IRR Calculator
What is an Internal Rate of Return (IRR) calculation?
This IRR calculator calculates an annualized rate-of-return plus profit (loss).
- Supports dated cash flows
- Easy bulk data entry
- Save entries to a file for later recall
- Know your rate of return across multiple accounts and investments
Answers the question: "How am I doing?"
The Internal Rate of Return (IRR) is the annualized rate of return on an investment. It is calculated from the amounts and dates of the cash flows. It does not require an externally specified interest rate. For this reason, it is called “internal.” This calculator uses the Newton–Raphson method to compute the IRR.
An Internal Rate of Return calculator (IRR) calculates the investment outcome. The results let you compare two or more investment options on a consistent basis.
This calculator determines the IRR for a complex series of cash flows. It also reports the total invested amount, the total returned amount, and the profit (or loss). The calculator supports both irregular time periods and exact date data entry.
The frequency option defines regular cash flows, such as daily, monthly, or quarterly payments. There are 11 frequency choices.
Review the usage tips below (click to scroll). …
The Calculator-Calculate the Internal-Rate-of-Return for an Irregular Cash Flow
Information
- Jan. 28, 2025: You can now use copy/paste (Ctrl-C/Ctrl-V [Cmd-C on a Mac]) to copy and paste a value from one cell to another cell.
Why is the IRR useful?
The Internal Rate of Return (IRR) converts uneven project cash flows into a single annualized rate of return. Investors can compare opportunities on a comparable basis. Because IRR reflects both the amounts and the timing of cash flows, it standardizes results across investments that have different patterns of outlays and receipts.
For example, consider two rental properties for sale. The asking prices are approximately the same, and the projected rents are approximately the same. One property requires a higher initial renovation cost. The other has higher property taxes. How can an investor determine which purchase is the better investment?
An investor can use an IRR calculator to make this determination.
Caution: Do not compare internal rates of return calculated with different calculators.
Why is this important?
Two different calculators may compute results slightly differently, and neither is necessarily incorrect. (For example, Microsoft Excel includes two IRR functions that may return different results for the same cash flows.) Users do not need to focus on this point, but it is important to be aware of it when interpreting results.
For the record, this calculator determines the IRR using Newton–Raphson method and by counting days (some calculators instead count periods).
To try a calculator that applies a different IRR algorithm, use this site’s Annual Percentage Rate (APR) calculator. The APR calculator follows the method specified in the Truth-in-Lending Act for calculating APR, which is a form of IRR.
Calculator usage and tips
- Zero amounts do not affect the IRR. For example, if the frequency is “Monthly,” and there are only four cash flows in a year, leave the remaining eight at 0. The same applies to 0 amounts after you enter the final liquidation value.
- Enter the investment’s current or final value as the last cash flow. If you are calculating the IRR for a stock or mutual fund and you still own the investment, enter the investment’s current value as the last amount.
- You do not need to enter cash flows in date order. The calculator will sort them before calculating the result. This feature is convenient if you realize that you missed a cash flow. In that case, enter the amount in any available cell, change the date for that cell, and then click
Calcto sort. - If you mistakenly duplicate a cash flow, set one of the duplicates to “0.”
- Changing
First Cash Flow Datewill reset the dates without clearing the values you have entered. - Depending on the order in which you use
First Cash Flow Date,Remove 0’s, andAdd Series, theFirst Cash Flow Datemay not be the first date in the input area. This is not an error. ChangingFirst Cash Flow Dateinitializes a series beginning on the selected date. However, the user can change the date, or the date can be removed withRemove 0’sif the value for the start date is 0. Finally, a user can insert a series with a date that occurs beforeFirst Cash Flow Date. - Calendar Tip: When using the calendar, click the month at the top to list months. If needed, click the year at the top to list years. Click to select a year, then select a month, and then select a day. You can also scroll through the months and days. Or, click
Todayto select the current date. - If you prefer not to use the calendar, single click on a date or use the Tab key (or Shift+Tab) to select a date. Then type eight digits only—there is no need to type the separators. Because the date is already selected, you do not need to clear the prior date before typing. For example, if your selected date format is
mm/dd/yyyy, then for August 1, 2025, type08012025. - Important reminder: You do not need to enter the cash flows in date order. The calculator will sort them once you click the
Calcbutton.
