{
    "name": "Projectile Range Calculator",
    "url": "https://calculators.geekmidst.com/calculators/projectile-range-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/projectile-range-calculator.md",
    "category": "Science & engineering",
    "description": "Calculate how far a projectile travels from launch speed, angle and launch height, with flight time, peak height, impact speed and a range-by-angle table.",
    "summary": "Without air resistance a projectile moves at constant horizontal speed while gravity pulls it down. The range is that horizontal speed times the time until it lands.",
    "also_called": [
        "Projectile motion calculator",
        "Trajectory 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": "speed",
            "label": "Launch speed",
            "type": "number",
            "default": "20"
        },
        {
            "name": "speed_unit",
            "label": "Speed unit",
            "type": "select",
            "default": "ms",
            "options": {
                "ms": "m/s",
                "kmh": "km/h",
                "mph": "mph",
                "fts": "ft/s",
                "kn": "knots"
            }
        },
        {
            "name": "angle",
            "label": "Launch angle above horizontal",
            "type": "number",
            "default": "45",
            "unit": "°"
        },
        {
            "name": "height",
            "label": "Launch height above landing level",
            "type": "number",
            "default": "0",
            "optional": true
        },
        {
            "name": "length_unit",
            "label": "Height unit",
            "type": "select",
            "default": "m",
            "options": {
                "m": "metres (m)",
                "cm": "centimetres (cm)",
                "mm": "millimetres (mm)",
                "km": "kilometres (km)",
                "ft": "feet (ft)",
                "in": "inches (in)",
                "mi": "miles (mi)"
            }
        },
        {
            "name": "gravity",
            "label": "Gravitational acceleration (g)",
            "type": "number",
            "default": "9.80665",
            "unit": "m/s²"
        }
    ],
    "outputs": [
        {
            "key": "range_m",
            "label": "Horizontal range",
            "format": "number"
        },
        {
            "key": "range_ft",
            "label": "Horizontal range",
            "format": "number"
        },
        {
            "key": "flight_time_s",
            "label": "Time of flight",
            "format": "number"
        },
        {
            "key": "max_height_m",
            "label": "Peak height above landing level",
            "format": "number"
        },
        {
            "key": "impact_speed_ms",
            "label": "Impact speed",
            "format": "number"
        },
        {
            "key": "impact_angle_deg",
            "label": "Impact angle below horizontal",
            "format": "number"
        }
    ],
    "formula": {
        "text": "t = (v sinθ + √((v sinθ)² + 2 g h)) ÷ g;  R = v cosθ × t;  on level ground R = v² sin 2θ ÷ g",
        "variables": {
            "R": "horizontal range in m",
            "v": "launch speed in m/s",
            "θ": "launch angle above horizontal",
            "h": "launch height above the landing level in m",
            "g": "gravitational acceleration",
            "t": "time of flight in s"
        }
    },
    "worked_example": {
        "inputs": {
            "speed": "10",
            "speed_unit": "ms",
            "angle": "0",
            "height": "20",
            "length_unit": "m",
            "gravity": "10"
        },
        "steps": [
            "Launched horizontally (θ = 0) from 20 m with g = 10 m/s²: t = √(2h ÷ g) = √(40 ÷ 10) = 2 s.",
            "R = 10 m/s × 2 s = 20 m."
        ],
        "result": "A ball thrown horizontally at 10 m/s from 20 m up lands 20 m away after 2 seconds (with g rounded to 10 m/s²)."
    },
    "interpretation": "On level ground the range is greatest at 45°, and complementary angles (30° and 60°) give the same range. Launching from a height shifts the best angle below 45°. The table shows how range changes with angle for your speed.",
    "assumptions": [
        "No air resistance, spin or wind.",
        "Flat landing surface at the stated level and constant g."
    ],
    "limitations": [
        "Real balls, arrows and shells fall well short of the vacuum range at high speed because drag grows with the square of speed."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is 45° the best angle?",
            "answer": "Range on level ground is v² sin 2θ ÷ g, and sin 2θ peaks at 1 when θ = 45°."
        },
        {
            "question": "Does mass affect the range?",
            "answer": "Not without air resistance. With drag, heavier and denser objects of the same shape keep their speed better and travel farther."
        }
    ],
    "sources": [
        {
            "title": "BIPM: The International System of Units (SI)",
            "url": "https://www.bipm.org/"
        }
    ],
    "related": [
        {
            "name": "Projectile Maximum Height Calculator",
            "url": "https://calculators.geekmidst.com/calculators/projectile-maximum-height-calculator"
        },
        {
            "name": "Kinetic Energy Calculator",
            "url": "https://calculators.geekmidst.com/calculators/kinetic-energy-calculator"
        },
        {
            "name": "Speed Calculator",
            "url": "https://calculators.geekmidst.com/calculators/speed-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}