{
  "id": "cagr",
  "version": "7be490b6dbf4",
  "status": "published",
  "name": "CAGR Calculator",
  "question": "What is the CAGR of my investment?",
  "summary": "Computes the compound annual growth rate (CAGR) between a start and an end value over a period, or solves for the start, end, or period.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/cagr-calculator",
  "markdown": "https://www.acalculator.org/finance/cagr-calculator.md",
  "kind": "formulas",
  "method": "CAGR = (End ÷ Start)^(1/n) − 1, where n is the period in years (months ÷ 12).",
  "assumptions": [
    "Growth is the same every year and compounds once a year; part years use the same power.",
    "A period in months is months ÷ 12 years.",
    "Money added or taken out during the period is not included; only the start and end values count."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "startValue": {
        "title": "Start value",
        "description": "The value at the start of the period.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "endValue": {
        "title": "End value",
        "description": "The value at the end of the period.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "period": {
        "title": "Period",
        "description": "The length of the period, in years or months (see the unit).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1200
      },
      "cagr": {
        "title": "CAGR",
        "description": "The compound annual growth rate: the steady yearly rate that turns the start value into the end value.",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": -100
      },
      "periodUnit": {
        "title": "Period in",
        "description": "Whether the period is in years or in months.",
        "type": "string",
        "enum": [
          "years",
          "months"
        ]
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "startValue",
      "endValue",
      "period",
      "cagr"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "start": {
      "label": "Start value",
      "description": "The value at the start of the period.",
      "format": "money"
    },
    "end": {
      "label": "End value",
      "description": "The value at the end of the period.",
      "format": "money"
    },
    "period": {
      "label": "Period",
      "description": "The length of the period, in the unit chosen under “Period in”.",
      "format": "number"
    },
    "cagr": {
      "label": "CAGR",
      "description": "The compound annual growth rate: the steady yearly rate that turns the start value into the end value.",
      "format": "percent"
    },
    "change": {
      "label": "Total change",
      "description": "The end value minus the start value.",
      "format": "money"
    },
    "changePercent": {
      "label": "Total change (%)",
      "description": "The total change divided by the start value, as a percent.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "periodUnit": "years",
      "startValue": 1000,
      "endValue": 2000,
      "period": 5
    },
    "outputs": {
      "cagr": 14.869835499703498,
      "change": 1000,
      "changePercent": 100
    },
    "text": "Going from $1,000.00 to $2,000.00 over 5 years is a compound annual growth rate of 14.87%."
  },
  "examples": [
    {
      "given": {
        "startValue": 1000,
        "endValue": 2000,
        "period": 5,
        "periodUnit": "years"
      },
      "expect": {
        "cagr": 14.869835499703509,
        "change": 1000,
        "changePercent": 100
      },
      "source": "the compound growth formula A = P(1 + r)^n (SEC Investor.gov) solved for r: (End ÷ Start)^(1/n) − 1; hand calculation in content.mdx"
    },
    {
      "given": {
        "startValue": 5000,
        "endValue": 4000,
        "period": 3,
        "periodUnit": "years"
      },
      "expect": {
        "cagr": -7.168223327744416,
        "changePercent": -20
      },
      "source": "hand calculation in content.mdx: 0.8^(1/3) − 1"
    },
    {
      "given": {
        "startValue": 1000,
        "endValue": 1500,
        "period": 18,
        "periodUnit": "months"
      },
      "expect": {
        "cagr": 31.03706971044482
      },
      "source": "hand calculation in content.mdx: 1.5^(12/18) − 1"
    },
    {
      "given": {
        "startValue": 1000,
        "endValue": 2000,
        "cagr": 10,
        "periodUnit": "years"
      },
      "expect": {
        "period": 7.272540897341713
      },
      "source": "hand calculation in content.mdx: ln 2 ÷ ln 1.1"
    },
    {
      "given": {
        "startValue": 1000,
        "cagr": 10,
        "period": 3,
        "periodUnit": "years"
      },
      "expect": {
        "endValue": 1331
      },
      "source": "hand calculation in content.mdx: 1,000 × 1.1^3"
    },
    {
      "given": {
        "startValue": 1000,
        "endValue": 1250,
        "period": 1,
        "periodUnit": "months"
      },
      "expect": {
        "cagr": 1355.1915228366852,
        "changePercent": 25
      },
      "source": "hand calculation in content.mdx: 1.25^12 − 1 = 13.551915 (Python 3: 1.25**12 - 1)"
    },
    {
      "given": {
        "endValue": 1331,
        "cagr": 10,
        "period": 3,
        "periodUnit": "years"
      },
      "expect": {
        "startValue": 999.9999999999997
      },
      "source": "hand calculation in content.mdx: 1,331 ÷ 1.1^3 = 1,000"
    }
  ],
  "sources": [
    "U.S. Securities and Exchange Commission, Investor.gov compound interest formula A = P(1 + r)^n. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator",
    "Geometric mean rate of return: S. A. Broverman, Mathematics of Investment and Credit, chapter 1."
  ],
  "related": [
    "compound-interest",
    "irr"
  ],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "The CAGR has no upper limit, so a short period with a large yearly rate has an answer (muse review)."
    },
    {
      "date": "2026-10-01",
      "note": "The period unit reads in lower case in the answer (“over 5 months”), it starts “Going from” so a fall reads plainly, and a solved period shows 2 decimals (“7.27”), not 6."
    }
  ]
}