancy",
  "version": "94714e036e1f",
  "status": "published",
  "name": "Buoyancy Calculator",
  "question": "What is the buoyancy force?",
  "summary": "Finds the buoyant force by Archimedes’ principle, F = ρ × V × g, for water, seawater and other fluids, and with the object’s mass, whether it floats or sinks and its apparent weight.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/buoyancy-calculator",
  "markdown": "https://www.acalculator.org/physics/buoyancy-calculator.md",
  "kind": "function",
  "method": "F_B = ρ × V × g, the weight of the fluid pushed aside. With the mass m: W = m × g, apparent weight W − F_B, object density m ÷ V; it floats when m ÷ V < ρ, with 100 × (m ÷ V) ÷ ρ percent under the surface.",
  "assumptions": [
    "The fluid is at rest and has the same density throughout.",
    "With a mass, V is the object’s whole volume, held fully under the surface.",
    "Typed values are read as the exact decimals you typed; each result is rounded once to show."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "fl": {
        "title": "Fluid",
        "description": "The fluid the object is in, with its density from OpenStax Tables 14.1 and 14.2, or your own.",
        "type": "string",
        "enum": [
          "water4",
          "water20",
          "water100",
          "sea",
          "mercury",
          "glycerin",
          "olive",
          "benzene",
          "ethanol",
          "gasoline",
          "air",
          "custom"
        ]
      },
      "rho": {
        "title": "Fluid density (ρ)",
        "description": "The density of the fluid.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "minimum": 0.000001,
        "maximum": 1000000
      },
      "V": {
        "title": "Volume under the surface (V)",
        "description": "The volume of the object that is under the surface: the volume of fluid it pushes aside.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "minimum": 1e-12,
        "maximum": 1000000000
      },
      "m": {
        "title": "Object mass (optional)",
        "description": "The mass of the object. With it, V is the whole object held under the surface, and the page says whether it floats.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 1e-12,
        "maximum": 1000000000000
      },
      "g": {
        "title": "Gravity (g), m/s²",
        "description": "The acceleration of gravity: 9.80665 m/s² is standard gravity on Earth.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000
      }
    }
  },
  "outputs": {
    "force": {
      "label": "Buoyant force (F_B), N",
      "description": "F_B = ρ × V × g, in newtons.",
      "format": "number"
    },
    "forceLbf": {
      "label": "Buoyant force, lbf",
      "description": "The buoyant force in pounds-force.",
      "format": "number"
    },
    "fluidMass": {
      "label": "Mass of fluid pushed aside, kg",
      "description": "ρ × V: the fluid whose weight is the buoyant force.",
      "format": "number"
    },
    "rho": {
      "label": "Fluid density (ρ), kg/m³",
      "description": "The fluid density used.",
      "format": "number"
    },
    "weight": {
      "label": "Object weight (W), N",
      "description": "The object’s weight, m × g.",
      "format": "number"
    },
    "apparent": {
      "label": "Apparent weight under the surface, N",
      "description": "W − F_B: what a scale reads under the surface. Below 0, the fluid pushes it up.",
      "format": "number"
    },
    "objectDensity": {
      "label": "Object density, kg/m³",
      "description": "m ÷ V, the object’s average density.",
      "format": "number"
    },
    "verdict": {
      "label": "Floats or sinks",
      "description": "Compares the object’s density with the fluid’s.",
      "format": "text"
    },
    "submerged": {
      "label": "Share under the surface when floating, %",
      "description": "100 × ρ_object ÷ ρ_fluid, for an object that floats.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "fl": "water4",
      "rho": "1000 kg/m³",
      "V": "10 L",
      "g": 9.80665
    },
    "outputs": {
      "force": 98.0665,
      "forceLbf": 22.046226218487757,
      "fluidMass": 10,
      "rho": 1000
    },
    "text": "The buoyant force is 98.0665 N (22.0462 lbf)."
  },
  "examples": [
    {
      "given": {
        "fl": "water4",
        "V": 0.01,
        "g": 9.80665
      },
      "expect": {
        "force": 98.0665,
        "fluidMass": 10,
        "forceLbf": 22.046226218487757
      },
      "source": "OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19); OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8 (standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 ft³ = 0.028316846592 m³, 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19); hand calculation in content.mdx: F = 1,000 × 0.01 × 9.80665 = 98.0665 N"
    },
    {
      "given": {
        "fl": "water4",
        "V": 0.028316846592,
        "g": 9.80665
      },
      "expect": {
        "force": 277.6934036314368,
        "forceLbf": 62.42796057614461
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8 (standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 ft³ = 0.028316846592 m³, 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19); hand calculation in content.mdx: F = 1,000 × 0.028316846592 × 9.80665 = 277.693 N = 62.428 lbf"
    },
    {
      "given": {
        "fl": "sea",
        "V": 1,
        "g": 9.8
      },
      "expect": {
        "force": 10094,
        "fluidMass": 1030
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); hand calculation in content.mdx: F = 1,030 × 1 × 9.8 = 10,094 N"
    },
    {
      "given": {
        "fl": "water4",
        "V": 0.1,
        "m": 97,
        "g": 9.8
      },
      "expect": {
        "objectDensity": 970,
        "submerged": 97,
        "verdict": "Floats: it is less dense than the fluid",
        "apparent": -29.4
      },
      "source": "OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19); hand calculation in content.mdx: 97 ÷ 0.1 = 970 kg/m³, 970 ÷ 1,000 = 97%"
    },
    {
      "given": {
        "fl": "water4",
        "V": 0.002,
        "m": 5,
        "g": 9.80665
      },
      "expect": {
        "weight": 49.03325,
        "force": 19.6133,
        "apparent": 29.41995,
        "verdict": "Sinks: it is denser than the fluid"
      },
      "source": "OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19); hand calculation in content.mdx: W = 49.03325 N, F_B = 19.6133 N, W − F_B = 29.41995 N"
    },
    {
      "given": {
        "fl": "air",
        "V": 1,
        "g": 9.80665
      },
      "expect": {
        "force": 12.6505785
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); hand calculation in content.mdx: F = 1.29 × 1 × 9.80665 = 12.6505785 N"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy: F_B = w_fl; a floating object has ρ_obj ÷ ρ_fl of its volume submerged; Example 14.4 (floating 97.0% submerged in fresh water means 970 kg/m³), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy",
    "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: Table 14.1 (densities of common substances, liquids at 0 °C, air at 0 °C and 101.3 kPa) and Table 14.2 (densities of water and seawater), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure",
    "NIST Special Publication 811, Appendix B.8: standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³, 1 gal = 0.003785411784 m³, 1 in³ = 0.000016387064 m³, retrieved 2026-10-19. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8"
  ],
  "related": [
    "density",
    "specific-gravity",
    "pressure",
    "force"
  ],
  "changelog": []
}