{
  "id": "free-fall",
  "version": "836b66956d82",
  "status": "published",
  "name": "Free Fall Calculator",
  "question": "How long and how fast is the free fall?",
  "summary": "Works out how long an object takes to fall a height from rest and how fast it hits the ground, h = ½gt² and v = gt, or the height from the time or the speed, with no air resistance.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/free-fall-calculator",
  "markdown": "https://www.acalculator.org/physics/free-fall-calculator.md",
  "kind": "formulas",
  "method": "h = ½gt², v = gt, v² = 2gh; t = √(2h ÷ g), v = √(2gh), h = v² ÷ 2g.",
  "assumptions": [
    "The object starts from rest and falls straight down.",
    "There is no air resistance, so the speed keeps growing; a real object in air reaches a terminal speed.",
    "Gravity is the same over the whole fall. On Earth the standard value is 9.80665 m/s²."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "h": {
        "title": "Fall height",
        "description": "How far the object falls, from where it is let go to where it lands.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000000
      },
      "t": {
        "title": "Fall time",
        "description": "How long the fall takes, from release to landing.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "v": {
        "title": "Impact speed",
        "description": "The speed at the end of the fall, just before it lands.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "exclusiveMinimum": 0,
        "maximum": 10000000000
      },
      "g": {
        "title": "Gravity (m/s²)",
        "description": "The acceleration of gravity in meters per second squared: 9.80665 on Earth, about 1.62 on the Moon.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 1000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "h",
      "t",
      "v",
      "g"
    ],
    "inputsOnly": [
      "g"
    ]
  },
  "outputs": {
    "height": {
      "label": "Fall height",
      "description": "h = ½gt².",
      "format": "quantity",
      "unit": "m"
    },
    "time": {
      "label": "Fall time",
      "description": "t = √(2h ÷ g), in seconds.",
      "format": "quantity",
      "unit": "s"
    },
    "velocity": {
      "label": "Impact speed",
      "description": "v = gt = √(2gh), in meters per second.",
      "format": "quantity",
      "unit": "mps"
    },
    "g": {
      "label": "Gravity (m/s²)",
      "description": "The acceleration of gravity in meters per second squared: 9.80665 on Earth, about 1.62 on the Moon.",
      "format": "number"
    },
    "mph": {
      "label": "Impact speed (mph)",
      "description": "The impact speed in miles per hour: v ÷ 0.44704.",
      "format": "number"
    },
    "kmh": {
      "label": "Impact speed (km/h)",
      "description": "The impact speed in kilometers per hour: v × 3.6.",
      "format": "number"
    },
    "feet": {
      "label": "Fall height (ft)",
      "description": "The fall height in feet: h ÷ 0.3048.",
      "format": "number"
    },
    "average": {
      "label": "Average speed (m/s)",
      "description": "The height ÷ the time, which is half the impact speed.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "h": "100 ft",
      "g": 9.80665
    },
    "outputs": {
      "time": 2.493228837133377,
      "velocity": 24.45022257567403,
      "mph": 54.6935902283331,
      "kmh": 88.02080127242651,
      "feet": 100,
      "average": 12.225111287837015
    },
    "text": "The fall takes 2.49323 s and ends at 54.6936 mph."
  },
  "examples": [
    {
      "given": {
        "h": 98,
        "g": 9.8
      },
      "expect": {
        "t": 4.47213595499958,
        "v": 43.82693235899588
      },
      "source": "OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02): y = −½gt² with y = −98 m gives t = √(2 × 98 ÷ 9.8) = √20 s; hand calculation in content.mdx"
    },
    {
      "given": {
        "t": 3,
        "g": 9.80665
      },
      "expect": {
        "h": 44.129925,
        "v": 29.41995,
        "mph": 65.81055386542592
      },
      "source": "hand calculation in content.mdx: h = ½ × 9.80665 × 3² = 44.129925 m, v = 9.80665 × 3; NIST Special Publication 811, Guide for the Use of the International System of Units, B.8 (standard acceleration of gravity gₙ = 9.80665 m/s² exactly; 1 ft = 0.3048 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02); OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)"
    },
    {
      "given": {
        "v": 20,
        "g": 9.80665
      },
      "expect": {
        "h": 20.394324259558566,
        "t": 2.0394324259558565
      },
      "source": "hand calculation in content.mdx: h = v² ÷ 2g = 400 ÷ 19.6133, t = v ÷ g; OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)"
    },
    {
      "given": {
        "h": 30.48,
        "g": 9.80665
      },
      "expect": {
        "t": 2.493228837133377,
        "v": 24.45022257567403
      },
      "source": "hand calculation in content.mdx: 30.48 m, t = √(60.96 ÷ 9.80665); NIST Special Publication 811, Guide for the Use of the International System of Units, B.8 (standard acceleration of gravity gₙ = 9.80665 m/s² exactly; 1 ft = 0.3048 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02); OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §3.5 Free Fall (kinematic equations with a = −g; worked examples), CC BY 4.0. https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (standard acceleration of gravity 9.80665 m/s²; 1 ft = 0.3048 m and 1 mi = 1,609.344 m exactly). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)"
  ],
  "related": [
    "velocity",
    "acceleration",
    "kinetic-energy",
    "speed"
  ],
  "changelog": []
}