How to Calculate IRR: The Formula, a Worked Example & IRR vs ROI

What Is IRR?

IRR (internal rate of return) is the annualized discount rate that makes the net present value of a series of cash flows equal to zero. In other words: it is the rate of return a project actually earns per year, taking into account when each dollar comes in or goes out.

The IRR is the rate r that solves:

0 = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … + CFₙ/(1+r)ⁿ

where CF₀ is usually negative (your initial outlay) and later cash flows are the returns. If you can set up that equation, you can describe the IRR — what makes it "internal" is that r is found from the cash flows themselves, not imposed from a market rate.

Worked example: a five-year project

You invest $100,000 today and receive $30,000 at the end of each of the next five years.

• CF₀ = −$100,000
• CF₁ … CF₅ = +$30,000 each year

Try a rate of 15%: 30,000 × (1 − 1.15⁻⁵)/0.15 − 100,000 = +$565. The NPV is positive, so 15% is too low. Try 16%: the same calculation gives −$1,771. The NPV is now negative, so the IRR lies between 15% and 16%. Refining (or letting a calculator do it) gives:

IRR ≈ 15.24%

Check: at 15.24%, the present value of the five $30,000 inflows is exactly $100,000 — the project breaks even at that rate, which is precisely what IRR means.

How is IRR actually calculated?

Unlike ROI, the IRR has no simple algebraic formula once there are more than two cash flows. In practice it is found numerically:

1. Bracket it — pick two trial rates whose NPVs have opposite signs (15% gave +$565, 16% gave −$1,771).
2. Narrow it — test rates between the bracket until the NPV is near zero.
3. Refine it — use linear interpolation or Newton's method for the exact value.

Spreadsheets (IRR and XIRR functions) and calculators automate all three steps. Our IRR Calculator takes your cash-flow list and returns the IRR, plus the NPV at any rate you choose for comparison.

IRR vs ROI

For the same five-year project: total inflows are $150,000, so ROI = (150,000 − 100,000) ÷ 100,000 = 50% over the whole period. That single number hides the fact that the money comes back in installments. The IRR of 15.24% tells you the annual pace — and it is higher than the CAGR of 8.45% you would get if the entire $50,000 profit arrived only at year 5, because the installments arrive earlier and can be reinvested sooner. See our ROI guide for the other side of this comparison, and the CAGR Calculator for the lump-sum version.

IRR Caveats

• Reinvestment assumption — IRR assumes intermediate cash flows are reinvested at the IRR itself, which can overstate realistic returns for high-IRR projects.
• Multiple IRRs — if cash flows change sign more than once (for example, a large cost at the end of a project), the equation can have two or more solutions. A single "the IRR" no longer exists.
• Scale blindness — a 40% IRR on $100 and a 40% IRR on $1,000,000 are the same percentage but very different in dollars. Compare the NPV or absolute profit as a second check.
• Use alongside, not instead of — the ROI Calculator gives the total return in one number; the IRR gives the annual pace. Both together tell the full story.

Calculating IRR Fast

Enter your cash flows — the initial investment followed by yearly returns, with negatives for outflows — into the IRR Calculator. It returns the IRR instantly, and you can sweep through discount rates to see the NPV curve. Everything runs in your browser; nothing is sent to a server.