What constant annual growth rate links a starting value to an ending value?
CAGR compresses a multi-year change into one compounded annual rate. It is a smoothing measure: the real path may have risen and fallen sharply even when the reported CAGR looks steady.
The compounded root of the value change
Growth multiple = Ending value ÷ Starting valueCAGR = [Growth multiple^(1 ÷ Years held) − 1] × 100Linking two values across several years
The default values describe a beginning amount, an ending amount and the years between them. The calculation finds the annual rate that would compound the first figure into the second.
Illustrative inputs; currency amounts below use USD. Rates and prices are assumptions, not live quotes.
- Starting value
- $10,000.00
- Ending value
- $18,000.00
- Years held
- 5
Step-by-step calculation
- Growth multiple = 18,000 ÷ 10,000 = 1.8.
- Annualise over 5 years: (1.8^(1 ÷ 5) − 1) × 100 = 12.474611%.
- Check by compounding: 10,000 × (1 + CAGR ÷ 100)^5 returns 18,000 before rounding.
Intermediate figures are rounded for reading. Results use the full calculation precision.
A smooth equivalent, not a yearly history
CAGR is useful for comparing growth over equal or different horizons because time is built into the rate. It should be read as an equivalent pace, not the return earned in every individual year.
When CAGR becomes misleading
An arithmetic average of yearly percentage changes is not CAGR. Compounding depends on multiplication across periods, and a zero or negative starting value cannot support the standard formula.
- The starting value is positive and the period is longer than zero years.
- No deposits or withdrawals occur between the start and end.
- The result describes a smooth equivalent rate, not actual yearly volatility.
Calculations related to cagr
The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.
References
Sources and conventions
- SEC Investor.gov: compound growth
A comparison tool for compound growth assumptions, not a promised investment return.
Quick answers
Frequently asked questions
Is CAGR the same as average annual return?
No. CAGR is a compounded annual rate and is generally more meaningful than the arithmetic average of yearly returns.
Does CAGR show investment volatility?
No. Different return paths can produce the same CAGR when their starting and ending values match.
What does years to double mean?
It estimates the time required to double at the calculated positive CAGR, assuming that rate continues.
Calculation method and limitations · Report an error
Educational content only. This guide is not financial advice.