{
  "id": "impulse",
  "version": "5ed863da9fad",
  "status": "published",
  "name": "Impulse Calculator",
  "question": "What is the impulse?",
  "summary": "Computes impulse from an average force and the time it acts (J = FΔt), or from a mass and its change in velocity (J = mΔv), with the average force of an impact, in N·s and lbf·s.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/impulse-calculator",
  "markdown": "https://www.acalculator.org/physics/impulse-calculator.md",
  "kind": "function",
  "method": "J = F_avg × Δt; J = Δp = m × (v₂ − v₁); F_avg = J ÷ Δt.",
  "assumptions": [
    "Motion along one line: a positive velocity or force points one way, a negative one the other way.",
    "The mass stays the same during the impact. Exact unit sizes: 1 lbf = 4.4482216152605 N; 1 lb = 0.45359237 kg; 1 mph = 0.44704 m/s; 1 km/h = 1/3.6 m/s; 1 ft/s = 0.3048 m/s."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Impulse from",
        "description": "Work out the impulse from an average force and a time, or from a mass and its change in velocity.",
        "type": "string",
        "enum": [
          "force",
          "momentum"
        ]
      },
      "F": {
        "title": "Average force",
        "description": "The average force during the contact; negative if it pushes backward.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "minimum": -1000000000000,
        "maximum": 1000000000000
      },
      "m": {
        "title": "Mass",
        "description": "The mass of the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "v1": {
        "title": "Initial velocity",
        "description": "The velocity before the impact; negative for the opposite direction.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": -100000000,
        "maximum": 100000000
      },
      "v2": {
        "title": "Final velocity",
        "description": "The velocity after the impact; negative for the opposite direction.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": -100000000,
        "maximum": 100000000
      },
      "t": {
        "title": "Contact time",
        "description": "How long the force acts. Optional when you start from the change in momentum.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "minimum": 1e-12,
        "maximum": 1000000000
      }
    }
  },
  "outputs": {
    "impulse": {
      "label": "Impulse (N·s)",
      "description": "The impulse J in newton-seconds, the same as kg·m/s of momentum change.",
      "format": "number"
    },
    "lbfs": {
      "label": "Impulse (lbf·s)",
      "description": "The same impulse in pound-force seconds.",
      "format": "number"
    },
    "average": {
      "label": "Average force (N)",
      "description": "The impulse ÷ the contact time.",
      "format": "number"
    },
    "averageLbf": {
      "label": "Average force (lbf)",
      "description": "The average force in pounds-force.",
      "format": "number"
    },
    "dv": {
      "label": "Change in velocity (m/s)",
      "description": "In the momentum mode: v₂ − v₁.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "force",
      "F": "500 N",
      "m": "0.145 kg",
      "v1": "-40 m/s",
      "v2": "50 m/s",
      "t": "0.1 s"
    },
    "outputs": {
      "impulse": 50,
      "lbfs": 11.240447154985524,
      "average": 500,
      "averageLbf": 112.40447154985524
    },
    "text": "The impulse is 50 N·s (11.2404 lbf·s)."
  },
  "examples": [
    {
      "given": {
        "from": "force",
        "F": 500,
        "t": 0.1
      },
      "expect": {
        "impulse": 50,
        "average": 500
      },
      "source": "OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; hand calculation in content.mdx: J = 500 × 0.1 = 50 N·s"
    },
    {
      "given": {
        "from": "momentum",
        "m": 0.145,
        "v1": -40,
        "v2": 50,
        "t": 0.001
      },
      "expect": {
        "impulse": 13.05,
        "dv": 90,
        "average": 13050
      },
      "source": "OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; hand calculation in content.mdx: J = 0.145 × (50 − (−40)) = 13.05 N·s; ÷ 0.001 s = 13,050 N"
    },
    {
      "given": {
        "from": "momentum",
        "m": 1000,
        "v1": 20,
        "v2": 0
      },
      "expect": {
        "impulse": -20000,
        "dv": -20
      },
      "source": "OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; hand calculation in content.mdx: J = 1,000 × (0 − 20) = −20,000 N·s"
    },
    {
      "given": {
        "from": "force",
        "F": 4.4482216152605,
        "t": 1
      },
      "expect": {
        "lbfs": 1,
        "impulse": 4.4482216152605
      },
      "source": "OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; NIST SP 811 (1 lbf = 4.4482216152605 N), https://www.nist.gov/pml/special-publication-811; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; the impulse-momentum theorem J = Δp). https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions (retrieved 2026-10-03)",
    "NIST SP 811, Appendix B.8 (1 lbf = 4.4482216152605 N; 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 2026-10-03)"
  ],
  "related": [
    "momentum",
    "force",
    "net-force"
  ],
  "changelog": []
}