Compound Growth Rate Calculator
Calculate the compound annual growth rate (CAGR) of your investment or business metrics over time.
How to Calculate Compound Growth Rate: The Complete Guide
The compound annual growth rate (CAGR) is one of the most important financial metrics for evaluating investment performance, business growth, and economic trends over multiple periods. Unlike simple growth rates, CAGR accounts for the compounding effect—where returns in each period are reinvested to generate additional returns in future periods.
Why CAGR Matters
CAGR provides a “smoothed” annual growth rate that helps compare investments with different time horizons. For example:
- A 10-year investment growing from $10,000 to $25,000 has a CAGR of 9.6%.
- A 5-year investment growing from $5,000 to $12,000 has a CAGR of 18.9%.
Without CAGR, comparing these investments would be misleading because their timeframes differ.
The CAGR Formula
The standard CAGR formula is:
CAGR = (EV / BV)(1 / n) - 1
- EV = Ending Value
- BV = Beginning Value
- n = Number of years
Step-by-Step Calculation
- Identify the beginning and ending values (e.g., $10,000 → $25,000).
- Determine the time period in years (e.g., 5 years).
- Divide the ending value by the beginning value (25,000 / 10,000 = 2.5).
- Raise the result to the power of (1 / n) (2.50.2 ≈ 1.193).
- Subtract 1 and convert to a percentage (1.193 – 1 = 0.193 → 19.3%).
CAGR vs. Simple Growth Rate
| Metric | Formula | Use Case | Example (5 years, $10k → $25k) |
|---|---|---|---|
| CAGR | (EV/BV)(1/n) – 1 | Multi-period growth (investments, revenue) | 19.3% |
| Simple Growth | (EV – BV) / BV / n | Linear growth (short-term trends) | 30% (misleading for compounding) |
Real-World Applications
1. Investment Performance
CAGR is the standard for comparing mutual funds, ETFs, and stocks. For example, the S&P 500’s CAGR from 1926–2023 is approximately 10.2% (source: SSA Historical Returns).
2. Business Revenue Growth
Companies use CAGR to report revenue growth over 3–5 years. Example:
| Company | 2018 Revenue | 2023 Revenue | 5-Year CAGR |
|---|---|---|---|
| Apple | $265.6B | $383.3B | 7.8% |
| Amazon | $232.9B | $574.8B | 20.1% |
Common Mistakes to Avoid
- Ignoring time periods: CAGR requires consistent units (e.g., years). Mixing months and years distorts results.
- Using simple averages: Averaging annual returns (e.g., 10%, -5%, 12% → 9%) ≠ CAGR (which would be ~8.6%).
- Neglecting fees/taxes: CAGR assumes no withdrawals or costs. Adjust inputs for real-world scenarios.
Advanced: Modified CAGR
For irregular cash flows (e.g., periodic contributions), use the Modified Dietz Method or XIRR (Excel function). Example:
=XIRR(values_range, dates_range, [guess])
Authoritative Resources
- U.S. SEC Guide to Compound Interest (Regulatory definitions)
- Investor.gov CAGR Calculator (Government tool)
- CFI’s CAGR Explanation (Detailed examples)