CAGR Calculator Formula
Understand the math behind the cagr calculator. Each variable explained with a worked example.
Formulas Used
CAGR
cagr = (pow(ending_value / beginning_value, 1 / years) - 1) * 100Total Return
total_return = (ending_value - beginning_value) / beginning_value * 100Absolute Gain
absolute_gain = ending_value - beginning_valueVariables
| Variable | Description | Default |
|---|---|---|
beginning_value | Beginning Value(USD) | 10000 |
ending_value | Ending Value(USD) | 25000 |
years | Number of Years(years) | 5 |
How It Works
CAGR Formula
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
CAGR smooths out the return over the period, giving you the consistent annual rate that would produce the same final result.
Worked Example
$10,000 invested grows to $25,000 in 5 years.
- 01CAGR = (25000/10000)^(1/5) - 1
- 02= 2.5^0.2 - 1
- 03= 1.2011 - 1 = 0.2011
- 04CAGR = 20.11%
- 05Total return = 150%
When to Use This Formula
- Reporting the annualized growth rate of revenue, portfolio value, or user base over a multi-year period in a way that smooths out yearly volatility.
- Comparing the performance of two investments held for different lengths of time by normalizing both to an equivalent annual growth rate.
- Forecasting future values by projecting a historically observed CAGR forward — for example, estimating what a market growing at 8% CAGR will be worth in 10 years.
- Benchmarking a company's growth rate against industry averages or competitors, where CAGR is the standard metric used in analyst reports.
- Evaluating fund manager performance by calculating the annualized return, which accounts for compounding and is directly comparable to benchmark indices.
Common Mistakes to Avoid
- Confusing CAGR with average annual return — CAGR accounts for compounding while a simple average of yearly returns does not, and the two can differ significantly when returns are volatile.
- Using the wrong number of periods — CAGR uses the number of years between the beginning and ending values, not the number of data points. If you have values for 2020 through 2025, n is 5, not 6.
- Assuming CAGR represents what actually happened each year — it is a smoothed, hypothetical constant rate that produces the same endpoint, and the actual path may have included large gains and losses.
- Applying CAGR to short periods where it exaggerates small changes — a 10% increase over 3 months annualizes to roughly 46% CAGR, which is misleading if the growth is not sustainable.
- Forgetting that CAGR cannot be calculated when the beginning value is zero or negative — the formula requires dividing by the beginning value and raising the result to a power, both of which fail with zero or negative inputs.
Frequently Asked Questions
What does CAGR tell you?
CAGR shows the annualized growth rate assuming smooth compounding. It is useful for comparing investments with different time periods.
What is a good CAGR?
A good CAGR depends on the asset class. The S&P 500 has historically delivered about 10% CAGR over long periods. A CAGR above 15% is considered excellent, while anything above 25% sustained over many years is exceptionally rare.
How is CAGR different from average annual return?
Average annual return is a simple arithmetic mean of each year's return, which can be misleading when returns are volatile. CAGR accounts for compounding and tells you the single steady rate that would have produced the same end result, making it more accurate for measuring actual growth.
Learn More
Guide
How to Calculate ROI (Return on Investment)
Learn how to calculate ROI for investments, business projects, and real estate. Covers the basic ROI formula, annualized returns, CAGR, and common pitfalls in ROI analysis.
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Open CAGR Calculator