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IRR calculator

Find the internal rate of return on a series of equally spaced cash flows, with the solving method named and every rate reported when the series has more than one.

Inputs
Currency
The outlay at the start, entered as a positive number. It is treated as money going out.
Cash flow each periodOne figure per period, equally spaced. Money coming in is positive and money going back out is negative. For flows on irregular dates, use the XIRR calculator instead.
Result
Internal rate of return, per period
16.28%
Total cash in
$180,000
Net cash flow
$60,000
Simple return, ignoring time
50%
Periods
4

Solved by bisection on the net present value equation, to a tolerance of 1e-9 in 20 iterations. IRR has no closed form, so every tool that reports it is iterating, whether or not it says so. The rate assumes each inflow is reinvested at the IRR itself, which is why a high figure on a short project overstates what you would really earn.

Key takeaways

  • IRR is the rate that makes the net present value of a cash flow series zero, and it has no closed-form solution.
  • Every IRR figure is produced by iteration; this one uses bisection to a tolerance of 1e-9 and shows the count.
  • A series that changes direction more than once can have several valid IRRs, and -4,000 then +25,000 then -25,000 has two: 25 percent and 400 percent.
  • Some series have no IRR at all, which is a property of the numbers rather than a calculator error.
  • IRR assumes cash thrown off is reinvested at the IRR itself, which flatters short high-return projects.

How the IRR calculator works

The internal rate of return is the discount rate at which a project's cash flows have a net present value of exactly zero. Enter the outlay and what the investment returns each period, and this solves for that rate, reports how it solved it, and tells you when the answer isn't unique.

Periods here are equal and evenly spaced. For flows on actual calendar dates, the XIRR calculator weights each one by how long it was invested.

The equation, and why there's no formula

Written out, IRR solves:

0 = -C0 + C1/(1+IRR) + C2/(1+IRR)^2 + ... + Cn/(1+IRR)^n

That's a polynomial in the rate. Polynomials above the fourth degree have no general algebraic solution, a result proved in the 1820s, so any project running more than four periods cannot be solved by rearranging. calculator.net says as much, that IRR can't be handled by simple algebraic manipulation for most real projects, and then doesn't say what it does instead.

Every IRR anywhere is produced by iteration. Corporate Finance Institute describes analysts trying different discount rates until net present value hits zero and points at Excel's Goal Seek. Omni cites Newton's Method through Wolfram. WallStreetPrep skips the question.

We use bisection: bracket the rate between -100% and 10,000%, halve the interval, keep the half where the sign flips, repeat to a tolerance of 1e-9. It's slower than Newton's method and it cannot diverge, which on a function that can bend sharply is the trade worth making. The tool prints its iteration count with every result.

An investment can have more than one IRR

This is the part the ranked calculators skip, and it isn't a corner case invented by textbooks.

The number of rates a series can satisfy is bounded by how many times its cash flows change direction, which is Descartes' rule of signs. Money out then in is one change and gives at most one rate. Money out, in, then out again is two changes and can give two.

Take -4,000, then +25,000, then -25,000. Both 25% and 400% make the net present value of that series exactly zero. Neither is more correct.

Worse, the series is negative at both ends of any sensible search range, so a solver that just bisects the whole interval finds no sign change and reports no solution at all. A solver that starts from a guess returns whichever root it happens to fall toward, which is why two spreadsheets can disagree on the same numbers and both be right.

This calculator scans the full range for every crossing and reports all of them. When it finds more than one, it says so, because a single number there would be a false answer to an ambiguous question.

Some series have no IRR at all. Try -1,000, then +3,000, then -2,500: nothing between -100% and 10,000% brings it to zero. That's a genuine property of the numbers, and the tool says so, where a blank would leave you guessing.

The assumption buried in every IRR

CFI states the flaw plainly, and it's the only ranked page that does: IRR assumes every positive cash flow is reinvested at the project's own rate rather than at the company's cost of capital.

Read that literally. A project reporting 40% assumes you have somewhere else paying 40% to park the proceeds as they arrive. Usually you don't. The effect is that IRR flatters short, high-return projects, because the shorter the project, the more of its result depends on an assumption about money it has already returned to you.

