Internal Rate of Return Calculator
The internal rate of return (IRR) is the annual percentage return an investment earns over its life, defined as the discount rate that sets net present value to zero. It is a single number that summarises whether a project pays off: if the IRR clears your required rate of return, the investment is expected to add value, and if it falls short, the project does not earn its keep. This calculator takes an initial investment and up to five yearly cash flows, then solves for the rate that exactly repays the upfront cost in present-value terms. Because there is no algebraic formula for IRR with several cash flows, it is found numerically by bisection, narrowing the rate until net present value lands on zero. Enter your own outlay and inflows to compare projects, value a stream of returns, or sense-check a capital budgeting decision against a hurdle rate. The result is computed deterministically from the standard discounted cash flow definition, never estimated by guesswork, and the worked example below reconciles exactly to the calculator. The US Office of Management and Budget publishes the discounting method federal agencies use for benefit-cost analysis in Circular A-94, which underpins the approach used here.
The internal rate of return is the discount rate that makes net present value equal to zero. For 10,000 invested, then 4,000 a year for three years, the IRR is 9.70%. Accept a project when its IRR exceeds your required return.
Internal rate of return formula
0 = -C_0 + ( sum from t=1 to n of CF_t / (1 + r)^t )
C_0 = initial investment at time zero
CF_t = cash flow in year t
r = the internal rate of return (the unknown)
t = year number, n = number of years
The IRR is the value of r that makes the right-hand side equal zero. There is no algebraic solution for several cash flows, so the rate is found numerically. This calculator applies bisection over r from -0.9 to 10, evaluating where net present value changes sign and halving the interval roughly 200 times until it reaches a tolerance of 1e-7.
Worked example
A project costs 10,000 today and returns 4,000 in each of the next three years, with nothing in years 4 and 5. Because the inflows are level, the IRR is the rate where the annuity factor equals 10,000 / 4,000 = 2.5.
- Set up the break-even condition: 4,000 / (1 + r) + 4,000 / (1 + r)^2 + 4,000 / (1 + r)^3 = 10,000
- Divide both sides by 4,000: the annuity factor (1 - (1 + r)^-3) / r must equal 2.5
- Solve for r by bisection between -0.9 and 10
- The rate converges to r = 0.0970, or 9.70%
- Check: net present value at 9.70% is 0.00, confirming the IRR
The IRR is about 9.70%, so the project beats any required return below that figure. These are the calculator's default inputs, so the result above matches the widget exactly.
IRR decision rule at a glance
Compare the IRR with your required rate of return (the hurdle rate) to decide on a single project.
| Situation | Net present value | Decision |
|---|---|---|
| IRR above hurdle rate | Positive | Accept |
| IRR equals hurdle rate | Zero | Indifferent |
| IRR below hurdle rate | Negative | Reject |
Method and discount rate guidance: US Office of Management and Budget, Circular A-94.
Internal rate of return calculator: frequently asked questions
What is the internal rate of return (IRR)?
The internal rate of return is the single discount rate that makes a project's net present value equal to zero. Put another way, it is the annual percentage return at which the discounted future cash flows exactly repay the initial investment. A higher IRR means the project earns more per dollar invested, so IRR is often compared against a required rate of return to decide whether a project clears the hurdle.
How is IRR calculated?
There is no closed-form formula for IRR with multiple cash flows, so it is found numerically. This calculator uses bisection: it tries a range of discount rates, narrows the interval where the net present value changes sign, and converges on the rate that drives NPV to zero. Around 200 iterations bring the answer to a tolerance of 1e-7, which is well within rounding for any practical decision.
How do I use IRR to make a decision?
Accept a single project when its IRR is greater than your required rate of return or cost of capital, and reject it when the IRR is lower. When ranking mutually exclusive projects, IRR can disagree with net present value because of scale and timing differences, so most finance textbooks treat NPV as the primary rule and use IRR as a supporting check.
When does IRR break down?
IRR assumes one sign change in the cash flows. When a project switches from negative to positive and back to negative, the polynomial can have more than one root, giving multiple IRRs or none. In those cases the net present value rule, with a discount rate you choose, is more reliable. This calculator searches a single sign change between an outflow and later inflows.
What is the difference between IRR and NPV?
Net present value is a dollar amount of value created at a discount rate you select. IRR is the percentage rate that would make that net present value zero. NPV tells you how much value a project adds; IRR tells you the break-even return. They use the same discounted cash flow inputs, so they are two views of the same calculation.
Official sources
- Discounting and net present value method for benefit-cost analysis: US Office of Management and Budget, Circular A-94 (Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs). As at 24 June 2026.
- Investing and time-value-of-money basics: US Securities and Exchange Commission, Investor.gov. As at 24 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 24 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.