{
  "id": "force",
  "version": "a35d8c212817",
  "status": "published",
  "name": "Force Calculator",
  "question": "What force does it take?",
  "summary": "Uses Newton’s second law F = m × a to find the net force from the mass and the acceleration, or the mass or the acceleration from the other two, in newtons, pounds-force, kilograms, pounds, m/s², ft/s² and g.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/force-calculator",
  "markdown": "https://www.acalculator.org/physics/force-calculator.md",
  "kind": "function",
  "method": "F = m × a; m = F ÷ a; a = F ÷ m. Forces in N = kg·m/s².",
  "assumptions": [
    "F is the net force: the sum of all forces on the object. To find a single push, add the other forces (such as friction) to the net force.",
    "Speeds are far below the speed of light, so the mass does not change.",
    "g here is standard gravity, exactly 9.80665 m/s²; real gravity varies slightly with place and height."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which of force, mass and acceleration to work out from the other two.",
        "type": "string",
        "enum": [
          "force",
          "mass",
          "accel"
        ]
      },
      "m": {
        "title": "Mass",
        "description": "The mass of the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "a": {
        "title": "Acceleration",
        "description": "The acceleration of the object, in the unit chosen below.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "au": {
        "title": "Acceleration unit",
        "description": "The unit of the acceleration: metres or feet per second squared, or g (standard gravity).",
        "type": "string",
        "enum": [
          "mps2",
          "fps2",
          "g"
        ]
      },
      "F": {
        "title": "Force",
        "description": "The net force on the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "minimum": 0.000001,
        "maximum": 1000000000000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures, in its main units.",
      "format": "text"
    },
    "newtons": {
      "label": "Force (N)",
      "description": "The net force in newtons: mass in kg × acceleration in m/s².",
      "format": "number"
    },
    "poundsForce": {
      "label": "Force (lbf)",
      "description": "The net force in pounds-force (1 lbf = 4.4482216152605 N).",
      "format": "number"
    },
    "kilograms": {
      "label": "Mass (kg)",
      "description": "The mass in kilograms.",
      "format": "number"
    },
    "pounds": {
      "label": "Mass (lb)",
      "description": "The mass in pounds (1 lb = 0.45359237 kg).",
      "format": "number"
    },
    "mps2": {
      "label": "Acceleration (m/s²)",
      "description": "The acceleration in metres per second squared.",
      "format": "number"
    },
    "fps2": {
      "label": "Acceleration (ft/s²)",
      "description": "The acceleration in feet per second squared.",
      "format": "number"
    },
    "gs": {
      "label": "Acceleration (g)",
      "description": "The acceleration as a multiple of standard gravity, 9.80665 m/s².",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "force",
      "m": 1000,
      "a": 3,
      "au": "mps2",
      "F": 3000
    },
    "outputs": {
      "result": "F = 3000 N (674.427 lbf)",
      "newtons": 3000,
      "poundsForce": 674.4268292991314,
      "kilograms": 1000,
      "pounds": 2204.622621848776,
      "mps2": 3,
      "fps2": 9.84251968503937,
      "gs": 0.30591486389337846
    },
    "text": "The answer is F = 3000 N (674.427 lbf)."
  },
  "examples": [
    {
      "given": {
        "find": "force",
        "m": 0.4,
        "a": 3,
        "au": "mps2"
      },
      "expect": {
        "newtons": 1.2,
        "result": "F = 1.2 N (0.269771 lbf)"
      },
      "source": "OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (Example 5.5: (0.400 kg)(3.00 m/s²) = 1.20 N along x); NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811"
    },
    {
      "given": {
        "find": "force",
        "m": 2100,
        "a": 49,
        "au": "mps2"
      },
      "expect": {
        "newtons": 102900,
        "gs": 4.996609443591849
      },
      "source": "OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (Example 5.4: m a = 2100 kg × 49 m/s²); hand calculation in content.mdx: 102,900 N, 4.99661 g"
    },
    {
      "given": {
        "find": "force",
        "m": 1,
        "a": 1,
        "au": "g"
      },
      "expect": {
        "newtons": 9.80665,
        "poundsForce": 2.2046226218487757
      },
      "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; NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811"
    },
    {
      "given": {
        "find": "mass",
        "F": 500,
        "a": 2,
        "au": "mps2"
      },
      "expect": {
        "kilograms": 250,
        "pounds": 551.155655462194,
        "result": "m = 250 kg (551.156 lb)"
      },
      "source": "hand calculation in content.mdx: m = F ÷ a = 500 ÷ 2 = 250 kg; OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law (F_net = m a), https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law"
    },
    {
      "given": {
        "find": "accel",
        "F": 4.4482216152605,
        "m": 0.45359237,
        "au": "fps2"
      },
      "expect": {
        "gs": 1,
        "mps2": 9.80665,
        "fps2": 32.17404855643044,
        "result": "a = 32.174 ft/s²"
      },
      "source": "hand calculation in content.mdx: 4.4482216152605 N ÷ 0.45359237 kg = 9.80665 m/s² = 32.1740 ft/s²; NIST Special Publication 811, Appendix B (1 lbf = 4.4482216152605 N; standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §5.3 Newton’s Second Law: F_net = m a; Example 5.4 (rocket sled, 2,100 kg at 49 m/s²) and Example 5.5 (0.400 kg ball at 3.00 m/s² along x). https://openstax.org/books/university-physics-volume-1/pages/5-3-newtons-second-law (retrieved 2026-10-02)",
    "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 2026-10-02)",
    "NIST Special Publication 811, Appendix B: 1 lbf = 4.4482216152605 N, 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, standard gravity g = 9.80665 m/s² (all exact). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)"
  ],
  "related": [
    "acceleration",
    "velocity",
    "power",
    "density"
  ],
  "changelog": []
}