Internal Rate of Return Calculator

What this calculator does

Find the yearly return an investment really earns, based on the money you put in and the money you get back. That return is the internal rate of return, or IRR. It's the one interest rate that the project's cash flows act like. Future money is worth less than money today, so each future amount gets marked down at that rate (this is called discounting). At the IRR, the marked-down amounts add up to exactly what you invested. In other words, the net present value (NPV), what the project is worth in today's money after its cost, is zero. That makes the IRR easy to compare with a target return, a loan rate or another investment.

Enter the starting investment and the cash flow for each later period. The calculator finds the IRR with a careful step-by-step search and shows the working. It turns quarterly or monthly results into yearly ones. It also draws the NPV profile, a chart showing where the NPV crosses zero. Sometimes cash flows switch between money in and money out more than once, and there's more than one IRR. Then the calculator reports them all, instead of quietly picking one. Add a reinvestment rate to get the modified IRR too.

Where it's used

Why this math matters outside the classroom:

• Project hurdle rates. A company accepts a project only if its IRR beats a 12% hurdle, after checking the cash flows change sign just once.
• Private investments. An investor compares a fund's IRR on its yearly capital calls and payouts with the return on a stock index fund.
• Comparing loans and leases. Finding the rate that equates a lease's payments with a purchase price reveals the lease's implied interest rate.
• Algebra by approximation. Students find the rate where −100 + 60 ÷ (1 + r) + 60 ÷ (1 + r)² = 0 by narrowing a table of values, landing near 13.07%.
• Real estate returns. A landlord computes the IRR of a purchase, five years of net rent and a final sale to compare with a savings account.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSA.REI.D.11. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

1. Enter the starting investment you pay today, as a positive number.
2. List the net cash flow for each later period, in order, separated by commas. Use a minus sign for any period where more money goes out than comes in.
3. Choose whether the periods are years, quarters or months. If you like, enter a reinvestment rate and a finance rate for the modified IRR.
4. Read the IRR and the steps. Then check the NPV profile table: the IRR is where the NPV switches from positive to negative.

What the inputs mean

Initial investment (paid today)

The cost you pay at the start (time 0). Enter 0 if the first cash flow in your list is the money you put in.

Cash flows, one per period

The net cash for each period, starting with the end of period 1. Every period needs a number, even if it's 0. That keeps the timing of later flows right.

Each period is a

The IRR is a rate per period. For quarterly or monthly cash flows, the calculator also turns it into a yearly rate, with compounding (growth on top of growth).

Reinvestment rate for MIRR (per period)

Optional. The return the project's incoming money can realistically earn once you receive it. The standard IRR quietly assumes it earns the IRR itself. That can make high-IRR projects look better than they are.

Finance rate for MIRR (per period)

Optional. The rate used to discount the money going out when working out the MIRR, such as your cost of borrowing. Leave it blank to use the reinvestment rate.

Formula and method

0 = −I + CF₁ ÷ (1 + IRR) + CF₂ ÷ (1 + IRR)² + … + CFₙ ÷ (1 + IRR)^n
annual IRR = (1 + IRR per period)^p − 1
MIRR = (FV of inflows at the reinvestment rate ÷ PV of outflows at the finance rate)^(1/n) − 1

I is the starting investment, and CFₖ is the cash flow at the end of period k. The letter n is the number of periods, and p is the number of periods in a year. FV means future value, what money grows to later. PV means present value, what it's worth today. MIRR is the modified IRR. Once there are more than a few periods, there's no formula that solves for the IRR directly. So it has to be found by searching.

First, the calculator rewrites the NPV using x = 1 ÷ (1 + r), where r is a trial rate. That turns it into a polynomial, a sum of powers of x. Then it checks a wide range of rates, from −99.99% to 1,000,000% per period. It looks for every place the NPV switches sign. It narrows each one with Brent's method, a root-finder that mixes safe halving with faster guessing. The answer is accurate far beyond the decimals shown.

The number of IRRs can't be more than the number of times the cash flows switch sign. This is known as Descartes' rule of signs. Ordinary projects, with money going out first and coming in after, switch sign once and have one IRR. A project with a large cost at the end, such as a cleanup, can have two. Then the IRR isn't a reliable way to rank projects.

Worked example

A project costs $10,000 today. It returns $3,000, $4,200 and $6,800 at the end of the next three years.

1. The flows switch sign once (one outflow, then inflows), so there is at most one IRR.
2. At 15% the NPV is $255.61, and at 20% it is −$648.15. So the IRR lies between them.
3. Narrowing the search gives r ≈ 16.3406%, where $3,000 ÷ 1.163406 + $4,200 ÷ 1.163406² + $6,800 ÷ 1.163406³ − $10,000 = $0.00.
4. Modified IRR with a 10% reinvestment rate: the inflows grow to $3,000 × 1.1² + $4,200 × 1.1 + $6,800 = $15,050 by year 3. So MIRR = (15,050 ÷ 10,000)^(1/3) − 1 ≈ 14.60%.

Result: The IRR is about 16.34% a year. With the incoming money reinvested at 10%, the modified IRR is about 14.60%.

Understanding the result

If the IRR is above the return you require, the project's NPV at that required return is positive. So, taken on its own, it's worth doing. In the example, a 16.34% IRR clears a 10% target easily. That matches the positive NPV of $1,307.29 at 10%.

The IRR assumes each cash flow you receive can be reinvested at the IRR itself. When that's unrealistic, the MIRR is usually closer to the return you'll really get, because it uses a reinvestment rate you choose. In the example, it's 14.60% rather than 16.34%.

When there are several IRRs, none of them is 'the' return. Judge the project by its NPV at your required return instead. Or use the MIRR, which always has a single value.

Assumptions and limitations

• Cash flows arrive at the end of each period, equally spaced. The starting investment is paid at the start.
• IRRs are searched between −99.99% and 1,000,000% per period.
• Cash flows are entered after whatever taxes and costs you want to count.
• In a rare case, the NPV only touches zero without crossing it (a repeated root). That IRR may not be reported.
• IRR doesn't show how big a project is. A small project can have a higher IRR but create less value than a large one. Compare NPVs for that.
• Cash flows on specific, uneven dates aren't supported. Every period must be the same length.

Frequently asked questions

How this calculator is checked

Method: IRR as the root of the NPV equation with end-of-period flows, found by a logarithmic sign-change scan and Brent's method; MIRR from the terminal value of inflows and the present value of outflows. Tested against Microsoft's documented IRR and MIRR examples and closed-form cases. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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