CFI adds a second limitation worth carrying: 30% tells you nothing about scale. Thirty percent of $10,000 and 30% of $1,000,000 are the same IRR and very different outcomes.

A worked case

A $120,000 outlay returning $30,000, $40,000, $50,000 and $60,000 over four years.

Total cash in$180,000
Net cash flow$60,000
Simple return, ignoring time50%
IRR16.28%

The 50% and the 16.28% describe the same four years. The first says how much came back, the second says at what rate, and the second is the only one you can compare against a bond yield or a cost of capital.

What this calculator does not do

It won't tell you whether to accept a project. A rate above your cost of capital is one input into that decision, alongside scale, risk, and what else the money could fund.

It doesn't compute MIRR. Omni discusses the modified version, which replaces the reinvestment assumption with a rate you nominate, and that's a different tool from this one.

It assumes equal spacing. Quarterly and annual flows in the same series will give a wrong answer here; put the actual dates into XIRR instead.

Results are arithmetic on your inputs, not financial advice. For decisions about your money, speak to a licensed financial adviser. To value the same flows at a rate you pick, the present value calculator does that, and the payback period calculator answers how long the capital stays exposed.

Frequently asked questions

What is the internal rate of return? IRR is the discount rate at which a project's cash flows have a net present value of exactly zero. Written out, it solves 0 = -C0 + C1/(1+IRR) + C2/(1+IRR)^2 + ... + Cn/(1+IRR)^n. Read plainly, it is the rate the project earns on the money while that money is still tied up in it.

What is the IRR formula and can it be solved directly? There is no closed form. The equation is a polynomial in the rate, and polynomials above the fourth degree have no general algebraic solution, so any project running more than four periods has to be solved numerically. Every calculator that returns an IRR is iterating, whether or not it tells you. This one uses bisection on the net present value equation to a tolerance of 1e-9, and reports how many iterations it took.

Can an investment have more than one IRR? Yes, and it is the metric's sharpest edge. The number of rates a series can have is bounded by how many times its cash flows change direction. Money out, then in, then out again gives two sign changes and can admit two rates. The textbook case is -4,000 followed by +25,000 and -25,000, which is solved by both 25 percent and 400 percent. This tool scans the whole range and reports every rate it finds, because a tool that returns just one of them is hiding the ambiguity.

Why does my spreadsheet give a different IRR from another tool? On a series with several valid rates, Excel returns whichever one its starting guess converges to, and a different guess gives a different answer. Neither is wrong and neither is complete. When more than one rate exists, the honest reading is that IRR does not settle the question, and net present value at a discount rate you choose does.

Can a project have no IRR at all? Yes. Some cash flow series have no rate that brings their net present value to zero, which happens with certain patterns of alternating flows. That is a real property of the numbers. The tool reports it plainly, since returning a figure there would mislead.

What is the difference between IRR and XIRR? Spacing. IRR assumes every cash flow arrives at the end of an equal period, so it suits an annual project schedule. XIRR takes the actual dates and weights each flow by how long it was invested, which is what a SIP or a portfolio with irregular top-ups needs. Use this page for equal periods and the XIRR calculator when the dates are uneven.

What is the reinvestment assumption and why does it matter? IRR implicitly assumes every cash the project throws off is reinvested at the IRR itself rather than at what you could realistically earn. A project showing 40 percent assumes you have somewhere else paying 40 percent to put the proceeds, which is usually not true. The effect is that IRR flatters short, high-return projects, which is why analysts read it alongside net present value.

What is the difference between IRR and ROI? ROI compares one amount in against one amount out and ignores when anything happened. IRR handles a whole schedule of flows and prices in the timing of each one. If money moved more than twice, ROI cannot describe it faithfully and IRR is the right measure.

Sources

Built and reviewed by DexTechLabs against the primary sources cited above. Last reviewed 2026-07-19. How we build and verify tools.

Mutual fund returns are market-linked and not guaranteed, so this is an estimate, not investment advice. Consult a SEBI-registered adviser before acting on it.