IRR Calculator
Enter the investment as a negative first cash flow and the money you get back each period to find the internal rate of return.
Free, no sign-upRuns in your browserHow we calculate
Negative = money you pay, positive = money you receive.
Your required return or cost of capital.
- Total invested
- $10,000.00
- Total received
- $14,000.00
- Net gain (undiscounted)
- $4,000.00
- Payback period
- 2.41 periods
- NPV at 8%
- $1,776.66
| Discount rate | NPV |
|---|---|
| 0% | $4,000.00 |
| 5% | $2,540.76 |
| 10% | $1,307.29 |
| 15% | $255.61 |
| 20% | -$648.15 |
| 16.341% (IRR) | $0.00 |
How this was calculated
- IRR is the rate r that makes Σ CFₖ ÷ (1 + r)^k = 0.
- The calculator brackets the root, then bisects it until the NPV is within a rounding error of zero.
- Check: NPV at 16.341% = $0.00.
Educational calculation, not financial advice. IRR assumes every inflow is reinvested at the IRR itself.
How the IRR is calculated
The internal rate of return (IRR) is the yearly rate at which the present value of everything an investment pays back equals what you put in. In symbols, it is the rate r that solves CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … = 0. There is no direct formula once there are more than two cash flows, so this IRR calculator finds r numerically: it brackets the root and halves the interval until the net present value is zero to within a rounding error. Enter the investment as a negative first number and the money you get back in the following periods.
Worked example
Invest $100 now and receive $60 after one year and $60 after two. The IRR solves −100 + 60/(1+r) + 60/(1+r)² = 0, which gives r = 13.07%. Check it: 60 ÷ 1.1307 + 60 ÷ 1.1307² = 53.06 + 46.93 = $100. The default example in the tool (−10,000, then 3,000, 4,200 and 6,800) returns an IRR of about 17%, and the table beneath shows the NPV falling to zero exactly at that rate.
IRR vs ROI and NPV
A plain ROI ignores timing: $1,000 back after one year and after ten years look identical. IRR accounts for when each payment arrives. It pairs naturally with the NPV calculator: if the IRR is above your required return (your discount rate), the NPV at that rate is positive and the project clears the bar. Use IRR to compare projects of different length, but use NPV when projects differ a lot in size, because a small project can show a high IRR and still add little money.
When IRR misleads
Cash flows that change sign more than once, such as a project with a large cleanup cost at the end, can have several IRRs or none. IRR also assumes each payment is reinvested at the IRR itself, which is optimistic for returns of 30% or more. This tool uses equally spaced periods; if your payments are on irregular dates, the result is only an approximation. The result is per period, so with monthly cash flows multiply the effect accordingly: a 1% monthly IRR is about 12.7% a year when compounded. See the Securities and Exchange Commission’s Investor.gov glossary for the standard definition of internal rate of return.
Frequently asked questions
What is IRR?
The internal rate of return is the discount rate at which the net present value of all cash flows equals zero. It is the yearly rate of return an investment effectively earns, taking the timing of each payment into account.
How do you calculate IRR?
Solve CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … = 0 for r. With more than two cash flows there is no direct formula, so it is found by trial, as this calculator does. Investing $100 and getting $60 twice gives an IRR of 13.07%.
What is a good IRR?
One above your required return or cost of capital. For a personal investment that is often the 7–10% long-run stock market return or the interest rate on debt you could repay instead.
Why does my IRR show no result?
An IRR only exists when the cash flows include both money paid and money received. All-positive or all-negative flows have no IRR, and some unusual patterns with several sign changes have none or several.
What is the difference between IRR and ROI?
ROI is the total gain divided by the amount invested and ignores timing. IRR is a yearly rate that accounts for when each payment arrives, so $1,000 returned after one year has a higher IRR than $1,000 returned after ten.