IRR Calculator

What is the internal rate of return on your investment? Enter your initial investment and the cash flows it produces at regular intervals — yearly, monthly or quarterly — and this calculator finds the annualized rate that makes their net present value exactly zero, with the full math shown step by step.

Please check your input values and try again.

Cash Flow Interval

IRR is solved per period and automatically annualized for the interval you choose.

Cash Flow Schedule

Period 0 is your initial investment (enter it as a negative number). Each following period is one interval later — enter positive amounts for money you receive and negative amounts for additional investments. Up to 20 periods.

# Period Amount ($)

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1. Classic 5-Year Investment

You invest $10,000 today and receive $3,000 at the end of each of the next 5 years (yearly intervals). What annual rate of return does that represent?

Year 0 -10,000.00 (initial investment)
Year 1 +3,000.00
Year 2 +3,000.00
Year 3 +3,000.00
Year 4 +3,000.00
Year 5 +3,000.00

IRR ≈ 15.24%

Step-by-step:

NPV(r) = (−10,000)/(1+r)⁰ + 3,000/(1+r)¹ + 3,000/(1+r)² + 3,000/(1+r)³ + 3,000/(1+r)⁴ + 3,000/(1+r)⁵ = 0

Test r = 15%: the annuity factor (1 − 1.15⁻⁵)/0.15 = 3.3522, so NPV = −10,000 + 3,000 × 3.3522 = +$56.46 — slightly positive, so 15% is a touch too low.

Test r = 16%: factor = 3.2743, NPV = −10,000 + 3,000 × 3.2743 = −$177.12 — too high.

Bisection between 15% and 16% converges to r = 15.24%. Payback: cumulative cash flow turns positive after 4 years (−10,000 + 12,000 = +$2,000).

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2. $50,000 Project With $12,000 Annual Returns

You invest $50,000 and receive $12,000 at the end of each of the next 5 years. The total cash returned is $60,000 — a 20% total profit — but because the money arrives over time, the true annualized return is much lower.

Year 0 -50,000.00 (initial investment)
Year 1 +12,000.00
Year 2 +12,000.00
Year 3 +12,000.00
Year 4 +12,000.00
Year 5 +12,000.00

IRR ≈ 6.40%

Step-by-step:

NPV(r) = (−50,000)/(1+r)⁰ + 12,000/(1+r)¹ + 12,000/(1+r)² + 12,000/(1+r)³ + 12,000/(1+r)⁴ + 12,000/(1+r)⁵ = 0

We need the annuity factor that equals 50,000 / 12,000 = 4.1667.

Test r = 6%: factor = 4.2124, NPV = −50,000 + 12,000 × 4.2124 = +$548.37 — rate slightly too low.

Test r = 7%: factor = 4.1002, NPV = −50,000 + 12,000 × 4.1002 = −$797.63 — rate slightly too high.

Bisection between 6% and 7% converges to r = 6.40%. Payback: 50,000 / 12,000 ≈ 4.17, so cumulative cash flow turns positive during year 5.

The IRR Formula

NPV(r) = Σ CF_t / (1 + r)^t = 0, for t = 0 … n

CF_t = Cash flow at period t (negative for the initial investment at t = 0)

r = Internal rate of return per period

t = Period number (0, 1, 2, … n) — equally spaced intervals

n = Total number of periods

How the Solver Works

IRR has no closed-form solution, so this calculator solves the equation numerically with the bisection method. It starts with a bracket of [−99.99%, +1000%] for the per-period rate and repeatedly halves it, keeping the half in which NPV changes sign, until the net present value is within 1 × 10⁻⁸ of zero (up to 200 iterations). The per-period result is then annualized: (1 + r)^m − 1, where m is 1 (yearly), 4 (quarterly) or 12 (monthly).

