{
    "name": "IRR Calculator",
    "url": "https://calculators.geekmidst.com/calculators/irr-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/irr-calculator.md",
    "category": "Finance",
    "description": "Find the internal rate of return of any series of cash flows, the annualised rate for monthly or quarterly flows, the net gain and the money multiple.",
    "summary": "The internal rate of return is the discount rate at which the cash flows of an investment are worth exactly zero today. List the money going out as negative numbers and the money coming back as positive ones, one per period.",
    "also_called": [
        "Internal rate of return 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": "flows",
            "label": "Cash flows, period 0 first",
            "type": "textarea",
            "default": "-1000\n600\n600"
        },
        {
            "name": "periods_per_year",
            "label": "Each period is",
            "type": "select",
            "default": "1",
            "options": {
                "1": "A year",
                "2": "Half a year",
                "4": "A quarter",
                "12": "A month"
            }
        }
    ],
    "outputs": [
        {
            "key": "irr",
            "label": "IRR per period",
            "format": "percent"
        },
        {
            "key": "irr_annual",
            "label": "IRR per year (effective)",
            "format": "percent"
        },
        {
            "key": "net_gain",
            "label": "Net gain (money in − money out)",
            "format": "number"
        },
        {
            "key": "multiple",
            "label": "Money multiple",
            "format": "multiple"
        }
    ],
    "formula": {
        "text": "0 = Σ CFₜ ÷ (1 + IRR)ᵗ  for t = 0 … n;  annual IRR = (1 + IRR)^(periods per year) − 1",
        "variables": {
            "CFₜ": "cash flow in period t (negative for money paid out)",
            "IRR": "the rate found by numerical search",
            "n": "number of periods after the first"
        }
    },
    "worked_example": {
        "inputs": {
            "flows": "-1000\n600\n600",
            "periods_per_year": "1"
        },
        "steps": [
            "Find r with −1,000 + 600 ÷ (1 + r) + 600 ÷ (1 + r)² = 0.",
            "Put x = 1 ÷ (1 + r): 600x² + 600x − 1,000 = 0, so x = (−600 + √2,760,000) ÷ 1,200 = 0.88444.",
            "r = 1 ÷ 0.88444 − 1 = 13.07%."
        ],
        "result": "Paying 1,000 now for 600 at the end of each of the next two years earns an IRR of 13.07% a year."
    },
    "interpretation": "Accept a project when its IRR is above your required return (cost of capital). IRR assumes interim cash can be reinvested at the IRR itself, so very high IRRs on short projects overstate long-run growth; compare NPV at your required rate when projects differ in size or length.",
    "assumptions": [
        "Cash flows occur at regular, equal intervals, with the first at time zero.",
        "Rates are found by search between −99% and +1,000% per period."
    ],
    "limitations": [
        "When the cash flows change sign more than once there can be several IRRs; the calculator reports the one nearest 10% and lists the others.",
        "Irregular dates need an XIRR-style calculation, which this tool does not do."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What is the difference between IRR and ROI?",
            "answer": "ROI is the total gain divided by the cost and ignores timing. IRR is a yearly (or per-period) rate that accounts for when each amount is paid or received."
        },
        {
            "question": "Why can there be more than one IRR?",
            "answer": "The NPV equation is a polynomial in 1 ÷ (1 + r). Each change of sign in the cash flows can add a root, so a project with a large cost at the end can have two IRRs."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "ROI Calculator",
            "url": "https://calculators.geekmidst.com/calculators/roi-calculator"
        },
        {
            "name": "Payback Period Calculator",
            "url": "https://calculators.geekmidst.com/calculators/payback-period-calculator"
        },
        {
            "name": "Present Value Calculator",
            "url": "https://calculators.geekmidst.com/calculators/present-value-calculator"
        },
        {
            "name": "Compound Interest Calculator",
            "url": "https://calculators.geekmidst.com/calculators/compound-interest-calculator"
        }
    ],
    "disclaimer": "Returns are illustrations at a constant rate, not predictions or guarantees. Investments can lose value. This is not investment advice.",
    "publisher": "GM¹X CalcVerse"
}