CAGR Calculator
Compound annual growth rate plus total gain and doubling time.
What it does
Compound annual growth rate answers what steady yearly pace connects two values. Investments, revenue, and populations all zigzag, and CAGR irons the path into the single rate that would produce the same endpoints.
The tool above takes start, end, and years. It returns the CAGR, the total gain percent, and the doubling time at that rate.
Averages mislead without it. Doubling in five years averages twenty percent arithmetically but compounds at 14.87%, and planning on twenty compounds into disappointment.
Sequence risk hides inside smooth rates. Two paths sharing a CAGR can empty a withdrawing account differently, since early losses hurt more than late ones.
How to use
- Enter the starting value.
- Enter the ending value.
- Enter the exact year span, fractions allowed.
- Read CAGR for comparisons, total gain for headlines.
Formula
- end / start
- Total growth multiple. Doubling is 2.
- 1/years
- Root spreading growth evenly per year.
- ln(2)
- Doubling constant 0.6931 for the time math.
Zero or negative starts break the ratio. Losses need positive values on both ends with the end below the start.
Worked example
Example: $10,000 to $20,000 in 5 years
Investment doubles over five years.
- Multiple: 20,000 / 10,000 = 2.
- Root: 2^0.2 = 1.148698.
- CAGR: 1.148698 - 1 = 14.87%, shown as 14.87%.
- Total: +100%. Doubling time: 0.6931 / 0.13863 = 5 years, checking out.
Reference table
| Years to double | CAGR needed | Rule of 72 check |
|---|---|---|
| 5 years | 14.87% | 72/5 = 14.4 (close) |
| 7 years | 10.41% | 72/7 = 10.3 (close) |
| 10 years | 7.18% | 72/10 = 7.2 (close) |
| 12 years | 5.95% | 72/12 = 6.0 (close) |
Limits
- Smooths volatility away. Bumpy paths share calm numbers.
- Needs positive values both ends.
- Ignores cash flows in and out mid span.
- Inflation excluded. Real rates run lower.
Common mistakes
- Dividing total gain by years instead of compounding.
- Comparing CAGR across different spans blindly.
- Ignoring withdrawals that change invested capital.
- Reading nominal CAGR as spending power.
- Chasing past CAGR into future plans.
Try it yourself
Quick checks. Answers sit tucked under each question.
$5,000 to $8,000 in 4 years?
(1.6)^0.25 - 1 = 12.47%.
Tripling in 10 years?
3^0.1 - 1 = 11.61%.
Questions
CAGR vs average return?
CAGR compounds geometrically to the true endpoint. Arithmetic averages overstate bumpy growth.
Can CAGR be negative?
Yes when the end sits below the start. The formula handles declines.
What is a good CAGR?
Stocks averaged near 10% nominal long run. Businesses vary wildly by risk.
How does rule of 72 fit?
It approximates doubling math: 72 divided by percent gives years, close to exact.
Does CAGR include dividends?
Only with total return values. Price only series understate it.
Why not just total gain?
Totals ignore time. Ten years to double differs from five.