Formula
IRR is the rate r where NPV = cash flow 0 + cash flow 1 ÷ (1+r)^1 + cash flow 2 ÷ (1+r)^2 + ... = 0. This calculator uses a bounded numeric search from -99.99% to 1,000%.
IRR Calculator
Estimate internal rate of return from an initial outflow, annual cash flows and terminal value using a transparent NPV zero-crossing method.
Worked example
With a 1,000 initial outflow and cash flows of 250, 300, 350, 400 and 600, the calculator searches for the discount rate that makes NPV approximately zero and reports that annual IRR.
Professional note
Master’s Tip: compare IRR with cash profit and NPV. A high IRR can still be attached to a small or risky project, and unusual cash flows can produce confusing IRR results.
Regional and unit assumptions
Standard or basis: annual end-of-period cash-flow IRR estimate using transparent NPV arithmetic. No accounting, tax, securities or valuation standard is claimed.
Assumptions and limitations
- Cash flows are treated as annual end-of-period values after the initial outflow.
- The initial outflow is entered as a positive number and converted to a negative cash flow internally.
- The result is a numeric estimate and may not exist as a single value for unusual cash-flow patterns.
- Taxes, inflation, financing costs, reinvestment assumptions and risk are not included.
- This is project-comparison arithmetic only, not investment advice.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
IRR is the rate r where NPV = cash flow 0 + cash flow 1 ÷ (1+r)^1 + cash flow 2 ÷ (1+r)^2 + ... = 0. This calculator uses a bounded numeric search from -99.99% to 1,000%.
Standard or basis
Standard or basis: annual end-of-period cash-flow IRR estimate using transparent NPV arithmetic. No accounting, tax, securities or valuation standard is claimed.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: compare IRR with cash profit and NPV. A high IRR can still be attached to a small or risky project, and unusual cash flows can produce confusing IRR results.
Related calculators
Questions
What is IRR?
IRR is the discount rate that makes the net present value of a cash-flow series equal approximately zero.
How is IRR different from ROI?
ROI compares net gain with initial investment. IRR also considers when cash flows happen over time.
Can IRR be missing or misleading?
Yes. Some cash-flow patterns do not produce a single useful IRR, especially when signs change more than once.
Does this calculator include tax or financing?
No. Enter cash flows after any tax, financing or fee assumptions you want included.
Should I use IRR alone?
No. Compare IRR with cash profit, NPV, risk and payback timing before using it for decisions.
Calculation note
IRR became popular because it turns uneven cash flows into a single annualized rate. That simplicity is useful, but it can hide scale, risk and unusual cash-flow timing.
ROI starts with the denominator
Return on investment uses the initial investment as the baseline. That makes unlike projects easier to compare, but it also means a small denominator can produce a dramatic percentage from a modest cash gain.
Costs change the story
A sale price or final value is not the same as return. Brokerage, platform fees, delivery, materials and other direct costs reduce the gain before the return percentage is calculated. The printable report keeps those costs visible.
Time and risk are separate checks
A 20% result over one month and a 20% result over five years are not equivalent. Annualising helps compare time periods, but it still does not measure risk, tax, inflation, liquidity or whether the cash flows arrived evenly.
Sources and further readingInvestor.gov: Compound Interest CalculatorHarvard Business School Online: Return on Investment