{
    "name": "Impulse Calculator",
    "url": "https://calculators.geekmidst.com/calculators/impulse-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/impulse-calculator.md",
    "category": "Science & engineering",
    "description": "Find impulse from force and contact time, or from a mass’s change in velocity, and the average force during an impact or push.",
    "summary": "Impulse is force multiplied by the time it acts, and it equals the change in momentum. Knowing either side gives the other, plus the average force over the contact.",
    "also_called": [
        "Impulse–momentum calculator",
        "Average force calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "method",
            "label": "Calculate from",
            "type": "segmented",
            "default": "momentum_change",
            "options": {
                "force_time": "Force and time",
                "momentum_change": "Change in velocity"
            }
        },
        {
            "name": "force",
            "label": "Average force",
            "type": "number",
            "default": "100",
            "shown_when": {
                "method": "force_time"
            }
        },
        {
            "name": "force_unit",
            "label": "Force unit",
            "type": "select",
            "default": "n",
            "options": {
                "n": "newtons (N)",
                "kn": "kilonewtons (kN)",
                "lbf": "pounds-force (lbf)",
                "kgf": "kilograms-force (kgf)"
            },
            "shown_when": {
                "method": "force_time"
            }
        },
        {
            "name": "mass",
            "label": "Mass",
            "type": "number",
            "default": "0.145",
            "shown_when": {
                "method": "momentum_change"
            }
        },
        {
            "name": "mass_unit",
            "label": "Mass unit",
            "type": "select",
            "default": "kg",
            "options": {
                "kg": "kilograms (kg)",
                "g": "grams (g)",
                "t": "tonnes (t)",
                "lb": "pounds (lb)",
                "oz": "ounces (oz)"
            },
            "shown_when": {
                "method": "momentum_change"
            }
        },
        {
            "name": "v_initial",
            "label": "Initial velocity",
            "type": "number",
            "default": "-40",
            "shown_when": {
                "method": "momentum_change"
            }
        },
        {
            "name": "v_final",
            "label": "Final velocity",
            "type": "number",
            "default": "50",
            "shown_when": {
                "method": "momentum_change"
            }
        },
        {
            "name": "velocity_unit",
            "label": "Velocity unit",
            "type": "select",
            "default": "ms",
            "options": {
                "ms": "m/s",
                "kmh": "km/h",
                "mph": "mph",
                "fts": "ft/s",
                "kn": "knots"
            },
            "shown_when": {
                "method": "momentum_change"
            }
        },
        {
            "name": "time",
            "label": "Contact time",
            "type": "number",
            "default": "1"
        },
        {
            "name": "time_unit",
            "label": "Time unit",
            "type": "select",
            "default": "ms",
            "options": {
                "s": "seconds",
                "ms": "milliseconds",
                "min": "minutes",
                "h": "hours"
            }
        }
    ],
    "outputs": [
        {
            "key": "impulse_ns",
            "label": "Impulse",
            "format": "number"
        },
        {
            "key": "impulse_lbfs",
            "label": "Impulse",
            "format": "number"
        },
        {
            "key": "avg_force_n",
            "label": "Average force",
            "format": "number"
        },
        {
            "key": "avg_force_lbf",
            "label": "Average force",
            "format": "number"
        },
        {
            "key": "time_s",
            "label": "Contact time",
            "format": "number"
        }
    ],
    "formula": {
        "text": "J = F Δt = m (v₂ − v₁);  average F = J ÷ Δt",
        "variables": {
            "J": "impulse in N·s",
            "F": "average force in N",
            "Δt": "contact time in s",
            "m": "mass in kg",
            "v₁, v₂": "velocities before and after, with sign for direction"
        }
    },
    "worked_example": {
        "inputs": {
            "method": "momentum_change",
            "force": "100",
            "force_unit": "n",
            "mass": "0.145",
            "mass_unit": "kg",
            "v_initial": "-40",
            "v_final": "50",
            "velocity_unit": "ms",
            "time": "1",
            "time_unit": "ms"
        },
        "steps": [
            "Change in velocity: 50 − (−40) = 90 m/s, because the ball reverses direction.",
            "J = 0.145 × 90 = 13.05 N·s.",
            "Average force = 13.05 ÷ 0.001 s = 13,050 N."
        ],
        "result": "Reversing a 145 g ball from 40 m/s to 50 m/s in 1 ms takes an impulse of 13.05 N·s, an average force of about 13 kN."
    },
    "interpretation": "For a fixed change in momentum, a longer contact time means a smaller force. Airbags, crumple zones and bending your knees on landing all work by stretching Δt.",
    "assumptions": [
        "Motion along one line; the force shown is the average over the contact time."
    ],
    "limitations": [
        "Peak force in a real impact is usually well above the average."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why does the sign of velocity matter?",
            "answer": "A ball that bounces back changes momentum by more than one that stops dead. Enter the incoming velocity as negative and the outgoing as positive to capture the full change."
        },
        {
            "question": "Is impulse the same as momentum?",
            "answer": "Impulse is the change in momentum, measured in the same units (N·s = kg·m/s)."
        }
    ],
    "sources": [
        {
            "title": "BIPM: The International System of Units (SI)",
            "url": "https://www.bipm.org/"
        }
    ],
    "related": [
        {
            "name": "Momentum Calculator",
            "url": "https://calculators.geekmidst.com/calculators/momentum-calculator"
        },
        {
            "name": "Force Calculator (F = ma)",
            "url": "https://calculators.geekmidst.com/calculators/force-mass-acceleration-calculator"
        },
        {
            "name": "Kinetic Energy Calculator",
            "url": "https://calculators.geekmidst.com/calculators/kinetic-energy-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}