{
  "id": "mass",
  "version": "c8852957e913",
  "status": "published",
  "name": "Mass Calculator",
  "question": "What is the mass?",
  "summary": "Finds a mass from density and volume (m = ρV), from a force and an acceleration (m = F ÷ a), or from a weight and the gravity (m = W ÷ g), in kilograms, grams and pounds.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/mass-calculator",
  "markdown": "https://www.acalculator.org/physics/mass-calculator.md",
  "kind": "function",
  "method": "m = ρ × V; m = F ÷ a; m = W ÷ g.",
  "assumptions": [
    "Density × volume assumes the material is the same all through the object (an average density otherwise).",
    "Force ÷ acceleration uses the net force; weight ÷ gravity uses the gravity where the object is weighed.",
    "Exact unit sizes: 1 lb = 0.45359237 kg; 1 ft³ = 0.028316846592 m³; 1 gal = 3.785411784 L; 1 lbf = 4.4482216152605 N; 1 kgf = 9.80665 N."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Find the mass from",
        "description": "Work out the mass from density and volume, from a force and an acceleration, or from a weight.",
        "type": "string",
        "enum": [
          "density",
          "force",
          "weight"
        ]
      },
      "rho": {
        "title": "Density",
        "description": "The density of the material: water is 1,000 kg/m³ (1 g/cm³).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "density",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "V": {
        "title": "Volume",
        "description": "The volume of the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "F": {
        "title": "Net force",
        "description": "The net force on the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "a": {
        "title": "Acceleration",
        "description": "The acceleration the force gives the object, in the unit chosen below.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "au": {
        "title": "Acceleration unit",
        "description": "The unit of the acceleration: m/s², ft/s² or g (standard gravity).",
        "type": "string",
        "enum": [
          "mps2",
          "fps2",
          "g"
        ]
      },
      "W": {
        "title": "Weight",
        "description": "The weight of the object: the force of gravity on it, in newtons or pounds-force.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "g": {
        "title": "Gravity (m/s²)",
        "description": "The acceleration of gravity in m/s²: 9.80665 on Earth, about 1.62 on the Moon.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "lb": {
      "label": "Mass (lb)",
      "description": "The mass in pounds (1 lb = 0.45359237 kg).",
      "format": "number"
    },
    "kg": {
      "label": "Mass (kg)",
      "description": "The mass in kilograms.",
      "format": "number"
    },
    "g": {
      "label": "Mass (g)",
      "description": "The mass in grams.",
      "format": "number"
    },
    "oz": {
      "label": "Mass (oz)",
      "description": "The mass in ounces (1 oz = 1/16 lb).",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "density",
      "rho": "1000 kg/m³",
      "V": "2 L",
      "F": "10 N",
      "a": 2,
      "au": "mps2",
      "W": "98.0665 N",
      "g": 9.80665
    },
    "outputs": {
      "lb": 4.409245243697551,
      "kg": 2,
      "g": 2000,
      "oz": 70.54792389916082
    },
    "text": "The mass is 4.40925 lb (2 kg)."
  },
  "examples": [
    {
      "given": {
        "from": "density",
        "rho": 1000,
        "V": 0.002
      },
      "expect": {
        "kg": 2,
        "g": 2000,
        "lb": 4.409245243697551
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure; hand calculation in content.mdx: m = 1,000 kg/m³ × 0.002 m³ = 2 kg = 4.40925 lb"
    },
    {
      "given": {
        "from": "force",
        "F": 10,
        "a": 2,
        "au": "mps2"
      },
      "expect": {
        "kg": 5
      },
      "source": "OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law; hand calculation in content.mdx: m = F ÷ a = 10 ÷ 2 = 5 kg"
    },
    {
      "given": {
        "from": "weight",
        "W": 4.4482216152605,
        "g": 9.80665
      },
      "expect": {
        "lb": 1,
        "kg": 0.45359237,
        "oz": 16
      },
      "source": "OpenStax, University Physics Volume 1, §5.4 Mass and Weight (w = m g), https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight; hand calculation in content.mdx: 4.4482216152605 N ÷ 9.80665 m/s² = 0.45359237 kg = 1 lb"
    },
    {
      "given": {
        "from": "density",
        "rho": 999.5521145351128,
        "V": 0.28316846592
      },
      "expect": {
        "lb": 624
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure; hand calculation in content.mdx: 62.4 lb/ft³ × 10 ft³ = 624 lb"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (ρ = m ÷ V). https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-03)",
    "OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F = m a). https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (retrieved 2026-10-03)",
    "OpenStax, University Physics Volume 1, §5.4 Mass and Weight (w = m g). https://openstax.org/books/university-physics-volume-1/pages/5-4-mass-and-weight (retrieved 2026-10-03)",
    "NIST SP 811, Appendix B.8 Factors for Units Listed Alphabetically (pound, cubic foot, gallon, pound-force). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-03)"
  ],
  "related": [
    "density",
    "force",
    "momentum"
  ],
  "changelog": []
}