Internal Rate of Return (IRR) Calculator

What This Calculator Works Out

Two questions get asked about an investment. How much did it make, and how well did it make it? The first is arithmetic. The second has to account for when the money moved, and that is what the internal rate of return measures.

The page has two modes because cash flows come in two shapes. The fixed cash flow mode handles an account: a sum in, a regular withdrawal or deposit, a balance at the end. The irregular cash flow mode handles a project: an amount in, then whatever comes back each year, in any pattern including years where more money goes out.

The figures it opens on describe a modest holding: $25,000 invested, $150 withdrawn every quarter, ending at $38,000 after four years. That is an IRR of 13.206% a year. Cumulative withdrawals come to $2,400, total return to $15,400, and the gross return to 61.6% — which sounds far more impressive than 13.206% until you remember it took four years to earn.

What IRR Actually Is

The internal rate of return is the discount rate at which an investment's net present value comes out to exactly zero.

That definition is precise and initially unhelpful, so here is the same thing said differently. Money arriving in five years is worth less than money arriving today, and a discount rate is how much less. Pick a low discount rate and a profitable project looks very valuable; pick a high one and its future cash shrinks until the project looks worthless. Somewhere between the two is a rate where it is worth exactly what it cost. That rate is the IRR.

Read that way, IRR is the break-even rate. If the project's IRR is above what your money costs you, the project pays for itself and more. If it is below, you are funding it at a loss even though the raw numbers may look positive.

How It Is Calculated

The equation is the net present value formula with the answer fixed at zero:

Here is the honest complication: that equation cannot be rearranged for r. The rate sits inside an exponent at every single time period, and there is no algebraic manoeuvre that pulls it out. For anything beyond two periods, no closed-form solution exists — this is a mathematical fact, not a shortcoming of the tool.

So it is solved numerically. This page sweeps a wide band of rates, watches for every point where the net present value crosses from positive to negative or back, and then narrows each crossing by repeated halving until it is exact to far more decimal places than anyone needs. Sweeping rather than starting from a single guess matters, because as the section on limitations explains, some cash flow patterns have more than one answer, and a solver that stops at the first one it stumbles on will hide that from you.

The discounted cash flow table below the results shows the working: every flow, its discount factor at the solved rate, its present value, and the running total. That last column should finish on zero, and it does — that is the check that the answer is right.

Which Mode to Use

• Fixed cash flow — for an account or holding with a regular rhythm. A brokerage account you draw from monthly, a rental deposit, a savings pot you top up quarterly. You know the start, the end, and the size of the repeating flow. Set the recurring amount to $0 and it becomes a straight annualised return between two balances.
• Irregular cash flow — for a project. A machine bought for $40,000 that returns different amounts each year, a property with an uneven rental history and a sale at the end, a business investment needing another injection in year two. Enter one figure per year, negative when more money goes in.

Both modes solve the same equation. The difference is only how the cash flow series is assembled before it gets there.

One limitation to know: the irregular mode works in whole years. For flows at irregular dates, a spreadsheet's XIRR function handles arbitrary dates, and for sub-annual regular patterns the fixed mode already covers it at seven frequencies.

What Each Input Means

Fixed cash flow mode

• Initial investment — what went in at the start.
• Holding period — how long you held it, in years and months.
• Ending balance — what it was worth at the end, before any final withdrawal.
• Recurring cash flow — the repeating amount, and whether it leaves the account or goes into it.
• How often — from annually down to weekly. The rate is solved per period and then annualised.
• At the — whether the flow lands at the beginning or the end of each period. Over n periods there are n beginnings and n ends, so the count is the same either way; only the timing shifts, and with it the return.

Irregular cash flow mode

• Initial investment — the upfront cost, entered as a positive number. It is treated as money out.
• Year 1, 2, 3… — the net cash flow for each year. Positive is money coming back, negative is more money going in. Add years as you need them.

Reading the NPV Curve

The chart beside the schedule plots net present value against every discount rate in a band around the answer. It is worth understanding because it makes IRR visible rather than abstract.

The curve slopes downward: the more heavily you discount future money, the less a project is worth today. Where it crosses the zero line is the IRR — that is the definition, drawn. Everything to the left of the crossing is a discount rate at which the project is worth more than it cost; everything to the right is a rate at which it is not.

The shape carries information too. A curve that plunges steeply through zero belongs to a project whose value is highly sensitive to the discount rate, typically because its cash arrives late. A shallow crossing means the answer is robust — you could be wrong about your cost of capital by a couple of points and the conclusion would not change. And if the curve crosses zero more than once, you can see immediately that a single IRR figure is not telling the whole story.

Why Timing Beats Totals

This is the point of the whole metric, and it is easiest to see with two investments that look identical on paper.

Both cost $80,000 and both return $100,000 over five years. The first pays $30,000, then $25,000, $20,000, $15,000 and $10,000. The second pays exactly the same amounts in reverse: $10,000 first, rising to $30,000 in year five.

Gross return is 25% for both. Total profit is $20,000 for both. Any measure that ignores timing calls them equal. But the IRRs are 9.655% and 6.697% — nearly three percentage points apart, on cash flows that add up to the same number.

The reason is that money returned early is free again early. It can pay down debt, fund the next project, or simply sit earning something. Money locked up until year five does none of that. IRR prices the difference; gross return cannot see it.

What IRR Is Used For

• Capital budgeting. Ranking competing projects when there is not enough money for all of them.
• Hurdle rate tests. Comparing a project's IRR against the cost of the capital funding it. Above the hurdle, proceed; below it, do not.
• Private equity and venture capital. The standard headline measure for fund performance, precisely because capital is drawn and returned unevenly over years.
• Real estate. Combining rental income across a holding period with the sale proceeds at the end into one comparable figure.
• Personal investing. Working out what an account actually earned when you have been paying in or drawing down along the way, which a simple start-to-finish percentage gets wrong.
• Lease and finance comparisons. Reducing several payment structures to a single rate.