An important reminder about IRR calculators
Different IRR calculators may use different algorithms to determine the rate of return. (There is no single formula for calculating IRR.) Do not compare the results from one IRR calculator for one investment with the results from a different calculator for another investment. Always use the same calculator when comparing multiple investments.
Internal Rate of Return—IRR Equations
Fig. 2—Step-by-step solution of the IRR equation.
Variables: PMT0 = −50,000; PMT1 = −10,000; PMT2 = −12,000; PMT3 = 90,000; n = 3; f = 1.
Variable Definitions
- r
- Periodic rate of return per period. For example, per year when cash flows are annual.
- IRR
- Nominal annualized rate of return, computed as
IRR = r × f. - f
- Frequency (the number of periods per year). For annual spacing,
f = 1. - PMT
- Cash flow at period index
t. By convention, outflows are negative and inflows are positive. Values may differ across periods. - n
- Total number of periods after
t = 0. The summation fromt = 0tot = nincludes both the initial cash flow att = 0and the final cash flow att = n. - t
- Period index. An integer with
t = 0, 1, …, n, measured in equal time steps. (The calculator does not require cash flows to be equally spaced.)
- How do you calculate IRR?
To calculate the Internal Rate of Return (IRR), solve for the interest rate that makes the Net Present Value (NPV) of a series of cash flows equal to zero. Because the IRR equation is nonlinear, it is usually solved using an iterative method such as Newton–Raphson.
Detailed Explanation
The IRR equation is nonlinear and cannot be solved algebraically. To find the rate r that makes NPV equal to zero, treat the problem as a root-finding problem. This requires solving the following equation:
We want r such that f(r) = 0. The Newton–Raphson method is applied for this purpose. It begins with an initial estimate and refines that estimate using both the value and the slope (derivative) of the function at that point.
The slope is the derivative of f(r), denoted f’(r), which shows how sensitive the NPV is to changes in r. It is computed as:
The Newton–Raphson update formula is:
Each iteration produces a value that is closer to the IRR. This process is illustrated in Fig. 2, which shows the calculation using sample cash flows.
Calculation Steps Explained—Fig. 2.
- What is the IRR for the cash flows −50,000 (investment), −10,000, −12,000, +90,000 (returned), each spaced one year apart?
Solve for the periodic IRR by setting the Net Present Value (NPV) to zero, defining
f(r)as the sum of discounted cash flows andf’(r)as its derivative, and then applying Newton–Raphson updates (Equation (6)) untilf(r)converges to zero.- Define the NPV function
f(r)from Equation (2):f(r) = −50,000 − 10,000 ÷ (1 + r)^1 − 12,000 ÷ (1 + r)^2 + 90,000 ÷ (1 + r)^3 - Apply the general derivative rule (Equation (5)) to compute
