π― IRR Calculator
Internal rate of return from your cash flow series.
The IRR is a per-period rate. With yearly cash flows it is an annual rate.
Internal Rate of Return
Estimates for planning only, not financial advice.
How to Use This Calculator
List your cash flows in order, one per line, starting with the initial investment as a negative number. Outflows are negative, inflows are positive. The calculator solves for the rate that makes the net present value of the whole series equal zero, and shows each period's discounted contribution in a table so you can see the math.
Type or paste your cash flows into the box, one number per line. The first line is time zero, usually your upfront investment written as a negative number.
Choose what each line represents: a year, a quarter, or a month. The IRR it returns is the rate per that period, so monthly cash flows give a monthly IRR.
Read the IRR and the verification line: NPV at the reported IRR should be essentially zero, which proves the answer is correct.
Check the table of discounted cash flows. If your flows change sign more than once, read the multiple-IRR warning before making decisions on the number.
The IRR Equation
IRR is defined implicitly: it is whatever rate r makes the equation true. Newton-Raphson starts from a guess (10 percent) and repeatedly subtracts NPV divided by its slope, which converges in a handful of steps for well-behaved cash flows. When the slope is flat or the iteration wanders, the calculator switches to bisection: it finds two rates whose NPVs have opposite signs, then halves the interval about 200 times until the answer is pinned down. Bisection is slower but nearly bulletproof, which is why it is the safety net.
Worked Example
Invest $100 today, receive $60 in one year and $60 in two years. The equation is -100 + 60/(1+r) + 60/(1+r)^2 = 0. Try r = 13 percent: -100 + 53.10 + 46.99 = +0.09, slightly positive, so the true rate is a touch higher. At r = 13.07 percent: -100 + 53.06 + 46.93 = -0.01, essentially zero. The IRR is 13.07 percent per year. Compare that with the simple total return of 20 percent over two years: annualizing 20 percent over two years gives 9.54 percent, which understates the IRR because it ignores that half the profit arrived in year one and could be reinvested.
IRR vs NPV: Which to Trust
IRR and NPV usually agree: if IRR exceeds your required rate, NPV is positive. But IRR has quirks. It assumes interim cash flows are reinvested at the IRR itself, which flatters projects with very high IRRs. It cannot rank mutually exclusive projects of different sizes: a 50 percent IRR on $1,000 beats a 20 percent IRR on $1 million in IRR terms but not in dollars. And with multiple sign changes it can return several valid answers. The professional habit is to compute both, decide by NPV at your real required rate, and use IRR as the intuitive "how good is this" headline number.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is IRR?
The internal rate of return is the discount rate that makes the net present value of a series of cash flows exactly zero. In plain terms, it is the annualized growth rate your money actually earned across the whole project, accounting for when each dollar went in and out. If the IRR beats your required return, the project creates value.
How is IRR calculated?
There is no closed-form formula for IRR with more than two periods, so it is found numerically. This calculator first tries Newton-Raphson, which follows the slope of the NPV curve to the zero crossing very fast, and falls back to bisection, which halves a bracketing interval until it traps the answer. Both methods solve NPV(r) = 0 for the rate r.
When does an IRR not exist?
When the cash flows never change sign, there is no rate that zeroes the NPV. All-positive flows (pure profit, no investment) have no IRR, and neither do all-negative flows (pure cost, no return). The calculator detects this and says so instead of guessing. Unconventional cash flows that change sign more than once can have multiple IRRs; the calculator returns one of them and flags the ambiguity.
What is the difference between IRR and ROI?
ROI measures total profit over cost and ignores timing completely. IRR is time-aware: $1,000 profit in year 1 gives a far higher IRR than the same $1,000 in year 10, while ROI calls them equal. For multi-year projects with uneven cash flows, IRR is the honest measure; for a simple buy-and-sell, annualized ROI and IRR are effectively the same number.
What is a good IRR?
Compare it to your hurdle rate: the return you could earn elsewhere at similar risk. For a small business project, owners often want 15 to 25 percent; for real estate, 8 to 12 percent unleveraged is common; for a safe bond-like investment, anything above the bond yield works. An IRR below your cost of capital destroys value even if the project shows an accounting profit.
Why can there be more than one IRR?
Each time the cash flow stream changes sign, the NPV equation gains another possible root. A project that goes negative, positive, then negative again (like a mine with cleanup costs at the end) can have two IRRs, both mathematically valid. When that happens, NPV at your actual required rate is the more reliable decision tool, and this calculator warns you when it detects multiple sign changes.