IRR calculator

Solve fixed-period internal rate of return and convert the periodic rate to an annualized equivalent.

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Interactive tool

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The IRR calculator finds rates above −100% where the net present value of 2 to 200 equally spaced cash flows is zero. It reports a periodic result, an annualized result for monthly, quarterly, or yearly periods, and explicit diagnostics for missing sign changes, no root, multiple roots, or failed convergence.

When to use this tool

  • Check the fixed-period return implied by an initial outflow and later inflows.
  • Compare the mathematical annualized equivalent of monthly or quarterly periodic IRR.

How to use

  1. Enter each cash flow in chronological period order, including period 0.
  2. Choose whether one period means a month, quarter, or year.
  3. Review the single result or the diagnostic explaining why one unambiguous IRR is unavailable.

Example

One-period reference

Cash flows of −1,000 and 1,100 produce a periodic IRR of 10%. If that period is yearly, the annualized IRR is also 10%.

How it works

  • IRR solves Σ(CFₜ/(1+r)ᵗ)=0 for r > −1. The solver scans a bounded transformed rate domain for candidate brackets and uses bounded bisection rather than an unprotected Newton iteration.
  • Annualized IRR is (1 + periodic IRR) raised to 12, 4, or 1 periods per year, minus 1.

Limits and notes

  • Cash flows must be equally spaced; actual dates and XIRR are not supported.
  • Non-conventional cash flows can have multiple IRRs. A bounded scan can identify multiple candidate roots but cannot prove global uniqueness for every possible sequence.
  • IRR is a mathematical result, not a guaranteed return or investment advice.

Frequently asked questions

Does this calculator support XIRR?

No. It accepts period numbers only and assumes equal spacing.

Why can one cash-flow sequence have multiple IRRs?

When cash-flow signs change more than once, the NPV equation can cross zero at more than one rate.

What does no root mean?

No stable zero crossing was found within the documented bounded search domain; the tool does not fabricate a rate.

References

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