What this calculator does
Three modes, one engine. CAGR(compound annual growth rate) is the right answer when you bought once and sold once — the textbook example is “I bought €10,000 of an index fund in 2020 and it's worth €16,289 today, five years later — what return did I earn?”. IRR (internal rate of return, or XIRR for irregular dates) is the right answer when there's a series of cash flows — you added more money along the way, took some out, received dividends, and finally sold. Compare stacks two or more scenarios next to each other so you can see which one actually won on a like-for-like basis.
CAGR — the closed-form formula
CAGR = (Ending / Starting)1/years − 1. That's it. €10,000 → €16,289 over 5 years gives (1.6289)0.2 − 1 ≈ 10.25%. Every other single-period annualisation is a special case of this formula. Doubling time is the inverse: ln(2) / ln(1 + r) — at 7% per year, money doubles in roughly 10 years. The calculator shows this directly alongside the headline CAGR.
IRR — what it actually measures
IRR is the constant annual rate of return that would make the present value of every cash flow sum to zero. In plain English: it's the “effective yield” on the money you put in, taking into account the dates each chunk went in and came out. A €10,000 lump sum that grew to €13,310 in 3 years has an IRR of exactly 10% — but if you added another €5,000 at the 18-month mark and ended with €18,500, the IRR changes because the time-weighting changes too.
Real-world IRR is XIRR: the same idea, but with each cash flow discounted by exact years-from-the-first-flow rather than by “periods”. This is what Excel's XIRR()function does and what most brokerage statements quote when they report “personal rate of return”. Our solver matches Excel's output to four decimal places on textbook cases, and is more robust on pathological ones: Excel's Newton-Raphson starts at 0.1 and fails when cash flows have unusual shapes; we fall back to bisection over a wide bracket if Newton diverges.
Sign convention — the part people get wrong
Negative cash flows are money out of your pocket: deposits into the investment, buys, fees you paid. Positive cash flows are money in: withdrawals, sells, dividends, the final liquidation value. If you don't have a final “sell” — because you're still holding the position — put the current market value as the final positive flow on today's date. The IRR you get is “the return you'd have earned if you sold today”.
The most common mistake is forgetting that lastcash flow. Without it, the IRR solver sees a bunch of money going out and nothing coming back, and refuses to converge — it'll tell you so, but the fix is always “add the current value as a positive flow on today”.
CAGR vs IRR — when to use which
- One-shot purchase, one-shot sale:CAGR. The two numbers are identical in this case, so CAGR's simpler.
- Recurring contributions (DCA, payroll): IRR. CAGR will overstate your return because it assumes all the money was invested from day one.
- Withdrawals (FIRE, drawdown): IRR. Same reason — the timing matters.
- Comparing two different strategies: IRR if the cash flows differ, CAGR if they have identical schedules. The Compare panel handles the simple case directly; for IRR-vs-IRR, compute each separately and read off the numbers.
- Real estate: always IRR — you put money in for the deposit, more for renovations, get rental income, eventually sell. CAGR ignores all the intermediate cash flows.
Money multiple (MOIC) vs IRR
Private equity reports both for a reason. The money multiple(also called MOIC or TVPI) is just total cash out ÷ total cash in. A 3× multiple sounds great, but a 3× over 25 years is only ~4.5% IRR — basically a government bond. A 3× over 5 years is ~24.6% IRR — top-decile. The calculator reports both so you can't fool yourself with a multiple that hides a glacial time horizon.
What about volatility?
CAGR and IRR are arithmeticon the endpoints — they don't see drawdowns along the way. Two investments with the same CAGR can have wildly different risk profiles: a bond ladder that returned 6% per year with no volatility looks identical to a stock that returned 6% per year after losing 45% in the middle. For most planning decisions, CAGR is the right metric (it's what your wallet actually feels at the end). For position sizing or sleep-at-night decisions, you also need to look at volatility (standard deviation of annual returns) and max drawdown — neither of which this calculator computes.
Reconciling against a brokerage statement
Most brokerages now quote a “personal rate of return” or “time-weighted return” on the monthly statement. They're using either XIRR or Modified-Dietz under the hood. Drop a brokerage PDF into the IRR panel — we'll extract every deposit, withdrawal, and the period-end value, then solve for IRR. The math the brokerage reports should match ours to within ~0.1% for a clean account; bigger gaps usually mean the brokerage is netting fees, dividends or FX adjustments into a single line you can't see line-by-line, or they're reporting time-weighted return rather than money-weighted (XIRR is money-weighted — it rewards good timing of contributions, which time-weighted return deliberately ignores).
If you need to compare investment-account performance to interest-bearing-savings, also see the interest rate calculator (single-shot compound) and the savings goal calculator (recurring deposits with a target). For multi-account performance attribution, drop the statements into our main converter and run each through the IRR panel separately.
Worked example: VC fund vs index fund
Imagine a venture fund that took €100,000 in 2018, returned €50,000 in 2022 and €350,000 in 2026. Total in: €100k. Total out: €400k. Money multiple: 4×. That looks spectacular until you compute the IRR: roughly 18.5% / year over 8 years. Now compare against the index-fund counterfactual — the same €100k in 2018 into an S&P 500 tracker grew to ~€220k by 2026 (~10% / year). The fund did beat the index, but not by 4× — by 4× / 2.2× ≈ 1.8× cumulative, or about 8.5 percentage points per year. That's the calculation people screw up because they compare 4× to 2.2× instead of 18.5% to 10%.