BYTETOOLS

IRR Calculator

Find the internal rate of return of a cash flow series by numeric root-finding, with an NPV check, a discount curve and clear warnings when no IRR exists.

Cash flows

Year 0
Year 1
Year 2
Year 3
Year 4

Year 0 is today and is not discounted. Enter the initial investment as a negative number and returns as positive ones.

14.49%
Internal rate of return
$0.00
NPV at that rate
$1,300.00
Total inflows
$1,000.00
Total outflows

The IRR of 14.49% clears your 10% hurdle rate, so the project has a positive NPV at that cost of capital.

NPV against discount rate

The red dot marks where the curve crosses zero — that crossing point is the IRR.

The NPV curve is sampled across the plausible rate range, every zero crossing is bracketed, and each bracket is narrowed by bisection capped at 200 iterations — so the solver always terminates and never returns a silent NaN. Worked check: flows of −1,000, 500, 400, 300 and 100 give an IRR of 14.49%. Calculated in your browser; arithmetic, not investment advice.

What is the IRR Calculator?

The ByteTools IRR Calculator finds the discount rate at which a series of cash flows has a net present value of exactly zero.

  • IRR solved by sign-change bracketing plus bounded bisection
  • NPV at the solved rate shown as an explicit convergence check
  • Honest warning when a series has no IRR or several possible ones
  • NPV-versus-rate curve drawn on canvas so you can see the root
  • Optional hurdle rate with an accept or reject verdict
  • Never returns a silent NaN or hangs — iterations are capped

How to use the IRR Calculator

  1. 1

    Enter the initial investment as period 0, normally a negative number.

  2. 2

    Add one row per period with that period's cash flow.

  3. 3

    Read the internal rate of return and the NPV check at that rate.

  4. 4

    Enter a hurdle rate to see whether the IRR clears it.

  5. 5

    Check the sign-change note if the tool warns about multiple roots.

About the IRR Calculator

The ByteTools IRR Calculator finds the discount rate at which a series of cash flows has a net present value of exactly zero. There is no algebraic formula for that rate, so the tool brackets a sign change in the NPV function and narrows it by bisection until it converges, then reports the NPV at the solved rate so you can verify the root really is a root.

Not every cash flow series has an internal rate of return, and this calculator says so plainly instead of quietly returning a wrong number. Series that never change sign — all inflows or all outflows — have no IRR at all, and series that change sign more than once can have several, so the tool counts the sign changes and warns you when the answer may not be unique.

An NPV-versus-discount-rate curve is drawn alongside the result so you can see the root visually, and you can enter your own hurdle rate to get an accept-or-reject reading. Everything is computed in your browser with nothing uploaded, and the output is arithmetic rather than investment advice.

Frequently asked questions

What is the internal rate of return?

IRR is the discount rate that makes the net present value of a cash flow series equal zero. For flows of −1,000, 500, 400, 300 and 100, the IRR is about 14.49% — discount those flows at 14.49% and they sum to zero.

How is IRR calculated if there is no formula?

Numerically. The calculator evaluates NPV at a range of rates, finds where the sign flips, then repeatedly halves that interval until the answer stops moving. The iteration count is capped, so it always terminates rather than looping forever.

Why does my cash flow series have no IRR?

Because the flows never change sign. If every number is positive, NPV stays positive at every discount rate and never crosses zero, so no internal rate of return exists. You need at least one outflow and one inflow for the question to have an answer.

Can a project have more than one IRR?

Yes. A series that changes sign more than once — say a big outflow late in the project for decommissioning — can cross zero several times, giving multiple mathematically valid IRRs. This tool counts sign changes and warns you, and in that case NPV at your actual cost of capital is the more reliable measure.

Should I pick the project with the highest IRR?

Not automatically. IRR ignores project size and implicitly assumes interim cash flows are reinvested at the IRR itself, which is often unrealistic. A small project with a spectacular IRR can add less value than a large one with a modest IRR, so check NPV as well.

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