CAGR Calculator
CAGR Calculator
Compound Annual Growth Rate
| Year | Beginning Balance | Smoothed Growth | Ending Balance |
|---|
What is CAGR? The Compound Annual Growth Rate represents the constant rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each year of the investment's lifespan.
Limitations: CAGR is a "smoothed" rate. In reality, investments (like stocks) fluctuate wildly from year to year. CAGR hides this volatility by only looking at the start and end points.
Formula: CAGR = [(Ending Value / Beginning Value) ^ (1 / Number of Years)] - 1
An investment's total return tells you how much its value has changed, but it does not explain how quickly that change occurred each year. Growing an investment from $10,000 to $20,000 over five years is very different from doubling the same amount over fifteen years. The final gain is identical, but the pace of growth is not.
A CAGR Calculator helps measure that pace by calculating the Compound Annual Growth Rate. It converts an investment's starting value, ending value, and holding period into one annualized growth rate. Investors use this metric to evaluate historical performance, compare assets, measure business growth, and understand how compounding influences long-term results.
CAGR is especially useful when annual results fluctuate. Rather than treating each year's return as a separate figure, it calculates the steady annual compound rate that would connect the initial value to the final value. The result makes comparisons easier, but it should not be mistaken for the actual return earned in every year.
What Is CAGR?
CAGR stands for Compound Annual Growth Rate. It represents the annualized rate at which an investment or another measurable value would have grown if it had increased at a constant compound rate throughout a specified period.
For example, suppose an investment increases from $10,000 to $16,000 over five years. Its total growth is $6,000, or 60%. However, 60% is the cumulative return, not the annual growth rate.
CAGR expresses that five-year change as an annual compound rate of approximately 9.86%. In other words, growing $10,000 at a constant annual compound rate of about 9.86% for five years would produce a final value of approximately $16,000.
The actual investment might have gained 15% in one year, lost 4% in another, and experienced different returns in the remaining years. CAGR summarizes the overall result without showing those individual movements.
CAGR Calculator Formula
The standard CAGR formula is:
Where:
- (EV) = ending value of the investment
- (BV) = beginning value of the investment
- (n) = investment period in years
Multiply the result by 100 to express CAGR as a percentage.
The calculation has three main steps. First, divide the ending value by the beginning value to determine the total growth multiple. Next, raise that multiple to the power of (1/n), which converts the full-period growth into an annual compound factor. Finally, subtract 1 to isolate the annual growth rate.
The formula requires a positive beginning value and a positive ending value for the usual investment-growth interpretation. The period must also be greater than zero. If the investment loses value but remains positive, CAGR can still be calculated and will be negative.
<LearningViz type_id="COMPOUND_INTEREST" initial_values={{"amount":10000,"ratePercent":9.86,"periods":5}}>
</LearningViz>
This interactive illustration shows the relationship between an initial amount, an annual compound rate, and time. CAGR works backward from the beginning and ending values to find the annual rate that connects them.
How to Calculate CAGR: A Worked Example
Consider an investor who purchases an asset for $25,000. After six years, the asset is worth $40,000. To find its compound annual growth rate, use the following inputs:
| Input | Value |
|---|---|
| Beginning value | $25,000 |
| Ending value | $40,000 |
| Investment period | 6 years |
Substitute these values into the formula:
Converting the decimal into a percentage gives:
The asset's compound annual growth rate was approximately 8.15% per year over the six-year period. This does not mean its value rose by exactly 8.15% every year. It means that a steady compound rate of 8.15% would produce approximately the same overall change.
CAGR vs. Total Return
CAGR and total return measure different aspects of investment performance. Total return describes the overall gain or loss over a period, while CAGR expresses the equivalent annual compound rate.
Suppose an investment grows from $10,000 to $15,000 over five years. Its total appreciation is $5,000, and its cumulative price return is 50%, assuming no additional contributions, withdrawals, or separately accounted-for distributions.
The CAGR is:
The investment gained 50% overall, equivalent to an annual compound growth rate of about 8.45%. These figures are not interchangeable. Reporting only the cumulative return can make it difficult to compare investments held for different lengths of time.
For a fair comparison, ensure that the beginning and ending values are measured consistently. If dividends, interest, fees, taxes, or cash flows are relevant, determine whether they are included in the values being compared.
CAGR vs. Average Annual Return
A simple average annual return is calculated by adding the annual returns and dividing by the number of years. CAGR instead accounts for compounding across the entire period.
Imagine an investment that rises by 20% in the first year and falls by 10% in the second year. The arithmetic average return is:\\frac{20%+(-10%)}{2}=5%
However, an initial investment of $100 becomes $120 after the first year and then falls to $108 after the second year.
Its CAGR is:
The simple average is 5%, while the CAGR is approximately 3.92%. The difference occurs because percentage gains and losses compound on changing balances. CAGR captures the overall compounded result more accurately, although it does not describe the path taken to reach that result.
What does CAGR stand for?
CAGR stands for Compound Annual Growth Rate. It measures the annualized compound rate that connects an initial value to a final value over a specified period.
What is a good CAGR?
There is no universal rate that qualifies as good. It depends on the asset, time period, inflation, risk, fees, and the performance of relevant benchmarks. A higher CAGR may indicate stronger historical growth, but it does not necessarily mean an investment is safer or more suitable.
Can CAGR be negative?
Yes. If the ending value is lower than the beginning value but both remain positive, the calculated CAGR will be negative. This represents an annualized compound decline over the period.
Can CAGR be calculated for less than one year?
An annualized rate can be calculated for a period shorter than one year using the actual fraction of a year. However, short-period results can be misleading when annualized because a brief price movement may not reflect a sustainable yearly rate.
Does CAGR include dividends?
Not automatically. If you calculate CAGR from beginning and ending market prices alone, dividends may be excluded. To measure total investment performance, use values or return data that appropriately account for distributions and reinvestment.
Is CAGR the same as IRR?
No. CAGR uses beginning value, ending value, and elapsed time to calculate an equivalent annual compound rate. Internal Rate of Return (IRR) accounts for the timing and amount of multiple cash flows. When contributions or withdrawals occur throughout an investment period, IRR or XIRR may provide a more meaningful return measure.
Can CAGR predict future returns?
CAGR can be used as an assumption in a future-value projection, but historical CAGR cannot reliably predict what will happen next. Future returns depend on market conditions, asset characteristics, and other uncertain factors.
How do I calculate CAGR manually?
Divide the ending value by the beginning value, raise the result to the power of one divided by the number of years, subtract one, and multiply by 100 to express the result as a percentage.