{
  "id": "momentum",
  "version": "e08590aee3ed",
  "status": "published",
  "name": "Momentum Calculator",
  "question": "What is the momentum?",
  "summary": "Finds the momentum p = m × v of a moving object from its mass and velocity, or the mass or velocity from the other two, with the kinetic energy.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/momentum-calculator",
  "markdown": "https://www.acalculator.org/physics/momentum-calculator.md",
  "kind": "formulas",
  "method": "p = m × v; v = p ÷ m; m = p ÷ v. Kinetic energy K = p² ÷ (2m). Units are converted to kilograms and meters per second first.",
  "assumptions": [
    "Speeds are far below the speed of light, so the classical p = mv applies.",
    "The motion is along one line: a negative velocity or momentum points the opposite way. A mass is more than 0.",
    "Values run in kilograms, meters and seconds, in double precision."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "m": {
        "title": "Mass",
        "description": "The mass of the moving object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "v": {
        "title": "Velocity",
        "description": "The speed in the direction of motion; a negative value means the opposite direction.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": -300000000,
        "maximum": 300000000
      },
      "p": {
        "title": "Momentum (kg·m/s)",
        "description": "Mass times velocity, in kilogram meters per second.",
        "type": "number",
        "minimum": -1e+21,
        "maximum": 1e+21
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "m",
      "v",
      "p"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "mass": {
      "label": "Mass",
      "description": "The mass of the moving object.",
      "format": "quantity"
    },
    "velocity": {
      "label": "Velocity",
      "description": "The speed in the direction of motion; a negative value means the opposite direction.",
      "format": "quantity"
    },
    "momentum": {
      "label": "Momentum (kg·m/s)",
      "description": "p = m × v in kilogram meters per second.",
      "format": "number"
    },
    "lbFtS": {
      "label": "Momentum (lb·ft/s)",
      "description": "The same momentum in pound feet per second: p ÷ 0.138254954376.",
      "format": "number"
    },
    "energy": {
      "label": "Kinetic energy (J)",
      "description": "K = p² ÷ (2m) = ½mv², in joules.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "m": "1400 kg",
      "v": "15 m/s"
    },
    "outputs": {
      "momentum": 21000,
      "lbFtS": 151893.29087540775,
      "energy": 157500
    },
    "text": "The momentum is 21,000 kg·m/s."
  },
  "examples": [
    {
      "given": {
        "m": 1400,
        "v": 15
      },
      "expect": {
        "p": 21000,
        "energy": 157500,
        "lbFtS": 151893.29087540775
      },
      "source": "OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02); hand calculation in content.mdx: K = 21,000² ÷ 2,800 = 157,500 J; Python 3: 21000/(0.45359237*0.3048)"
    },
    {
      "given": {
        "m": 6e-25,
        "v": 500
      },
      "expect": {
        "p": 3e-22
      },
      "source": "OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02)"
    },
    {
      "given": {
        "p": 21000,
        "m": 1400
      },
      "expect": {
        "v": 15
      },
      "source": "hand calculation in content.mdx: v = p ÷ m = 21,000 ÷ 1,400; OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02)"
    },
    {
      "given": {
        "p": 3000,
        "v": 26.8224
      },
      "expect": {
        "m": 111.84681460272012
      },
      "source": "hand calculation in content.mdx: 60 mph = 26.8224 m/s, m = 3,000 ÷ 26.8224; Python 3: 3000/(60*1609.344/3600); OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02)"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv; SI unit kg·m/s; the car and air molecule examples). https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02)",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (1 lb = 0.45359237 kg, 1 ft = 0.3048 m, exactly). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)"
  ],
  "related": [
    "kinetic-energy",
    "velocity",
    "acceleration",
    "speed"
  ],
  "changelog": []
}