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Investing & Retirement
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IRR Calculator

Find the internal rate of return on a series of cash flows

📊 Cash flows

$

Entered as a positive number; counted as a negative cash flow.

Year 1
$
Year 2
$
Year 3
$
Year 4
$
Year 5
$

Enter a negative number for a year with a net outflow (e.g. extra capital).

Your required return / cost of capital. If IRR beats this, NPV is positive.
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Last updated June 2026

Method: IRR is the rate where the net present value of all cash flows equals zero, NPV = ∑ CFt / (1 + r)t = 0. It is solved numerically with Newton's method and a bisection fallback, then verified with an NPV-at-IRR check.

Included: Initial investment at year 0, an unlimited series of yearly cash flows (inflows or outflows), the IRR, a net-present-value comparison at your chosen discount rate, and a discounted cash-flow table.

Not included: Taxes, inflation adjustment, mid-year or irregular-date cash flows, and MIRR. Cash flows are assumed to occur at the end of each year. Results are estimates, not financial advice.

IRR calculator: everything you need to know

Suppose you invest $100,000 in a project today and it pays back $30,000, $35,000, $40,000, $45,000 and $50,000 over the next five years. The cash adds up to $200,000 - double your money - but how good is that really, once you account for the years you waited? The internal rate of return (IRR) answers exactly that: it is the single annual rate of return that makes those future cash flows worth precisely $100,000 today. For this example the IRR is about 25.75% per year, which is the number this IRR calculator finds for you.

What IRR actually measures

IRR is the discount rate at which the net present value (NPV) of an investment is zero. NPV adds up every cash flow after shrinking each one for the time you wait to receive it. When that sum equals zero, you have found the break-even rate - the effective compound return the project earns if everything goes to plan. A higher IRR means a more attractive investment, and an IRR above your required return means the deal is expected to create value.

The IRR formula

IRR is the rate r that satisfies the net-present-value equation:

NPV = ∑t=0n CFt ÷ (1 + r)t = 0

where CFt is the cash flow in period t (with CF0, the initial investment, entered as a negative number), n is the number of periods, and r is the IRR. There is no algebraic way to isolate r, so it must be found by iteration. This calculator starts with Newton's method - repeatedly improving a guess using the slope of the NPV curve - and falls back to bisection (narrowing a bracket between a low and high rate) if the first method does not converge.

How to use this IRR calculator

  1. Initial investment: enter the cash you put in today as a positive number. The calculator treats it as the year-0 outflow.
  2. Yearly cash flows: add one row per year and enter the inflow you expect. Use the "Add year" button for longer projects, and enter a negative number for any year that needs more capital out.
  3. Discount rate: enter your required return (hurdle rate or cost of capital). This does not change the IRR, but it drives the NPV comparison so you can see whether the IRR clears your bar.
  4. Calculate: read the IRR at the top, confirm the NPV-at-IRR check is about $0, and scan the discounted cash-flow table to see how each year contributes.

Who this calculator is for

  • Real-estate investors comparing a rental's cash flows and eventual sale against other deals.
  • Business owners evaluating whether a piece of equipment or an expansion earns more than its cost of capital.
  • Finance students checking homework on capital budgeting, NPV and IRR.
  • Angel and small-fund investors sizing up the return on a multi-year stake with uneven distributions.
  • Anyone who has irregular cash flows over several years and wants a single comparable rate of return.

Key terms explained

  • Cash flow (CF): money in (positive) or money out (negative) in a given period.
  • Net present value (NPV): the sum of all discounted cash flows; positive means the project adds value at the chosen rate.
  • Discount rate: the rate used to shrink future dollars to today's value, often your cost of capital or required return.
  • Hurdle rate: the minimum acceptable rate of return; a project is attractive when its IRR exceeds the hurdle rate.
  • Time value of money: the principle that a dollar today is worth more than a dollar later, which is what discounting captures.
  • MIRR: the modified internal rate of return, which assumes interim cash is reinvested at a separate rate rather than at the IRR.

