IRR (Internal Rate of Return) is the discount rate at which the net present value of a series of cash flows equals zero. It represents the annualized rate of return an investment is expected to generate.

Why can't IRR be solved with a simple formula?

With more than two cash flows, the equation for IRR has no closed-form algebraic solution, so it must be found numerically — typically by testing rates until the net present value is as close to zero as possible.

IRR Calculator — Internal Rate of Return

How IRR is calculated

IRR is the discount rate r that makes the net present value (NPV) of the full cash flow series — the initial investment as a negative outflow at time zero, plus every future cash flow — equal exactly zero.

0 = −investment + Σ CF_t ÷ (1+r)^t for t = 1 to n

Unlike CAGR, there's no algebraic shortcut for this with more than two cash flows — this calculator finds it numerically, testing rates between -99% and 1000% until the NPV lands as close to zero as possible.

How IRR differs from CAGR

CAGR only needs a starting and ending value. IRR handles any sequence of cash flows in between — irregular contributions, distributions, or returns at different points in time — which makes it the standard metric for evaluating real investments, business projects, and private equity deals where money moves in and out at multiple points.

Common uses

Project evaluation: comparing the IRR of different capital projects against a required rate of return.
Real estate: factoring in purchase price, annual net cash flow, and eventual sale proceeds as the final cash flow.
Private equity and venture: evaluating a fund or deal's return across an irregular series of capital calls and distributions.

Frequently asked questions

What if the calculator says no solution was found?

This usually means the cash flows don't have a clear single sign change — for example, all cash flows are positive (no real investment), or there are multiple sign changes that produce more than one mathematically valid IRR. Double-check that the initial investment is entered as a positive number and that your future cash flows make sense as a sequence.

Should I include the sale or exit value as a cash flow?

Yes — if the investment ends with a lump sum (selling a property, exiting a fund), add that amount to the final period's cash flow, combined with any regular cash flow for that period.