Online Tool Store
CAGR Calculator
Work out the compound annual growth rate between two values, with total growth, doubling time, and the smoothed year-by-year path. Runs in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Compound annual growth rate
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Example shown — enter your own figures. Decimals are fine for part-years.
- Total growth over the period
- Absolute change
- Growth multiple
- Years to double at this rate
The smoothed path
What each year would look like if growth were exactly steady — real results almost never are.
| Year | Value | Gain that year |
|---|
How it works
- Enter what the value started at, what it ended at, and how many years passed.
- Read the annual rate, plus total growth, the growth multiple, and doubling time.
- Check the smoothed path to see what steady growth at that rate would have looked like each year.
The formula, and a worked example
CAGR is the geometric average of the growth, not the arithmetic one:
CAGR = (ending ÷ beginning)^(1 ÷ years) − 1
Take 10,000 growing to 18,000 over five years. The ratio is 1.8, and the fifth root of 1.8 is 1.1247 — so the rate is 12.47% a year. You can check it in reverse: 10,000 × 1.1247⁵ comes back to exactly 18,000. Total growth was 80% over the whole period, which is a very different number from 12.47% a year, and confusing the two is the most common mistake with growth figures.
Why averaging the yearly percentages misleads
This is the trap CAGR exists to avoid. Suppose an investment gains 50% one year and loses 50% the next:
100 → +50% → 150 → −50% → 75
arithmetic mean: (+50 − 50) ÷ 2 = 0% // looks like you broke even
CAGR: (75 ÷ 100)^(1÷2) − 1 = −13.40% // what actually happened
You are a quarter poorer, and the arithmetic mean says you are flat. The gap appears because a percentage gain and the same percentage loss apply to different amounts — the 50% loss is taken from the larger 150. Averaging percentages always flatters a volatile series, which is why fund performance is quoted as an annualised figure rather than an average of yearly returns.
The flip side is that CAGR hides the ride entirely. Two investments can share a 12% CAGR while one climbed steadily and the other halved before recovering. The smoothed path above is deliberately labelled as such: it is what steady growth would have looked like, not what happened.
FAQ
What is CAGR actually telling me?
The single steady rate that would have taken you from the start value to the end value over the period. Real growth is never that smooth, so CAGR is a summary rather than a description — it answers "what constant rate would have got me here?".
Why not just average the yearly percentages?
Because percentages compound rather than add, and averaging them overstates your result. Gain 50% then lose 50% and the average looks like zero — but 100 became 150 and then 75, an actual loss of 13.40% a year. CAGR is the honest figure.
Why does it refuse a beginning value of zero?
Because growth from nothing has no rate. The formula divides the end by the start, and dividing by zero has no answer — no percentage describes going from 0 to 100. The same applies to a negative starting point.
Can it handle a negative ending value?
No, and that is a mathematical limit rather than a missing feature. Working out CAGR takes a fractional root of the ratio, and a fractional root of a negative number is not a real number. A value that falls to exactly zero is fine — that is a clean −100%.
Can I use part-years?
Yes — decimals work, so 18 months is 1.5. That matters more than it sounds: using 1 instead of 1.5 would inflate the annual rate considerably, since the same growth is being spread over a third less time.
What is the doubling time figure?
How long the value takes to double if the same rate continues, from log(2) ÷ log(1 + rate). It is the precise version of the "rule of 72" shortcut — at 12.47%, the rule gives 5.8 years and the exact answer is 5.9.
How we compare
| Feature | Online Tool Store | Ad-supported finance sites | Spreadsheet |
|---|---|---|---|
| Refuses inputs with no valid answer | ✓ | Many return NaN or a silent zero | Shows an error code |
| Separates total growth from annual rate | ✓ | Often only one figure | If you write both formulas |
| Doubling time and growth multiple | ✓ | ✗ | More formulas |
| Nothing typed leaves the page, no ads | ✓ | ✗ | ✓ |
| Handles irregular cash flows in and out | ✗ | Some offer an IRR tool | ✓ |
| Charts the actual year-by-year history | ✗ | Sometimes | ✓ |
Use it to turn two numbers and a timespan into a comparable annual rate — revenue over three years, a portfolio since you opened it, users since launch. It assumes a single sum in and a single sum out; if money went in and out along the way, you want IRR instead, and a spreadsheet is the place for that.