Worked example, step by step

Take the $100,000 investment with inflows of $30k, $35k, $40k, $45k and $50k. Discount each inflow at the IRR of roughly 25.75%: $30k becomes about $23.9k, $35k about $22.1k, $40k about $20.1k, $45k about $18.0k and $50k about $15.9k. Those discounted values add to about $100,000, which - minus the $100,000 you paid - nets to essentially zero. That zero is the definition of IRR. If your required return were only 10%, the same inflows would be worth about $148,000 today, giving a healthy NPV of roughly $48,000 and confirming the project clears the bar.

Scenario 1: equipment purchase

A shop buys a $50,000 machine that saves $14,000 a year for five years and is then worth nothing. The IRR on those cash flows is about 12.4%. If the company's cost of capital is 9%, the machine clears the hurdle and is worth buying; if its cost of capital is 15%, the IRR falls short and the cash is better deployed elsewhere.

Scenario 2: rental property

An investor puts $200,000 into a rental, collects net cash of $12,000 a year for four years, then sells in year five for $250,000 net (so year five is $12,000 + $250,000 = $262,000). The IRR is about 10.1%. Most of the return rides on the sale price, which is why IRR is so sensitive to the exit assumption - a topic the limitations section covers below.

Scenario 3: front-loaded vs back-loaded returns

Two projects both invest $100,000 and return $150,000 total over three years. Project A pays $90k, $40k, $20k; Project B pays $20k, $40k, $90k. Project A's IRR is far higher because it returns cash sooner, even though the headline total is identical. This is the clearest demonstration of why timing - not just the sum - drives IRR.

What changes the IRR the most

  • Timing of cash flows: earlier inflows lift the IRR sharply; back-loaded cash lowers it.
  • Size of the initial investment: a larger upfront cost for the same inflows reduces the rate.
  • Terminal or sale value: a big final-year cash flow (like a property sale) can dominate the result.
  • Project length: stretching the same total cash over more years dilutes the annual rate.
  • Negative interim years: additional outflows mid-project drag the IRR down and can create multiple IRRs.

Tips for using IRR well

  • Always check IRR against NPV at your real discount rate; a high IRR on a tiny project may create little actual value.
  • Be conservative with the terminal value - it often drives the headline number and is the least certain input.
  • If cash flows switch sign more than once, distrust a single IRR and lean on NPV or MIRR.
  • Use the same time basis for every figure (this tool assumes end-of-year cash flows).
  • Run a low and a high inflow scenario to see how sensitive the IRR is before you commit.

Limitations and assumptions

  • It assumes cash flows occur at the end of each year; mid-year or irregular dates are not modeled (that requires an XIRR approach).
  • The standard IRR implicitly reinvests interim cash at the IRR itself, which can overstate returns when the IRR is high - use MIRR for a more conservative view.
  • Cash flows with multiple sign changes can have more than one IRR; this tool returns one root and you should cross-check with NPV.
  • It does not adjust for taxes or inflation; enter after-tax, real cash flows if you want a real after-tax return.
  • IRR ignores project scale, so it is a poor sole criterion when ranking projects of very different sizes.

IRR vs MIRR: the reinvestment problem

The single biggest criticism of IRR is its hidden assumption that every interim cash flow is reinvested at the IRR itself. If a project shows a 30% IRR, the math quietly assumes you can park each payout in something else earning 30% until the project ends - which is rarely realistic. The modified internal rate of return (MIRR) fixes this by separating two rates: a finance rate for any negative cash flows and a reinvestment rate (often your safe cost of capital, say 6-8%) for positive ones. Because MIRR uses a more conservative reinvestment assumption, it almost always comes out lower than IRR - and the gap widens as the IRR climbs. If your IRR looks spectacular, computing the MIRR is the quickest reality check; a 28% IRR can collapse to a 14% MIRR once you stop assuming you can redeploy cash at 28%. This tool reports the standard IRR, so treat a very high figure as an optimistic ceiling rather than a promise.

IRR vs ROI vs CAGR: which return metric to use

Three return metrics get confused constantly because they all output a percentage. Knowing which one your question calls for saves you from comparing apples to oranges:

  • ROI is the simplest: total gain divided by cost, expressed as one lifetime percentage. It ignores time entirely, so a 100% ROI earned in one year and a 100% ROI earned over ten years look identical even though the first is far better. Use the ROI Calculator when you just want the headline profit on a single buy-and-sell.
  • CAGR turns a starting value and an ending value into one smoothed annual growth rate, assuming a single deposit and a single withdrawal with nothing in between. It is the right tool for "what annual rate did my fund grow at?" - see the CAGR Calculator. CAGR is actually a special case of IRR with only two cash flows.
  • IRR is the most general of the three: it handles an arbitrary stream of inflows and outflows at different times and finds the one rate that ties them together. Whenever there are more than two cash flows - an initial investment plus several uneven returns - IRR is the metric that respects the timing of each one.