f’(r):f’(r) = 10,000 ÷ (1 + r)^2 + 24,000 ÷ (1 + r)^3 − 270,000 ÷ (1 + r)^4(Each term follows−t × PMT_t ÷ (1 + r)^(t+1).) - Choose an initial guess for the periodic rate:
r₀ = 0.10. - Compute discount factors at
r₀(first iteration shown in full):(1 + r₀) = 1.10 (1 + r₀)^−1 = 1 ÷ 1.10 ≈ 0.90909091 (1 + r₀)^−2 = 1 ÷ (1.10)^2 ≈ 0.82644628 (1 + r₀)^−3 = 1 ÷ (1.10)^3 ≈ 0.75131480 (1 + r₀)^−4 = 1 ÷ (1.10)^4 ≈ 0.68301346 - Evaluate
f(r₀)using Equation (2):f(r₀) = −50,000 + [−10,000 × 0.90909091] + [−12,000 × 0.82644628] + [90,000 × 0.75131480] ≈ −50,000 − 9,090.90910 − 9,917.35536 + 67,618.33200 ≈ −1,389.93238167Result:
f(r₀) ≈ −1,389.93238167 - Evaluate
f’(r₀)using Equation (5) (term by term):- t = 1, PMT₁ = −10,000:
−1 × (−10,000) ÷ (1 + r₀)^2 = +10,000 × (1 + r₀)^−2 ≈ 10,000 × 0.82644628 - t = 2, PMT₂ = −12,000:
−2 × (−12,000) ÷ (1 + r₀)^3 = +24,000 × (1 + r₀)^−3 ≈ 24,000 × 0.75131480 - t = 3, PMT₃ = +90,000:
−3 × (+90,000) ÷ (1 + r₀)^4 = −270,000 × (1 + r₀)^−4 ≈ −270,000 × 0.68301346
Sum: 10,000×0.82644628 + 24,000×0.75131480 − 270,000×0.68301346 ≈ −158,117.61491701Result:
f’(r₀) ≈ −158,117.61491701 - t = 1, PMT₁ = −10,000:
- Apply the Newton–Raphson update (Equation (6)):
r₁ = r₀ − f(r₀) ÷ f’(r₀) = 0.10 − (−1,389.93238167) ÷ (−158,117.61491701) = 0.10 − 0.00879049676 ≈ 0.09120950 - Discount factors at
r₁(results only):(1 + r₁)^−1 ≈ 0.91641431(1 + r₁)^−2 ≈ 0.83981518(1 + r₁)^−3 ≈ 0.76961865(1 + r₁)^−4 ≈ 0.70528954 - Evaluate at
r₁(results only):f(r₁) ≈ 23.75294757f’(r₁) ≈ −163,559.17595169 - Update (results only):
r₂ = r₁ − f(r₁) ÷ f’(r₁) ≈ 0.09135473 - Discount factors at
r₂(results only):(1 + r₂)^−1 ≈ 0.91629236(1 + r₂)^−2 ≈ 0.83959169(1 + r₂)^−3 ≈ 0.76931145(1 + r₂)^−4 ≈ 0.70491420 - Evaluate at
r₂(results only):f(r₂) ≈ 0.00666170f’(r₂) ≈ −163,467.44351228 - Update (results only):
r₃ = r₂ − f(r₂) ÷ f’(r₂) ≈ 0.09135477 - Discount factors at
r₃(results only):(1 + r₃)^−1 ≈ 0.91629233(1 + r₃)^−2 ≈ 0.83959163(1 + r₃)^−3 ≈ 0.76931136(1 + r₃)^−4 ≈ 0.70491410 - Final convergence (results only):
f(r₃) ≈ 0.00000000f’(r₃) ≈ −163,467.41777956r ≈ r₃ − f(r₃) ÷ f’(r₃) ≈ 0.09135477 - Annualize using frequency
f = 1:IRR = r × f ≈ 0.09135477IRR ≈ 9.135477%
Thus, the periodic IRR is
r ≈ 0.09135477, and with annual spacing (f = 1) the internal rate of return isR ≈ 9.135477%.- Define the NPV function
Notes:
- First iteration shown in full: Discount factors, function values, the derivative, and the update are expanded with explicit arithmetic. Later iterations show results only; they follow the same structure.
f(rₖ)vs.f’(rₖ):f(rₖ)is the NPV at stepk.f’(rₖ)is the slope (derivative) of the NPV with respect torat that step and appears in the denominator of the Newton–Raphson update (Equation (6)).- Stopping criterion: Iteration stops when
|f(rₖ)|is sufficiently close to zero so another update would not materially changer.
Final Answer
The final answer (IRR) is approximately 9.135%.
