Compound Annual Growth Rate Calculator: Measure Growth Accurately
The Compound Annual Growth Rate (CAGR) represents the mean annual growth rate of an investment, business metric, or financial variable over a specified time period longer than one year. Unlike simple average growth rates that can distort performance by ignoring compounding effects and volatility, CAGR provides a smoothed rate that represents steady year-over-year growth from beginning to ending value. Understanding CAGR calculations enables investors to compare investment returns across different timeframes, evaluate business growth trajectories, assess historical performance accurately, and project future values using consistent growth assumptions. This comprehensive calculator helps you compute CAGR for investments, revenue growth, population changes, and any metric requiring annualized growth rate analysis.
Compound Annual Growth Rate Calculators
Calculate CAGR
Investment CAGR with Additional Contributions
Calculate Future or Past Value
Compare Multiple Growth Rates
Option A
Option B
Understanding CAGR
The Compound Annual Growth Rate smooths out volatility and irregular growth patterns to present a single annualized rate that would produce the same result if growth occurred steadily each year. For example, if an investment grows from $10,000 to $18,000 over five years with significant ups and downs, CAGR calculates the equivalent constant annual growth rate that would take you from beginning to ending value. This provides a clear, comparable metric for evaluating performance across different timeframes and investments.
CAGR proves particularly valuable when comparing investments with different time horizons or assessing business metrics that fluctuate year-to-year. Rather than averaging simple year-over-year growth rates—which can produce misleading results due to mathematical quirks—CAGR accounts for compounding effects and provides the true geometric mean growth rate. This makes CAGR the standard metric for reporting long-term investment returns, revenue growth, user acquisition rates, and any metric requiring consistent annualized growth measurement.
CAGR Formula
The CAGR formula calculates the constant annual rate that would grow an initial value to a final value over a specified time period.
\[ \text{CAGR} = \left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{\text{Number of Years}}} - 1 \]
Or equivalently:
\[ \text{CAGR} = \left(\frac{V_f}{V_i}\right)^{\frac{1}{t}} - 1 \]
Where:
\( V_f \) = Final value
\( V_i \) = Initial value
\( t \) = Time period in years
In percentage form:
\[ \text{CAGR} = \left[\left(\frac{V_f}{V_i}\right)^{\frac{1}{t}} - 1\right] \times 100\% \]
Basic CAGR Example
Investment Scenario:
- Initial Investment: $10,000
- Value After 5 Years: $18,000
- Time Period: 5 years
Apply CAGR Formula:
\[ \text{CAGR} = \left(\frac{\$18{,}000}{\$10{,}000}\right)^{\frac{1}{5}} - 1 \] \[ \text{CAGR} = (1.8)^{0.2} - 1 \] \[ \text{CAGR} = 1.1248 - 1 = 0.1248 \] \[ \text{CAGR} = 12.48\% \]Results:
- CAGR: 12.48% per year
- Total Growth: 80% over 5 years
- Average Annual Growth: 12.48%
Interpretation: If your investment grew at a steady 12.48% annually for five years, it would grow from $10,000 to exactly $18,000. This smoothed rate makes it easy to compare with other investments or benchmark returns.
Verification:
\[ \$10{,}000 \times (1.1248)^5 = \$10{,}000 \times 1.8 = \$18{,}000 \]Step-by-Step CAGR Calculation
Detailed Calculation Example
Business Revenue Growth:
- Revenue in Year 1: $500,000
- Revenue in Year 6: $1,200,000
- Time Period: 5 years (Year 1 to Year 6)
Step 1: Calculate Growth Ratio
\[ \text{Growth Ratio} = \frac{\$1{,}200{,}000}{\$500{,}000} = 2.4 \]Step 2: Apply Exponent (nth Root)
\[ \text{Root} = 2.4^{\frac{1}{5}} = 2.4^{0.2} \]Using calculator or logarithms:
\[ 2.4^{0.2} = 1.1914 \]Step 3: Subtract 1 and Convert to Percentage
\[ \text{CAGR} = 1.1914 - 1 = 0.1914 = 19.14\% \]Annual Growth Breakdown:
| Year | Beginning Value | Growth (19.14%) | Ending Value |
|---|---|---|---|
| Year 1-2 | $500,000 | $95,700 | $595,700 |
| Year 2-3 | $595,700 | $114,000 | $709,700 |
| Year 3-4 | $709,700 | $135,800 | $845,500 |
| Year 4-5 | $845,500 | $161,800 | $1,007,300 |
| Year 5-6 | $1,007,300 | $192,700 | $1,200,000 |
Analysis: The business revenue grew from $500,000 to $1,200,000 over five years, representing a 19.14% CAGR. While actual year-to-year growth likely varied, the CAGR provides a single metric showing equivalent steady annual growth.
CAGR vs. Average Growth Rate
Simple average growth rates can significantly misrepresent actual performance, especially with volatile values. CAGR provides accurate annualized growth while simple averages can distort reality.
Why Average Growth Rates Mislead
Investment Performance:
- Year 0: $10,000
- Year 1: $12,000 (20% growth)
- Year 2: $9,600 (-20% decline)
- Year 3: $11,520 (20% growth)
Simple Average Growth:
\[ \text{Average} = \frac{20\% + (-20\%) + 20\%}{3} = \frac{20\%}{3} = 6.67\% \]Actual CAGR:
\[ \text{CAGR} = \left(\frac{\$11{,}520}{\$10{,}000}\right)^{\frac{1}{3}} - 1 \] \[ \text{CAGR} = (1.152)^{0.333} - 1 = 1.0483 - 1 = 4.83\% \]Comparison:
- Simple Average: 6.67%
- Actual CAGR: 4.83%
- Difference: 1.84 percentage points
Explanation: The simple average of 6.67% overstates actual growth because it ignores compounding effects. You gained $1,520 (15.2% total) over three years, which translates to 4.83% CAGR, not 6.67%. The simple average fails because percentage changes apply to different base amounts.