A practical rule: use ROI for a quick profit check, CAGR for a smoothed two-point growth rate, and IRR the moment your cash flows arrive on more than two dates.

Annual IRR vs XIRR for irregular dates

This calculator assumes each cash flow lands at the end of a clean yearly period, which is perfect for textbook problems and most planning. Real investments, though, often pay on irregular calendar dates - a distribution in March, another in November, an exit the following August. When the gaps between cash flows are uneven, the annual model is an approximation. The precise tool for dated cash flows is XIRR, which discounts each flow by the exact number of days from the start rather than by whole years. For ballpark decisions the difference is usually small, but for a deal with large, lumpy, oddly-spaced payments, an XIRR will be more accurate than rounding everything to year-end. If your cash flows are roughly annual, the result here is reliable; if they are wildly irregular, treat the annual IRR as a close estimate and verify dated deals with an XIRR.

A quick worked NPV cross-check

Because IRR is just the rate where NPV equals zero, you can sanity-check any IRR by hand with one calculation. Take a $10,000 investment that returns $6,000 in year one and $6,000 in year two. Guess an IRR of 13.1%: discount the first $6,000 by 1.131 to get about $5,305, and the second $6,000 by 1.131² (about 1.279) to get about $4,692. Add them: $5,305 + $4,692 = $9,997, which is essentially the $10,000 you paid - so 13.1% is the IRR. If your guess had produced a discounted sum well above $10,000, the true IRR is higher; if well below, it is lower. That bracketing logic is exactly what the calculator's bisection fallback automates, and doing one round by hand makes the result feel a lot less like a black box.

How it compares to related calculators

IRR answers "what annual rate does this stream of cash flows earn?" If your question is slightly different, a sister tool fits better:

Sources & further reading

⚠️ Common mistakes & edge cases

Forgetting the initial investment

If you enter only positive inflows and no upfront outflow, there is no rate that makes NPV zero, so the IRR is undefined. The year-0 investment must be included (as money out) for IRR to exist.

Trusting a single IRR with multiple sign changes

When cash flows go out, in, then out again, the equation can have several valid IRRs. A lone IRR figure is then misleading - rely on NPV at your discount rate, or use MIRR, to make the decision.

Picking the higher IRR over the higher NPV

IRR is a rate and ignores size. A small project can post a higher IRR while a larger one adds far more total value. For mutually exclusive choices, compare NPVs, not just IRRs.

Over-optimistic terminal value

For property and business deals, the final-year sale or exit value often dominates the IRR. An inflated exit assumption can make a mediocre project look great - stress-test it with a conservative number.

Note: This calculator gives an estimate, not financial advice. IRR depends entirely on the cash flows you forecast, which are uncertain - treat the result as one input among several.

❓ Frequently asked questions

What is the internal rate of return (IRR)?

The internal rate of return is the annual discount rate that makes the net present value (NPV) of all of a project's cash flows equal to zero. In plain terms, it is the effective compound rate of return an investment is expected to earn over its life. A higher IRR means a more attractive project, all else equal.

How is IRR calculated?

IRR is the rate r that solves the equation NPV = sum of CF_t / (1 + r)^t = 0, summed from period t = 0 to the final period, where CF_0 is the initial investment (a negative cash flow). There is no closed-form formula, so it is found numerically - this calculator uses Newton's method with a bisection fallback to converge on the rate where NPV is essentially zero.

What is the difference between IRR and NPV?

NPV gives you a dollar amount of value created at a chosen discount rate, while IRR gives you a single percentage rate of return that ignores the size of the discount rate. NPV answers 'how much value?' and IRR answers 'at what rate?'. They agree on accept/reject for a standalone project (positive NPV means IRR exceeds the discount rate), but NPV is the more reliable tiebreaker when ranking competing projects.

