Quick answer
The internal rate of return is the discount rate r at which the present value of future cash flows equals the investment: −C₀ + Σ CFₜ ÷ (1 + r)ᵗ = 0. Investing $1,000 and receiving $300, $400, $500 and $600 over four years gives an IRR of 24.89%.
Enter the initial investment and the cash flows for each year. The calculator returns the IRR.
Related tools: Investment Calculator: Project investment growth from a rate of return you choose. Financial Calculator: Time-value-of-money solver for N, rate, present value, payment or future value. CAGR Calculator: Compound annual growth rate between two values.
How to use the IRR Calculator
- Enter initial investment ($) (above 0).
- Type cash flows (years 1, 2, 3 …), for example 300, 400, 500.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Initial investment | A number, in $ | > 0 |
| Cash flows (years 1, 2, 3 …) | Text, such as 300, 400, 500 | — |
Formula and method
Formula
Find r such that −C₀ + Σ CFₜ ÷ (1 + r)ᵗ = 0
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Solved by bisection. Cash flows with more than one sign change can have several IRRs; the lowest sign change found is reported.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Initial investment = 1000; Cash flows (years 1, 2, 3 …) = 300, 400, 500, 600.
| Result | Value |
|---|---|
| IRR | 24.8883% |
Example 2
Inputs: Initial investment = 5000; Cash flows (years 1, 2, 3 …) = 1500, 1500, 1500, 1500.
| Result | Value |
|---|---|
| IRR | 7.7138% |
Example 3
Inputs: Initial investment = 1000; Cash flows (years 1, 2, 3 …) = 400, 400, 100.
| Result | Value |
|---|---|
| IRR | -6.0764% |
The first line is the headline result (iRR). IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Checking the example
At 24.89%, the present values are 300 ÷ 1.2489 = 240.2, 400 ÷ 1.2489² = 256.4, 500 ÷ 1.2489³ = 256.7 and 600 ÷ 1.2489⁴ = 246.6, which add to 1,000. That is how IRR is defined.
Limitations
No IRR exists if the cash flows never repay the investment. Projects with changing signs can have multiple IRRs, and IRR assumes cash flows are reinvested at the same rate. NPV and IRR together give a fuller picture.
How the result changes with initial investment
Holding every other input at the first worked example, this table changes only initial investment. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Initial investment | IRR |
|---|---|
| 500 | 68.1659% |
| 1000 | 24.8883% |
| 2000 | -3.6933% |
| 4000 | -23.8477% |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Cash flows (years 1, 2, 3 …): left empty shows "Enter cash flows (years 1, 2, 3 …)." beside that field and no result.
- Initial investment: entering "0" shows "Initial investment must be greater than 0." beside that field and no result.
Choosing between the IRR Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [Financial Calculator](/finance/financial-calculator/) | solve for, periods per year and payments | Future value (FV) |
| [CAGR Calculator](/finance/cagr-calculator/) | beginning value, ending value and years | CAGR |
| [Present Value Calculator](/finance/present-value-calculator/) | future value, annual discount rate and years | Present value |
| [Mutual Fund Calculator](/finance/mutual-fund-calculator/) | initial investment, monthly contribution and expected annual return | Value after fees |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- No IRR exists if the cash flows never repay the investment
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for cash flows (years 1, 2, 3 …) and initial investment to confirm this.
Frequently asked questions
What is a good IRR?
One above your required return or cost of capital.
How is IRR different from ROI?
IRR accounts for timing.
Can it be negative?
Yes, if total inflows are less than the investment.
What does the IRR Calculator calculate?
Internal rate of return of an investment from its yearly cash flows. It returns IRR.
What formula does the IRR Calculator use?
Find r such that −C₀ + Σ CFₜ ÷ (1 + r)ᵗ = 0. Solved by bisection.
What do I need to enter in the iRR Calculator?
You enter Initial investment ($) and Cash flows (years 1, 2, 3 …).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. No IRR exists if the cash flows never repay the investment.
What is an example of a iRR result?
With initial investment 1000 and cash flows (years 1, 2, 3 …) 300, 400, 500, 600, the iRR is 24.8883%.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: No IRR exists if the cash flows never repay the investment.
Related calculators
- Investment Calculator — Project investment growth from a rate of return you choose.
- Financial Calculator — Time-value-of-money solver for N, rate, present value, payment or future value.
- CAGR Calculator — Compound annual growth rate between two values.
- Present Value Calculator — Today's value of a future amount at a given discount rate.
- Mutual Fund Calculator — Growth of a fund investment after its expense ratio.
- Net Present Value Calculator — NPV of an initial outlay and a series of yearly cash flows.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.