{
  "slug": "projectile-motion",
  "title": "Projectile Motion Calculator",
  "heading": "Projectile Motion Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/projectile-motion",
  "summary": "Range, peak height, and flight time from speed and angle.",
  "description": "Classic kinematics with no air resistance: launch speed and angle give you hang time, apex, and horizontal range.",
  "formula": "R = v² sin(2θ) ÷ g; h = v² sin²θ ÷ 2g",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=projectile-motion",
  "inputs": [
    {
      "id": "v0",
      "label": "Launch speed",
      "kind": "number",
      "hint": null,
      "default": 20,
      "unit": "m/s",
      "min": 0,
      "max": null
    },
    {
      "id": "angle",
      "label": "Launch angle",
      "kind": "number",
      "hint": null,
      "default": 45,
      "unit": "°",
      "min": 0,
      "max": 90
    },
    {
      "id": "g",
      "label": "Gravity",
      "kind": "number",
      "hint": null,
      "default": 9.81,
      "unit": "m/s²",
      "min": 0.1,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "range",
      "label": "Horizontal range (m)",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "apex",
      "label": "Max height (m)",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "time",
      "label": "Flight time (s)",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "vx",
      "label": "Horizontal velocity (m/s)",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Launch speed: 20 m/s",
      "Launch angle: 45 °",
      "Gravity: 9.81 m/s²"
    ],
    "outputs": [
      "Horizontal range (m): 40.77",
      "Max height (m): 10.19",
      "Flight time (s): 2.88",
      "Horizontal velocity (m/s): 14.14"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter launch speed (m/s).",
      "Enter launch angle (°).",
      "Enter gravity (m/s²).",
      "Read your horizontal range (m) on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "v0": 12,
        "angle": 27,
        "g": 5.886
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "v0": 20,
        "angle": 45,
        "g": 9.81
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "v0": 32,
        "angle": 72,
        "g": 15.696000000000002
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the projectile motion calculator work?",
      "a": "Classic kinematics with no air resistance: launch speed and angle give you hang time, apex, and horizontal range. The underlying maths is: R = v² sin(2θ) ÷ g; h = v² sin²θ ÷ 2g"
    },
    {
      "q": "What do I need to enter?",
      "a": "3 values: launch speed, launch angle, and gravity. Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the horizontal range (m) result mean?",
      "a": "It is returned as a decimal number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Projectile Motion Calculator (https://www.revenuelab.fyi/toolbox/projectile-motion)"
}