What is a good IRR?

It depends on your hurdle rate - the minimum return you require, often your cost of capital. An IRR above your hurdle rate means the project is expected to add value; below it, the project destroys value. There is no universal 'good' number: a stable bond-like project might target single digits, while venture or real-estate deals often aim for 15-25% or more to compensate for risk.

Why does my IRR not match a simple average return?

IRR accounts for the timing of every cash flow using compounding, not just the total. Money received earlier is worth more, so a project that returns most of its cash early will have a higher IRR than one that returns the same total later. A simple average ignores this time value of money, which is why the two figures differ.

Can a set of cash flows have more than one IRR?

Yes. When cash flows change sign more than once (for example, an outflow, then inflows, then another large outflow), the NPV equation can have multiple roots, so there can be several mathematically valid IRRs. In those cases IRR is ambiguous and you should rely on NPV, or use a modified internal rate of return (MIRR) that assumes a single reinvestment rate.

What does it mean if no IRR can be found?

IRR only exists when the cash flows include at least one negative value and at least one positive value - money going out and money coming in. If every cash flow is positive (or every one is negative), there is no rate that makes NPV zero, so the calculator reports N/A. Make sure your initial investment is entered and that the inflows total more than the outflows.

Does IRR assume reinvestment of cash flows?

The standard IRR calculation implicitly assumes that interim cash flows are reinvested at the IRR itself, which can overstate the realized return when the IRR is high. The modified internal rate of return (MIRR) fixes this by letting you set a separate, usually lower, reinvestment rate. If your IRR looks unusually high, treat it as an upper bound and sanity-check it against NPV.

Should I use IRR to choose between two projects?

Be careful. IRR can rank projects differently from NPV when they differ in size or timing, because IRR is a rate and ignores scale - a small project can show a high IRR while creating little total value. When picking between mutually exclusive projects, compare their NPVs at your discount rate; use IRR as a supporting return metric, not the sole decision rule.

What discount rate should I enter for the NPV comparison?

Use your required rate of return - commonly your weighted average cost of capital, the return on a comparable investment, or a hurdle rate that reflects the project's risk. The discount rate does not affect the IRR itself (IRR is intrinsic to the cash flows), but it determines the NPV shown alongside it and tells you whether the IRR clears your bar.

What is the difference between IRR and MIRR?

The standard IRR assumes interim cash flows are reinvested at the IRR itself, which can overstate returns when the IRR is high. The modified internal rate of return (MIRR) uses two explicit rates instead: a finance rate for outflows and a separate, usually lower reinvestment rate for inflows. Because MIRR uses a more realistic reinvestment assumption, it is almost always lower than the IRR, and the gap grows as the IRR rises. If your IRR looks unusually high, the MIRR gives you a more conservative, defensible figure.

How do I calculate IRR in Excel or Google Sheets?

List your cash flows in a column starting with the negative initial investment in the first cell, then use =IRR(range) to get the rate. For cash flows on irregular calendar dates, use =XIRR(values, dates) instead, which discounts by the exact number of days. Both functions solve the same NPV-equals-zero equation this calculator solves; if a spreadsheet returns a #NUM! error, give the function a guess (for example =IRR(range, 0.1)) or check that your cash flows include at least one negative and one positive value.

Is a higher IRR always better?

Not necessarily. IRR is a rate and ignores the size of the investment, so a small project can show a higher IRR while a larger one creates far more total value. A high IRR can also be misleading when it relies on the reinvestment assumption or on a single uncertain terminal value. For mutually exclusive choices, compare net present value at your discount rate as the primary decision rule and use IRR as a supporting return metric.

💡 Good to know

IRR and NPV are two views of the same math

IRR is just the discount rate at which NPV crosses zero. If your project's IRR is above your discount rate, its NPV at that rate is positive; if it is below, the NPV is negative. The calculator shows both so you can see the link.

A very high IRR can be a mirage

The standard IRR assumes you can reinvest every interim payout at that same high rate, which is rarely true. If your IRR looks too good, compare it with the modified IRR (MIRR) or simply trust the NPV number instead.

Timing beats totals

Two projects can return the same total cash and have very different IRRs. Getting your money back sooner always raises the rate - so weigh when cash arrives, not just how much.

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