Investment Calculators
Compound annual growth rate.
Enter a start value, an end value and a holding period to get the CAGR: the single constant yearly rate that would have produced the same result. The number every fund fact sheet quotes, and the only fair way to compare investments held for different lengths of time.
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Your return
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Total return vs CAGR
Total return is the dollar gain or loss over the whole holding period. CAGR is the smoothed yearly rate that would produce the same final value if growth had been constant. Use CAGR to compare investments held for different time periods on equal footing.
What CAGR actually is
CAGR is a geometric mean, not an average. It answers one narrow question: what constant annual rate, compounded, turns the starting value into the ending value over this many years? The formula is (end ÷ start) raised to the power of 1÷years, minus one. Everything that happened in between (the crashes, the flat years, the one spectacular quarter) is deliberately erased.
That erasure is the point. It is also the reason CAGR is the only honest way to compare a holding you owned for 3 years against one you owned for 11. A 60% total gain sounds better than a 40% total gain until you learn the first took eight years and the second took three.
Why an average return is misleading
Take an investment that gains 50% in year one and loses 50% in year two. The arithmetic average of +50% and −50% is zero, which sounds like you broke even. You did not. A dollar became $1.50, then $0.75. You are down 25%, and the CAGR is roughly −13.4% a year.
The gap between the arithmetic average and the CAGR is caused entirely by volatility, and it always runs the same direction: the average is always the flattering number. Two portfolios can report the same average annual return and deliver very different amounts of money, and the more violently a portfolio swings, the wider that gap gets. When a marketing document quotes an “average annual return” rather than a compound annual return, that choice is doing work.
What CAGR does not tell you
- Risk. A 7% CAGR from a GIC ladder and a 7% CAGR from a single small-cap stock are the same number describing two completely different experiences. CAGR has no volatility term in it at all.
- Sequence. Two paths to the same endpoint produce identical CAGR, but if you were withdrawing money along the way the order of the returns changes how much you end up with. This is sequence-of-returns risk, and it is why CAGR is a poor guide for anyone drawing down a portfolio.
- Your own contributions. CAGR assumes one lump sum in and one value out. If you were adding money monthly, CAGR describes the investment, not your personal result. For that you want a money-weighted return (an internal rate of return) which weights each dollar by how long it was actually invested.
- Fees, tax and inflation. CAGR is whatever you feed it. A 7% nominal CAGR on a fund with a 2% management expense ratio is a 5% CAGR to you, and if inflation ran at 3% your purchasing power grew by roughly 2%. Feed it net-of-fee values if you want a number you can spend.
Reading a CAGR in a Canadian context
Canadian fund fact sheets and ETF factsheets quote compound annual returns, not averages, and they quote them net of the management expense ratio but before any tax and before any sales charge. So a fund’s published 10-year figure is already closer to your reality than a raw index CAGR, but it still ignores the account it sits in.
That account matters more than most people assume. The same 7% CAGR compounds untouched inside a TFSA or RRSP, but in a non-registered account the tax drag arrives every year that the holding distributes income, which quietly lowers your realised CAGR even before you sell. Comparing a registered result against a non-registered result on headline CAGR alone flatters the taxable account.
Two related tools: ROI for the simple total-return version of the same question, and compound interest to run the calculation forwards from a rate you assume rather than backwards from a result you got.
TNAADO Inc. · Toronto
What a compound annual growth rate hides
CAGR is the single constant rate that would have taken the starting value to the ending value over the period. It is the honest way to compare investments held for different lengths of time, and it is deliberately smooth: it says nothing about the path. Two investments with the same CAGR can have behaved completely differently, and the one that fell 60% in the middle was a very different thing to hold.
The mistake people make. Comparing a CAGR against an average annual return as though they measured the same thing. They do not, and the average is always the flattering one. A year of +50% followed by a year of -50% averages 0% and has a CAGR of -13.4%, because losses need larger gains to undo them. Only the compound figure reflects that.
Frequently asked questions
What is the CAGR formula?
CAGR equals the ending value divided by the beginning value, raised to the power of one divided by the number of years, minus one. In words: the constant annual growth rate that would have taken you from the start value to the end value over that period.
It is a geometric mean rather than an arithmetic one, which is why it accounts for compounding. Because only three inputs go in (start, end and time) every intermediate year, however dramatic, is smoothed out of the answer.
What is the difference between CAGR and average annual return?
An average annual return adds the yearly percentages together and divides; CAGR compounds them. Whenever returns vary, the average is higher than the CAGR, and the more volatile the returns, the bigger that gap.
The standard illustration: +50% then −50% averages to 0%, but a dollar has become 75 cents; a CAGR of about −13.4% a year. The average describes the returns; the CAGR describes what happened to your money.
Is CAGR the same as annualised return?
For a single lump sum with no further contributions or withdrawals, yes: they are two names for the same calculation. The terms diverge once cash moves in or out during the period.
With ongoing contributions, CAGR still describes the investment’s growth but no longer describes your return, because your later dollars were invested for less time. The measure that handles that is a money-weighted return, also called an internal rate of return, and it is what a fair performance report on a portfolio you have been adding to should show.
What counts as a good CAGR?
Only in comparison to something. A CAGR is meaningful against a relevant benchmark over the same window, against inflation, and against the risk you took to get it, and it should be after fees, because a headline rate you never actually received is not a result.
The formula also has a genuine blind spot worth knowing: a short window that happens to start at a market bottom or end at a peak produces a spectacular CAGR that says more about your choice of dates than about the investment. Always check the period, not just the number.
Disclaimer
Educational only. Actual investment returns will vary based on market conditions, fees, and taxes. Past performance does not guarantee future results.