Guard: if all cash flows have the same sign (all positive or all negative), no IRR exists and an error is shown. For non-conventional cash flows — where the sign changes more than once — multiple IRRs can mathematically exist; the solver returns the first root found in the bracket.

List the cash flows at regular intervals

Write the initial investment at period 0 as a negative number and each expected cash flow at periods 1, 2, 3… as positive (income) or negative (extra investment). Every period must be the same length: yearly, monthly or quarterly.

Write the NPV equation

Discount every cash flow back to period 0 using (1 + r)^t. The sum of all discounted flows is the net present value at rate r.

Find the rate that makes NPV = 0

Adjust r until the present value of money out exactly equals the present value of money in. That rate — the break-even return of the cash flow stream — is the IRR. The calculator does this with bisection, accurate to 8 decimal places.

Annualize the result

The solved rate is per period. For monthly flows, convert with (1 + r)¹² − 1; for quarterly, (1 + r)⁴ − 1. Yearly flows need no conversion. The annualized figure is the number to compare against other investments or your cost of capital.

Interpret it with the IRR rule

In capital budgeting, accept an investment when its IRR exceeds your required rate of return (cost of capital). When comparing mutually exclusive projects, prefer NPV for the final decision — IRR can rank them incorrectly when sizes or timings differ.

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Bisection Solver

Robust numeric solution of the classic IRR equation — bracket [−99.99%, 1000%], 200 iterations, accurate to 8 decimal places.

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Payback Period

See exactly how many periods it takes for your cumulative cash flow to turn positive, alongside your IRR.

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Any Regular Interval

Yearly, monthly or quarterly cash flows — the IRR is solved per period and automatically annualized for fair comparison.

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Step-by-Step Math

Every calculation is shown: the NPV equation with your numbers, the solved rate, the annualization and the verification.

What Is IRR and What Does It Tell You?

IRR (Internal Rate of Return) is the discount rate that makes the net present value (NPV) of a series of cash flows equal to zero. It is the break-even rate of return of the investment: at that rate, the present value of everything you put in exactly equals the present value of everything you get out.

For cash flows at regular intervals — yearly, monthly or quarterly — IRR is the money-weighted, per-period return of the stream. Because it accounts for when each dollar moves, it is a far better measure of true performance than a simple profit percentage: receiving $3,000 a year for 5 years is worth less than receiving $15,000 all at once, and IRR captures that difference.

Common Uses of IRR

Investment analysis — comparing opportunities with different cash flow patterns on a single annualized percentage.
Capital budgeting — deciding whether a project earns more than the company's cost of capital.
Bonds and loans — the yield to maturity of a bond is exactly its IRR.
Business valuations — benchmarking expected returns of acquisitions and expansions.
Personal finance — judging annuities, pension payouts and installment purchases.

If your investment's IRR is 15.24%, every dollar behaved as if it had grown at a steady 15.24% per year — the rate this calculator solves for automatically.

IRR vs ROI vs CAGR vs XIRR

Return measures are easy to confuse. The table below shows what each one really measures and when to use it.

Method	What It Measures	When to Use
IRR	Annualized rate that makes NPV = 0, for cash flows at equal intervals	Investments with regular periodic cash flows (yearly, monthly, quarterly)
ROI	Total percentage gain over the whole holding period; ignores timing	Quick, timing-free summaries: "I made 20% on this deal"
CAGR	Constant annual growth from a single start value to a single end value	Lump-sum comparisons with no intermediate cash flows
XIRR	Same idea as IRR but weighted by each cash flow's actual calendar date	Irregular cash flows: SIPs, private equity, real estate with uneven dates

In short: ROI ignores time, CAGR needs only two points, IRR handles regular periodic cash flows, and XIRR handles irregular dates. For investments where money moves at fixed intervals, IRR is the accurate annualized measure.

The IRR Rule and Its Limitations

The IRR rule: in capital budgeting, accept an investment when its IRR is greater than the required rate of return (typically the cost of capital), and reject it when the IRR is lower. Because IRR is a percentage, it is intuitive to compare against hurdle rates and borrowing costs — which is why it remains one of the most widely used decision metrics.