Where IRR Misleads

IRR is a good metric with well-known failure modes, and knowing them matters more than knowing the formula.

• It is blind to scale. A 60% IRR on $1,000 is a smaller amount of actual money than a 12% IRR on $2 million. IRR ranks percentages, not profits, so it will happily prefer the trivial project.
• It assumes reinvestment at the IRR itself. The arithmetic implicitly requires every interim cash flow to be reinvested at the same rate. For a project returning 30%, that is usually fantasy. MIRR exists specifically to let you set a realistic reinvestment rate.
• Multiple IRRs are real. When cash flows change direction more than once, the equation can have several valid solutions. The standard illustration — $4,000 out, $25,000 back, $25,000 out again — has net present value of zero at both 25% and 400%, and neither is more correct. This page counts the sign changes and warns you when the pattern permits it.
• No solution at all. If every flow points the same way, there is nothing to break even against and no IRR exists. The calculator says so rather than inventing a number.
• It says nothing about risk. Two projects with identical IRRs can carry wildly different odds of achieving them. IRR takes the forecast as given.

IRR vs. NPV vs. ROI

Three measures, three different questions.

• ROI asks what fraction of the money came back as profit. Simple and time-blind: the two five-year investments above both score 25%.
• NPV asks what a project is worth in today's dollars at a discount rate you choose. It answers in currency, so it respects scale, which makes it the better tool for choosing between projects of different sizes.
• IRR asks what rate the project earns. It answers in percent, which makes it easy to compare against a hurdle rate but blind to how much money is involved.

They come from the same equation, so they rarely disagree about whether a single project is worthwhile. They disagree about ranking, and when they do, NPV is the one to trust. Most analysts calculate both and treat a large IRR-versus-NPV divergence as a signal to look harder rather than as a tie to break.

What This Calculator Leaves Out

• Irregular dates. The irregular mode works in whole years. For flows on specific calendar dates, XIRR in a spreadsheet is the right tool.
• Tax. Every figure is pre-tax. Real after-tax returns depend on the account type and your own rates.
• Fees. Management fees, transaction costs and carried interest are not modeled unless you fold them into the cash flows yourself.
• MIRR. No separate reinvestment rate; the standard IRR assumption applies.
• Inflation. The result is a nominal rate. Subtract expected inflation for the real one, or see the Inflation Calculator for actual price data.
• Risk. Nothing here reflects the probability that the forecast cash flows actually arrive.

For a simpler growth projection with a known rate, the Investment Calculator is a better fit; to find the rate on a loan rather than an investment, see the Interest Rate Calculator; and for discounting a single future amount, the Present Value Calculator.

Frequently Asked Questions

What is the internal rate of return in plain terms?

It is the annual rate at which an investment exactly breaks even once you account for when the money moves. Discount every cash flow back to today at the IRR and the pluses and minuses cancel to zero. That makes it the return the project earns on the money while it is actually tied up, which is why two investments returning the same total can have very different IRRs.

How is IRR calculated?

By trial. The equation sets net present value to zero and asks for the discount rate, but the rate appears inside an exponent at every time period, so there is no way to isolate it algebraically. Calculators and spreadsheets test rates until the net present value lands on zero. This page scans a wide range, finds every point where the value crosses zero, then narrows each crossing to well beyond the precision you need.

What is a good IRR?

Only in comparison to something. IRR is judged against a hurdle rate — your cost of capital, or the return you could get elsewhere for similar risk. Above the hurdle the project adds value; below it, the money is better used elsewhere. A 12% IRR is excellent against a 6% hurdle and a poor result against 20%. There is no threshold that is good in isolation.

Why do two investments with the same total return have different IRRs?

Timing. Take $80,000 invested with $100,000 coming back over five years. Received front-loaded — $30,000 then $25,000, $20,000, $15,000, $10,000 — the IRR is 9.655%. Received in the reverse order it is 6.697%. The gross return is 25% in both cases, but early cash is free to be used again sooner, and IRR is the only one of the two measures that notices.

Can an investment have more than one IRR?

Yes, whenever the cash flows change direction more than once — money out, then in, then out again. The textbook case is $4,000 out, $25,000 back, then $25,000 out, which produces zero net present value at both 25% and 400%. Neither is more correct than the other. This page counts the sign changes and warns you when the pattern allows it, because a single IRR figure quietly stops meaning much at that point.

What is the difference between IRR and NPV?

They are the same equation read in opposite directions. NPV fixes a discount rate and tells you the value in today's money; IRR fixes the value at zero and tells you the rate. NPV answers how much a project is worth, IRR answers what rate it earns. When ranking projects of different sizes, NPV is usually the sounder guide, because a small project can post a spectacular IRR on a trivial amount of money.

What does the calculator assume about reinvesting the cash?

That every interim cash flow is reinvested at the IRR itself. That assumption is built into the arithmetic and it is often optimistic — a project returning 30% rarely has somewhere to put the proceeds at 30%. The modified internal rate of return, MIRR, exists to let you set a realistic reinvestment rate separately. Treat a very high IRR with that in mind.

Why does the fixed cash flow mode ask for a holding period and an ending balance?

Because that mode describes an account rather than a project: you put an amount in, you withdraw or add a set sum on a schedule, and at the end there is a balance. The calculator turns that into a cash flow series and solves it the same way. Set the recurring amount to $0 and you get a plain buy-and-hold annualised return between the two balances.

Results are pre-tax and assume the cash flows you enter occur as scheduled. Provided for general information only and not financial or investment advice.