Turning a total gain into a yearly rate
An investment that grew 80% is impressive over two years and unremarkable over fifteen. This calculator strips the time out, producing the constant annual rate that would have delivered the same result — the only basis on which two investments can honestly be compared.
The formula
The exponent is what makes it a compound rate rather than an average. Dividing the total gain by the number of years overstates the answer, sometimes badly.
Worked example: $10,000 grows to $18,000 over 5 years
- Total growth: 80%
- Annualised: (18,000 ÷ 10,000)1/5 − 1 = 12.47%
- The naive answer, 80 ÷ 5, would be 16%
The 3.5-point gap is compounding. Each year grows a larger base than the year before, so a lower rate reaches the same destination.
Why the naive average always overstates
| Total gain | Years | Divided by years | True annualised |
|---|---|---|---|
| 50% | 3 | 16.7% | 14.5% |
| 80% | 5 | 16.0% | 12.5% |
| 100% | 10 | 10.0% | 7.2% |
| 200% | 20 | 10.0% | 5.6% |
The error grows with the horizon. Over twenty years the simple average is nearly double the truth.
What this figure hides
It describes the path as if it were smooth, which no market is. A fund that returns 12.47% annualised may have delivered +40%, −25%, +30%, −10% and +25% along the way. The destination is identical; the experience is not, and the drawdown is what makes investors sell.
It also assumes no money was added or withdrawn. If you contributed along the way, this formula overstates your return, because contributions made late did not compound for the full period.
What this calculator leaves out
Inflation, fees and tax. At 2% inflation a 12.47% nominal return is 10.3% real. A 1% platform fee takes it to 9.3%.
Comparing two investments honestly
Suppose one holding turned $10,000 into $18,000 over five years and another turned $4,000 into $6,000 over two. The first made more money; the second compounded faster, at 22.5% a year against 12.47%.
Which was better depends on what you could do with the money afterwards. If the two-year holding was followed by three years in cash, the five-year investment wins on the full period. Annualised returns compare rates, not outcomes, and the comparison only holds if the horizons match.
When the series is not a single investment
The same formula annualises anything that grew from one figure to another over a known period: revenue, subscriber count, property value, salary. Business plans usually quote growth this way rather than as a total.
A company going from $10m to $18m of revenue in five years is growing 12.47% a year. Stated as 80% it sounds like a different company. When someone quotes a total growth figure without the period, the omission is rarely accidental.
One limit worth naming: the formula uses only the first and last values. A business that grew 40% in year one and flatlined afterwards produces the same annualised figure as one that grew steadily, and the two are not equally healthy.
Related calculators
- CAGR calculator — the same maths applied to revenue or any other series
- IRR calculator — the right tool when money went in and out over time
- Real return calculator — what remains after inflation