{
  "slug": "half-life",
  "title": "Half-Life Calculator",
  "heading": "Radioactive Half-Life Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/half-life",
  "summary": "Remaining quantity after any elapsed time.",
  "description": "Exponential decay: every half-life cuts the remaining amount in half. Works for isotopes, drug clearance, and anything with a fixed decay rate.",
  "formula": "N = N₀ × (1/2)^(t ÷ t½)",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=half-life",
  "inputs": [
    {
      "id": "n0",
      "label": "Starting quantity",
      "kind": "number",
      "hint": null,
      "default": 100,
      "unit": null,
      "min": 0,
      "max": null
    },
    {
      "id": "half",
      "label": "Half-life",
      "kind": "number",
      "hint": null,
      "default": 12,
      "unit": "hours",
      "min": 0.0001,
      "max": null
    },
    {
      "id": "time",
      "label": "Elapsed time",
      "kind": "number",
      "hint": null,
      "default": 36,
      "unit": "hours",
      "min": 0,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "remaining",
      "label": "Remaining quantity",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "pct",
      "label": "Percent remaining",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "decayed",
      "label": "Amount decayed",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "halves",
      "label": "Half-lives elapsed",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Starting quantity: 100",
      "Half-life: 12 hours",
      "Elapsed time: 36 hours"
    ],
    "outputs": [
      "Remaining quantity: 12.5",
      "Percent remaining: 12.5",
      "Amount decayed: 87.5",
      "Half-lives elapsed: 3"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter starting quantity.",
      "Enter half-life (hours).",
      "Enter elapsed time (hours).",
      "Read your remaining quantity 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": {
        "n0": 60,
        "half": 7.199999999999999,
        "time": 22
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "n0": 100,
        "half": 12,
        "time": 36
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "n0": 160,
        "half": 19.200000000000003,
        "time": 58
      }
    }
  ],
  "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 radioactive half-life calculator work?",
      "a": "Exponential decay: every half-life cuts the remaining amount in half. Works for isotopes, drug clearance, and anything with a fixed decay rate. The underlying maths is: N = N₀ × (1/2)^(t ÷ t½)"
    },
    {
      "q": "What do I need to enter?",
      "a": "3 values: starting quantity, half-life, and elapsed time. 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 remaining quantity 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 — Half-Life Calculator (https://www.revenuelab.fyi/toolbox/half-life)"
}