Internal Rate of Return (IRR) Calculator
Internal rate of return for a cash-flow series.
Details
what you put in at the start (Year 0)
Cash flow by year
Up to 40 years.
Internal rate of return (IRR)
9.76%
The discount rate at which NPV equals zero
Total invested
$10,000
Total returned
$12,200
This finds the internal rate of return on a series of cash flows: the annualised return a project earns.
It works with uneven cash flows and any number of periods.
What internal rate of return means
Internal rate of return is the discount rate at which a project's [NPV](/financial/npv-calculator) is exactly zero. Put more usefully: it is the annualised return the project earns on the money you have tied up in it.
That makes it easy to communicate. "This returns 15.2% a year" lands immediately, and comparing it against your cost of capital is a natural test: if the IRR beats the rate you could get elsewhere, the project adds value.
It has no algebraic solution. There is no formula to rearrange for IRR, so every tool finds it by iteration, trying rates until NPV lands on zero.
The IRR is where the NPV line crosses zero. Above that rate the project destroys value; below it, it creates value.
What to enter
- Initial investment
- Entered as a negative cash flow at time zero. IRR requires at least one negative and one positive flow.
- Cash flows
- What the project returns in each period. They can be uneven and any of them can be negative.
- Period length
- Usually years. The IRR comes out in the same unit, so monthly cash flows produce a monthly rate.
IRR against the alternatives
- IRR
- A percentage return. Intuitive and easy to communicate, but blind to project size.
- [NPV](/financial/npv-calculator)
- A dollar amount of value created. Less intuitive, and the right tiebreaker when the two disagree.
- MIRR
- Modified IRR. Assumes reinvestment at your actual cost of capital rather than at the IRR, which is more realistic.
- Payback period
- How long until you recover the outlay. Simple, and it ignores the time value of money entirely.
What this assumes
IRR implicitly assumes interim cash flows are reinvested at the IRR itself. For a high IRR that is usually unrealistic, which is what MIRR corrects.
Cash flows must change sign at least once. Multiple sign changes can produce more than one mathematically valid IRR.
How to calculate internal rate of return
There is no formula. You find the rate that makes NPV zero by trying rates and narrowing in.
- Cₜ
- Cash flow in period t, with the initial investment negative
- r
- The IRR, found by iteration rather than rearrangement
List the cash flows in order. Starting with the negative initial investment at time zero.
Calculate NPV at a trial rate. 10% is a reasonable starting guess for most projects.
Adjust and repeat. A positive NPV means the IRR is higher, so try a higher rate. Keep halving the interval until NPV is close enough to zero.
Compare against your cost of capital. An IRR above it means the project creates value. Below it means your money does better elsewhere.
See a worked example: narrowing in on the rate
- Investment
- $100,000 today
- Returns
- $30,000 a year for 5 years
At a 10% discount rate the NPV is +$13,724, so the IRR must be higher.
At 20% the NPV is −$10,282, so it is lower than that.
Narrowing between them gives 15.24%, where the NPV is zero.
So the project returns 15.24% a year. If your cost of capital is 10%, it is worth doing.
An IRR of 15.24%
Frequently asked questions
- What is a good IRR?
Anything above your cost of capital, which is the only benchmark that means anything. A 12% IRR is excellent against an 8% cost of capital and poor against 15%.
Different asset classes carry different expectations. Real estate deals are often underwritten in the low-to-mid teens; venture capital targets far higher because most investments return nothing.
- IRR or NPV: which should I use?
NPV when they disagree, because it measures value created in dollars and is comparable across projects of different sizes.
IRR is blind to size. A 50% return on $1,000 is $500; a 15% return on $1 million is $150,000. IRR ranks the first higher, and NPV correctly ranks the second.
- Why can there be more than one IRR?
Because the equation is a polynomial, and it can have as many roots as the cash flows have sign changes.
A project that goes negative, positive, then negative again (a large cleanup cost at the end, say) can have two mathematically valid IRRs. When that happens, use NPV instead.
- What is MIRR and when should I use it?
Modified IRR. Standard IRR assumes interim cash flows are reinvested at the IRR itself, which for a 30% project is usually fantasy.
MIRR assumes reinvestment at your actual cost of capital, which is realistic. It typically produces a lower and more honest figure, particularly for high-IRR projects.
- Why is there no formula for IRR?
Because it means solving a polynomial for its root, and polynomials above degree four have no general algebraic solution.
Every spreadsheet and calculator finds it numerically instead. That is also why a bad starting guess can occasionally make a tool fail to converge.
- Can IRR be negative?
Yes. A negative IRR means the project returns less than you put in, so you lose money in absolute terms, before even considering the time value.
If the cash flows never turn positive at all, there is no IRR to find. The tool will report no solution rather than a number.
Problems people actually run into
Ranking projects on IRR alone
A small project with a spectacular percentage can rank above a large one that creates far more value. IRR cannot see the size of the opportunity.
Use IRR as a screen and NPV as the decision. Where capital is limited, the goal is maximising total value created, not the highest percentage.
Believing the reinvestment assumption
A reported 30% IRR quietly assumes every interim cash flow is reinvested at 30%. If you are actually redepositing them at 5%, the realised return is much lower.
For projects with large interim distributions, MIRR is the more honest measure. The gap between the two is usually where the optimism lives.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026