Key Insight: Never average percentage growth rates directly. Always use CAGR for accurate annualized growth measurement.
Calculating Future Values with CAGR
Once you know a CAGR, you can project future values assuming growth continues at the same rate.
\[ FV = PV \times (1 + \text{CAGR})^t \]
Where:
\( FV \) = Future value
\( PV \) = Present value
\( \text{CAGR} \) = Compound annual growth rate (as decimal)
\( t \) = Number of years
Future Value Projection
Scenario:
- Current Revenue: $2,000,000
- Historical CAGR: 15%
- Projection Period: 5 years
Calculate Projected Revenue:
\[ FV = \$2{,}000{,}000 \times (1.15)^5 \] \[ FV = \$2{,}000{,}000 \times 2.0114 \] \[ FV = \$4{,}022{,}800 \]Year-by-Year Projections:
- Year 1: $2,000,000 × 1.15 = $2,300,000
- Year 2: $2,300,000 × 1.15 = $2,645,000
- Year 3: $2,645,000 × 1.15 = $3,041,750
- Year 4: $3,041,750 × 1.15 = $3,498,013
- Year 5: $3,498,013 × 1.15 = $4,022,715
Interpretation: If the company maintains its 15% CAGR, revenue will approximately double from $2 million to $4 million over five years. This projection assumes consistent growth, though actual results will likely vary.
Calculating Past Values with CAGR
CAGR can also calculate historical values when you know current values and historical growth rates.
\[ PV = \frac{FV}{(1 + \text{CAGR})^t} \]
Or equivalently:
\[ PV = FV \times (1 + \text{CAGR})^{-t} \]
Historical Value Example
Scenario:
- Current Stock Price: $150
- Known CAGR: 12% over past 10 years
- Question: What was the stock price 10 years ago?
Calculate Historical Price:
\[ PV = \frac{\$150}{(1.12)^{10}} \] \[ PV = \frac{\$150}{3.1058} = \$48.30 \]Verification:
\[ \$48.30 \times (1.12)^{10} = \$48.30 \times 3.1058 = \$150 \]Interpretation: If the stock currently trades at $150 and has grown at 12% CAGR for ten years, it traded at approximately $48.30 a decade ago. The stock more than tripled in value through consistent compound growth.
CAGR Applications
Investment Returns
CAGR standardizes investment returns across different time periods, enabling direct comparison between a 3-year investment and a 10-year investment. Portfolio managers report CAGR to demonstrate long-term performance smoothed over multiple market cycles.
Business Growth
Companies report revenue, earnings, and user growth using CAGR to communicate business trajectory to investors. A 25% revenue CAGR over five years signals strong business momentum more clearly than listing individual year-to-year growth rates.
Economic Indicators
Economists use CAGR to analyze GDP growth, population changes, inflation rates, and other macro indicators over multiple years. CAGR removes year-to-year volatility to reveal underlying trends.
Market Analysis
Industry analysts project market size using CAGR, such as "the AI market will grow at a 30% CAGR through 2030." This provides a single growth metric rather than complex year-by-year forecasts.
CAGR with Additional Contributions
When investments include regular contributions, calculating true CAGR becomes more complex. The money-weighted rate of return accounts for contribution timing.
Important Note: For investments with regular contributions, CAGR of the total value overstates returns since some money was invested for shorter periods. Use Internal Rate of Return (IRR) or time-weighted return for more accurate performance measurement when contributions occur throughout the period.
Limitations of CAGR
Ignores Volatility: CAGR smooths all fluctuations into a single rate. An investment with 50% gains and 40% losses shows a positive CAGR despite significant volatility and risk.
Assumes Steady Growth: CAGR implies constant growth, but actual performance typically varies dramatically year-to-year. Don't assume future growth will match historical CAGR.
Timing Insensitive: CAGR ignores when growth occurred. An investment might show negative returns for nine years then explode in year ten, producing high CAGR despite poor intermediate performance.
No Risk Adjustment: Two investments with identical CAGR may have vastly different risk profiles. CAGR alone doesn't indicate whether returns came from stable growth or risky speculation.
Contribution Complexity: When adding money over time, simple CAGR calculations become meaningless. The total value includes contributions made at different times, distorting apparent returns.
CAGR vs. Other Growth Metrics
| Metric | Use Case | Advantages | Limitations |
|---|---|---|---|
| CAGR | Long-term growth | Smooths volatility, easy comparison | Ignores interim fluctuations |
| Simple Average | Quick estimate | Easy to calculate | Mathematically incorrect for percentages |
| IRR | Irregular cash flows | Accounts for contribution timing | Complex calculation |
| Absolute Return | Total gain/loss | Simple, intuitive | No time adjustment |
Common Mistakes
- Averaging Growth Rates: Never calculate the arithmetic mean of annual growth percentages—use CAGR
- Ignoring Time Periods: Comparing a 5-year CAGR to a 10-year CAGR without context; longer periods typically show lower CAGR
- Extrapolating Forever: Assuming historical CAGR will continue indefinitely; all growth rates eventually moderate
- Misapplying to Contributions: Using basic CAGR formula when regular contributions occur throughout the period
- Overlooking Starting Points: CAGR varies dramatically based on start/end dates chosen; cherry-picking dates distorts reality
- Ignoring Survivorship Bias: Calculating CAGR only for surviving investments ignores failed ones that went to zero