Limitations to Keep in Mind

Multiple IRRs — if cash flows change sign more than once (invest, receive, invest again), the NPV curve can cross zero several times, producing multiple mathematically valid IRRs. In that case, rely on NPV instead.
Reinvestment assumption — IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself. If you can only reinvest at a lower rate, the realized return will be lower than the computed IRR.
Scale blindness — a 50% IRR on $100 beats a 15% IRR on $1,000,000 in percentage terms but not in wealth created. When choosing between mutually exclusive projects of different sizes, NPV is the safer criterion.
Timing illusion — a project that pays early has a higher IRR than one that pays late, even with identical totals, purely because of discounting.

Use IRR as your first screen, then confirm the decision with NPV when projects compete for the same capital.

Frequently Asked Questions (FAQ)

What is a good IRR?

A "good" IRR depends on the risk of the investment and your opportunity cost — the return you could get elsewhere at similar risk. As a rough guide, diversified equity investments have historically returned 10% to 15% per year, bonds and debt instruments 5% to 9%, and real estate often 6% to 12%. The most meaningful test is the IRR rule: your investment is attractive if its IRR exceeds your required rate of return (cost of capital). An IRR of 15% on a risky startup is not necessarily better than 8% on a government-backed bond.

How is IRR different from ROI?

ROI is the total percentage gain over the entire holding period and ignores timing completely — it treats $15,000 received over 5 years the same as $15,000 received today. IRR is annualized and time-weighted: it measures the constant rate at which your money grew, accounting for exactly when each cash flow occurred. That is why IRR is almost always lower than the total ROI for a profitable multi-period investment, and why IRR is the better tool for comparing investments with different durations or cash flow patterns.

Can IRR be negative?

Yes. A negative IRR simply means the investment lost money in present-value terms — you received back less than you put in. For example, investing $10,000 and receiving $9,000 one year later gives an IRR of exactly −10%. A negative IRR is a clear signal that the investment destroyed value, and you should compare it against what you could have earned in a risk-free alternative.

Why does my IRR calculation show an error?

The most common cause is entering all cash flows with the same sign — if every value is positive or every value is negative, the NPV can never reach zero and no IRR exists. Another cause is a cash flow stream whose NPV never crosses zero within the solver's bracket [−99.99%, +1000%] — for example, a stream that loses money in every scenario. Finally, non-conventional cash flows (signs changing more than once) can produce multiple IRRs, and some solvers struggle to converge; in those cases, prefer an NPV analysis. Check that your initial investment is negative and your returns are positive.

IRR vs XIRR — which should I use?

Use plain IRR when your cash flows occur at regular, equal intervals — yearly, monthly or quarterly. Use XIRR when cash flows happen at irregular dates, such as SIP investments with contributions and withdrawals on arbitrary days, private equity capital calls, or real estate with an irregular purchase-to-sale timeline. XIRR weights each flow by its exact calendar date (days/365); IRR assumes equal spacing. If your flows are truly regular, both give nearly identical results and IRR is the classic, simpler measure.

What does NPV at IRR = 0 mean?

It is the defining property and the built-in verification of the calculation: the IRR is, by definition, the rate that makes the net present value zero. When the calculator reports "NPV at IRR ≈ $0.00", it confirms that at the solved rate, the present value of all money out exactly equals the present value of all money in. If that verification value were significantly different from zero, the solver would not have converged correctly. NPV at any other rate tells you how much value the investment adds (positive) or destroys (negative) relative to that rate.

⚠️ Disclaimer: IRR assumes that intermediate cash flows are reinvested at the computed IRR, which may not be achievable in practice. Cash flow streams that alternate between positive and negative values can produce multiple IRRs. This tool is for educational purposes only and is not investment advice.