Validate the calculator. Three-year internal rate of return calculation.
| Initial Investment: | −50,000.00 |
|---|---|
| Initial Investment Date: | |
| First Cash Flow Date: | |
| Cash Flow Frequency: | Annually |
| Discount Rate (optional): | 0.0% |
| No. | Date | Description | Amount |
|---|---|---|---|
| 1 | Additional investment | −10,000.00 | |
| 2 | Additional investment | −12,000.00 | |
| 3 | Investment return | 90,000.00 | |
| If any period includes February 29 (leap year), the result may differ slightly. | |||
Calculated result:
| Internal Rate of Return (IRR): | =9.135% |
|---|
Notes:
- This example uses the same calculation shown in Fig. 2.
- The calculator computes an Extended Internal Rate of Return (equivalent to a spreadsheet’s
XIRRfunction). Extended IRR offers greater flexibility and accuracy because cash flow entries use actual dates. A one-day difference will result in a slightly different (X)IRR.
IRR Calculator Help
The Internal Rate of Return (IRR) is the annualized rate of return on an investment, expressed as a percentage.
An investment can include a series of cash flows. There may be more than one investment (outflow) and more than one withdrawal or return (inflow). However, there must be at least one investment (outflow) and at least one return (inflow). Cash flows may occur on any date and for any amount.
It is essential to use the correct sign (positive or negative) for each cash flow. How do you determine the correct sign?
Consider this rule: When you first invest, you make a payment or transfer funds. A payment decreases your account balance. Therefore, enter all investment cash flows, including the “Initial Investment,” as negative values.
When you receive money from the investment, you deposit it into your account. A deposit increases your account balance. Therefore, enter all investment returns, including the final liquidation value of your investment, as positive values.
The scheduled dates update each time you change the Cash Flow Frequency. The new dates are calculated based on the First Cash Flow Date. However, the Cash Flow Frequency setting does not by itself affect the IRR result. The calculator uses the Cash Flow Frequency only to create dates that match your expected investment cash flows. For example, if you generally make additional investments or withdrawals twice per year, set Cash Flow Frequency to Semiannually.
cheryl says:
I am looking to calculate the IRR for an investment that had an initial investment contribution and several more subsequent investment contributions. There is a return rate set of 7% and there have been distributions made approx. quarterly. This has spanned approximately the last 6-7 years. Since only a portion of each distribution amount is a return of capital, not all of the original investment amount has been returned yet. What would be the best way to calculate the IRR for the partner considering their total investment and what distributions they have received over time? Is there an online calculator that would be helpful since there are multiple tranches?
Karl says:
This page’s IRR calculator is the correct calculator to use. Did you try it and have a problem?
To calculate the IRR, you’ll enter all the investment amounts as of the dates made. Make sure they are negative values.
Enter the withdrawals as positive values.
Then, for today’s date, enter the current value of the investment as a positive number (that is the value of the investment if you were going to withdrawal the remaining amount today).
The resulting IRR will be the IRR through today.
Joe says:
I used your IRR calculator for a home development project, it worked great with money going into the project at different times and cash flo being earned with the sale of each house, is there a calculator that will do this and show you your biggest drawdown or what your peak capital is at any time?
Karl says:
Hi Joe, yes there is. This financial calculator should do what you need. To see the IRR click on "settings" and then "analytics" to turn the IRR option on. This calculator will create a more detailed, printable schedule.
Scroll down the page for the tutorials.
Xander says:
Why do i get different IRR’s when i have a one time investment vs when i make multiple investments over say 5 years? Example, say i invest $1M today vs investing $200k over 5 years?
Karl says:
The reason is due to what is known as the time value of money. The IRR is the rate-of-return, with "rate" being the operative word. It is the return annualized or over a year.
Let’s make the example even simpler. Would you rather invest a million today and get back 1.1 million in six months or in 12 months? Of course, you would rather get it back in 6 months. In both cases the gross returned is 10%, but the rate-of-return will be higher for the 6 month term.
In your example, if the investment’s value is the same after 5 years, it’s better to invest the money in $200k increments, because a) you have less at risk in each of the preceding years; and b) if you have the funds, the money could be invested in other investments. The IRR result reflects these facts.
