IRR Calculator
Calculate internal rate of return from fixed or irregular cash flows.
Estimate an effective annual IRR from equally spaced fixed cash flows; choose frequency and beginning/end timing.
Result
All headline rates are effective annual IRRs. Initial investment is a positive amount entered here and is converted into a negative time-zero outflow. Subsequent negative flows represent additional investment; zeros preserve empty periods.
The numerical search is bounded to approximately −99.9994% through 16,275,379% per year. Multiple or repeated roots can exist; detected roots are not a guarantee that every root was found. Nearly repeated roots are numerically sensitive. IRR is not ROI and does not measure risk.
Cash-flow frequency: Annually. Final value is received at the exact end of the holding period. For a partial final period, only recurring payment dates within the holding period are included; no prorated recurring payment is invented. Additional investment treats the entered periodic amount as an outflow. The no-recurring-flow selection ignores the periodic amount.
Calculation details
Scroll horizontally or vertically to see more. Download CSV for the complete schedule.
| Period | Time (years) | Net cash flow |
|---|---|---|
| 0 | 0 | -10,000 |
| 1 | 1 | 3,000 |
| 2 | 2 | 3,000 |
| 3 | 3 | 3,000 |
| 4 | 4 | 3,000 |
| 5 | 5 | 4,000 |
How to use this calculator
Estimate an effective annual IRR from equally spaced fixed cash flows; choose frequency and beginning/end timing. Enter amounts in the units shown, select the applicable options, and click Calculate. Use Reset to restore the starting values.
Calculation formula
NPV = Σ CFₜ/(1+r)^t = 0.
Assumptions and accuracy
Review timing, rates, fees and result notes when comparing scenarios. Future returns and rates are assumptions rather than guaranteed outcomes. Monetary display follows the currency’s precision; intermediate calculations retain additional digits.
Choose what to calculate
IRR calculator with unequal cash flows
Find annual internal rates of return from unequal year-end cash flows. Multiple or no valid rates may exist; use Average Return for calendar-dated cash flows.
Open this calculationUnderstanding this calculation
The internal rate of return is a discount rate that makes the net present value of the entered cash flows zero. Cash-flow timing matters, so equal total profits can produce different IRRs.
Worked examples
A 40,000 investment with three annual inflows
Initial investment $40,000; year-end inflows $10,000, $20,000 and $30,000.
- Solve −40000 + 10000/(1+r) + 20000/(1+r)^2 + 30000/(1+r)^3 = 0.
The detected annual IRR is approximately 19.438%.
Try these inputsMonthly cash-flow periods, annual IRR
Invest 100 USD at time zero, receive 121 at the end of one year, and use twelve monthly periods with no interim flows.
- The monthly rate solves 100 × (1+r)^12 = 121.
- Effective annual IRR = (1+r)^12 − 1 = 121/100 − 1 = 21%.
Annual IRR is 21%; this is not a 21% monthly return.
Try these inputsA cash-flow pattern with two IRRs
Initial outflow 100 USD, year-one inflow 230, year-two outflow 132.
- NPV = −100 + 230/(1+r) − 132/(1+r)^2.
- At 10%: −100 + 230/1.1 − 132/1.1² = 0.
- At 20% the same NPV is also zero; neither root alone is an unambiguous investment ranking.
The calculator detects annual IRRs of 10% and 20%.
Try these inputsAnnualize a six-month investment without interim flows
Invest $100 and receive $121 after six months, with no recurring cash flow.
- Holding period is 6/12 = 0.5 years.
- Annual IRR solves 100 = 121/(1+r)^0.5, so r = 1.21² − 1 = 46.41%.
Effective annual IRR is 46.41%; the actual six-month gain is 21%.
Try these inputsCommon questions
Can an investment have more than one IRR?
Yes. Cash flows that change sign more than once can produce multiple solutions. Examine the cash flows and NPV rather than treating a single rate as a complete investment recommendation.
Does IRR include risk?
No. It summarizes the cash-flow pattern entered. It does not establish that forecast cash flows are reliable or account for risk by itself.
Is this IRR result annual or monthly?
Headline results are effective annual rates. Cash-flow dates are expressed in years and the solver finds an annual discount rate. For regularly spaced monthly flows this is equivalent to compounding a monthly rate, not multiplying it by twelve.
Can I enter cash flows on irregular dates?
Recurring flows follow the selected frequency; an additional terminal value is received at the exact holding date, including a partial final period. For freely chosen calendar dates, use the dated cash-flow mode of Average Return Calculator. Keep zero entries for empty years in the unequal annual form.
Scope and assumptions
The unequal-flow form uses successive year ends, not arbitrary dates. Fixed-flow rates are converted to effective annual rates from the selected payment period. The numerical search is bounded, and nearly repeated roots are sensitive to rounding; detected roots do not guarantee every root was found.
Sources
- Calculator.net: IRR definition and the worked machine-investment example
- Dated cash-flow return calculator
Calculation notes checked . Examples are mathematical checks under the stated assumptions.
Calculation methods and formulas
Fixed Cash Flow
Estimate an effective annual IRR from equally spaced fixed cash flows; choose frequency and beginning/end timing.
NPV = Σ CFₜ/(1+r)^t = 0.
Unequal Annual Cash Flows
Estimate an annual IRR from unequal amounts at successive year ends. Amounts may vary, but dates remain one year apart.
NPV = Σ CFₜ/(1+r)^t = 0.
See our calculation methodology and review status for data versions, rounding and validation limitations.