Investment Return Calculator

What this computes

"My investment doubled" is a statement about magnitude, not speed. Doubling in five years is excellent; doubling in thirty is barely keeping pace with inflation. To compare investments held for different lengths of time, you need the return expressed as a per-year compound rate — and that's what this calculator produces:

• Total return — the whole-period gain, end ÷ start − 1. Big, satisfying, and useless for comparison on its own.
• CAGR — compound annual growth rate, the single steady yearly rate that turns your start value into your end value over the holding period. This is the honest, comparable number.
• Real CAGR — the same rate restated in purchasing power, after your inflation assumption.
• Growth multiple — end ÷ start, the "my money 2.5×'d" figure.
• Simple average — total return ÷ years, shown only so you can see how much it overstates the truth.

This is the backward-looking companion to the compound interest calculator: that one projects a balance forward from an assumed rate; this one extracts the realized rate from a balance you already have.

The math

Growth multiple   = End ÷ Start
Total return      = End ÷ Start − 1
CAGR              = (End ÷ Start)^(1 ÷ Years) − 1
Real CAGR         = (1 + CAGR) ÷ (1 + Inflation) − 1
Simple average    = Total return ÷ Years   (shown as the trap)

Years can be fractional — 18 months is 1.5. The real-return line uses the exact Fisher relation rather than the common "subtract inflation" shortcut, which slightly overstates the result.

A worked example

You put $10,000 into an index fund and ten years later the position is worth $25,000. You assume 3% inflation.

• Growth multiple: $25,000 ÷ $10,000 = 2.50×
• Total return: 2.50 − 1 = 150%
• CAGR: 2.5^(1/10) − 1 = 9.60% per year
• Real CAGR: 1.09596 ÷ 1.03 − 1 = 6.40% per year
• Simple average: 150% ÷ 10 = 15.0% per year — and this is the trap

The arithmetic shortcut claims 15% a year. But money compounding at 15% for ten years would have grown 4.05×, not 2.50×. The rate that actually reproduces your outcome is 9.60% — a third lower than the naive figure. Every year the difference between the two numbers compounds, which is why the gap widens with longer holding periods:

Same doubling, four different verdicts. A 100% total return over 5 years is a genuinely strong 14.87% CAGR; over 30 years it's 2.34% — likely below inflation, meaning the investor lost purchasing power while the account statement grew.

Total return tells you how much. CAGR tells you how fast. Only the second one lets you compare.

Why CAGR, not the average

CAGR is a geometric mean: it multiplies the year-by-year growth factors together and asks what constant rate would have produced the same product. An arithmetic average just adds the yearly percentages and divides. The two disagree whenever returns vary — and the more volatile the path, the bigger the disagreement. The classic demonstration:

• Year 1: +50%. $10,000 becomes $15,000.
• Year 2: −50%. $15,000 becomes $7,500.
• Arithmetic average: (+50% − 50%) ÷ 2 = 0% per year.
• Actual outcome: 0.75× your money. CAGR = 0.75^(1/2) − 1 = −13.40% per year.

The average says you broke even; your account says you lost a quarter of it. Losses hurt more than equal-sized gains help — a −50% year needs a +100% year to undo, not a +50% one. Because CAGR is computed from the actual start and end values, it bakes this asymmetry in automatically. That's why fund factsheets report annualized (geometric) returns, and why any pitch quoting an "average annual return" across volatile years deserves a second look. The ROI vs. CAGR guide walks through more of these cases.

The real-return line deserves a word too. U.S. inflation has averaged near 3% per year over the past century, which is why 3% is the calculator's default assumption. At that rate, prices double roughly every 24 years — so a portfolio that "doubled" over 24 years in nominal dollars bought you approximately nothing in real terms. Long-horizon claims should always be read in real CAGR; the inflation calculator shows the same erosion from the purchasing-power side.

How to use this

1. Use clean start and end points. The formula assumes a lump sum with no money added or removed in between. A buy-and-hold position, a single fund purchase, or a house works; a brokerage account you contribute to monthly does not — contributions masquerade as returns.
2. Count the years honestly, fractions included. Held from March 2019 to September 2025? That's 6.5 years, not "about six." On a doubling, 6 years annualizes to 12.2% but 6.5 years to 11.3% — half a year of rounding moves the answer by nearly a full point.
3. Compare investments on CAGR, never total return. A stock that's "up 300%" since 2010 and one "up 80%" since 2021 can't be ranked until both are annualized.
4. Check the real CAGR before celebrating. Anything below your inflation assumption grew your account statement while shrinking your purchasing power.
5. Stress-test the doubling intuition. The rule of 72 says money doubles in roughly 72 ÷ rate years: at 10%, about 7.2 years (the exact figure is 7.27). Enter a doubling over 7.27 years and the calculator returns 10.0% — a quick way to convince yourself the formula and the folklore agree.

What this doesn't model

• Cash flows. Deposits and withdrawals during the period break the end-over-start math. Measuring those requires money-weighted (IRR) or time-weighted returns, which this tool doesn't attempt. For projecting forward with regular contributions, use the compound interest calculator.
• Dividends you didn't reinvest. If a position paid dividends to cash, the end value understates your true return. Add what you received to the end value for a rough total-return figure.
• Taxes and external fees. Results are gross. Fund expense ratios are typically embedded in the end value already; advisory fees and capital gains tax are not.
• Risk. Two investments with identical CAGRs can carry wildly different volatility and drawdowns. CAGR is one summary statistic of a path, not a verdict on whether the risk was worth taking.
• The future. A realized CAGR is a fact about the past. U.S. large-cap stocks compounded at roughly 10% nominal per year over 1926–2025 — closer to 7% in real terms — but no period guarantees the next one. Treat any forward-looking rate as an assumption, not an entitlement.