Gerald GIOVANELLI says:
I have investments that pay dividends monthly based on the number of units I own which change every month because I purchase (DRIP) additional units with my dividends. I believe your IRR calculator is. the answer.
Please confirm or make a suggestion before I purchase.
Thank you for your answer
Karl says:
First, there is nothing that you have to purchase. The use of this IRR calculator is free.
The IRR calculator will calculate an annualized rate of return for you. If that’s your goal, then this is the calculator. Enter the amount(s) you invest (-) on the day(s) you make the investment, and enter the withdrawals (+) from the investment on the days you make the withdrawal. The final value (+) you enter is the value of the investment as of the final date.
Jaycee says:
What does “wave Browser” have to do with your IRR Calculator which I would like to purchase?
Karl says:
Where do you see "wave Browser?" I don’t know what that’s referring to. Perhaps you are looking at an ad on the page?
And by the way, the IRR calculator is free. There is no need to purchase anything.
Dawn Jones says:
I am trying to provide a rate of return for a quarterly investments report. We periodically make deposits and withdrawals. Is this the calculator I should use? If so, do I also enter the interest earned as a cash flow?
Karl says:
Yes, you would use the IRR calculator. No, the interest rate is not a cash flow. The annualized rate of return (IRR) is calculated from the actual cash flows paid out or received. If you check out this page, there are a couple of examples. After reviewing them, if you have any other questions, just ask.
Nate says:
Can this calculator be used with a plugin or with HTML on a website we’ve built for a client?
Karl says:
No. I offer 7 WordPress plugins here.
Jack Cassidy says:
I have a couple of questions. 1) I use a very old version of this IRR product that I beleive I purchased for $5 and loaded onto a Windows friendly computer that I now keep only for purposes of running that program. I obviously believe it is an indispensible tool and I have looked high and low for one that is as good without success. In my earlier version of this program there is a column on the spread sheet that allows for me to enter comments that do not factor into the calculation i.e., “sold 7 Febraury 18, 50 strikes for $1.40.” I can’t see where this online version of the product allows for the input of commentary or notes. What am I missing. 2) I love the old program I purchased a million years ago. Is it possible to transfer the program and data files from my old computer to a new Windows friendly device? As I vaguely recall, when I purchased the Windows friendly computer I now run IRR on (ten years ago maybe). I simply paid another $5 to PGS to get a new program disk. Thanks for your help. I’ve used your tool weekly for many, many years and it is simply the best. I don’t know how I could acccurately judge the return on my investmetns without it.
Karl says:
Currently, the online version does not allow users to make a comment on a cash flow (as you have discovered). I have plans to add that feature, but I’m not sure when it will happen.
I had forgotten that the calculator was sold separately for a short time in the past. That is no longer the case.
To get a copy of the calculator, that will run on the latest version of Windows, you can purchase SolveIT!. SolveIT! has over 50 calculators it is available for a one-time fee of $69.95.
Jack says:
Thanks so much. I bought the package you suggested and the IRR calculator is perfect (it has my needed description column). I loaded it on the cheapest Windows friendly computer I could find ($200) and it runs much better than it did on my ten year old desk top which will soon be headed to the Goodwill. I don’t think I would ever have found a suitable program replacement for my old version of IRR without your help. I’d buy you a beer if I could. Thanks again.
Karl says:
Thank you for letting me know. And I think you just did buy me SEVERAL beers. 🙂
steve says:
I have made made different investment amounts on different dates over the years in a mutual fund. I would like to calculate the average annual rate of return on my investment from the start and not sure how to do it with your financial calculators. i have dates and amounts of each deposit into the mutual fund and the ending value of the account. i assumed i would enter deposits amounts with respective dates then enter withdraw of total account value on the current date amount (account value) with interest rate to be the calculated factor. I started the investments back in 2001. can you help with any suggestions?
Karl says:
I think you have the right calculator for what you want to do.
Do you have any specific questions? Have you tried the calculator with a few investments and you are having problems understanding the results?