How to Calculate Compound Annual Growth Rate (CAGR)
CAGR Calculator
Calculation Results
CAGR = ((Ending Value / Starting Value) ^ (1 / Number of Years)) – 1
This formula annualizes the growth rate of an investment over a specified period, smoothing out volatility.
Intermediate Values:
CAGR Data Visualization
CAGR Data Table
| Year | Starting Value | Ending Value | Annual Growth Rate |
|---|---|---|---|
| Enter values to see the table. | |||
What is Compound Annual Growth Rate (CAGR)?
The Compound Annual Growth Rate (CAGR) is a financial metric that represents the mean annual growth rate of an investment over a specified period of time greater than one year. It's essentially a way to smooth out volatile returns and provide a single, representative annual growth figure. CAGR is widely used to compare the historical performance of different investments, even if their volatility varied significantly over the period. It's crucial to understand that CAGR is a hypothetical rate; it doesn't represent actual year-to-year returns but rather the steady rate at which an investment would have grown if it had compounded at a steady pace.
Who Should Use CAGR? Investors, financial analysts, business owners, and portfolio managers frequently use CAGR. It's particularly useful for:
- Assessing the historical performance of stocks, bonds, mutual funds, or entire portfolios.
- Evaluating the growth of a company's revenue, profits, or market share over time.
- Comparing the growth trajectories of different assets or businesses.
- Setting realistic growth targets for future periods.
Common Misunderstandings A key misunderstanding is that CAGR reflects actual year-over-year returns. It does not account for the volatility or risk associated with achieving that growth. An investment with a high CAGR might have experienced significant fluctuations, while another with a slightly lower CAGR might have had a smoother, more predictable growth path. Also, CAGR is not a predictor of future performance; it only describes past trends.
CAGR Formula and Explanation
The formula for calculating Compound Annual Growth Rate is as follows:
CAGR = [ (EV / SV)1/n ] – 1
Where:
- EV = Ending Value (the value of the investment at the end of the period)
- SV = Starting Value (the value of the investment at the beginning of the period)
- n = Number of Years (the total number of years over which the growth occurred)
The result of this formula is a decimal. To express it as a percentage, you multiply by 100.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| EV (Ending Value) | Final value of the investment or metric. | Unitless (e.g., dollars, shares, revenue) | Non-negative, typically greater than SV |
| SV (Starting Value) | Initial value of the investment or metric. | Unitless (e.g., dollars, shares, revenue) | Positive |
| n (Number of Years) | Duration of the investment period in years. | Years | > 1 |
| CAGR | Compound Annual Growth Rate. | Percentage (%) | Varies widely; can be negative, zero, or positive. |
Practical Examples of CAGR Calculation
Example 1: Investment Growth
Suppose you invested $10,000 in a mutual fund five years ago, and today it's worth $18,000.
- Starting Value (SV): $10,000
- Ending Value (EV): $18,000
- Number of Years (n): 5
Using the CAGR formula:
CAGR = [ ($18,000 / $10,000)1/5 ] – 1
CAGR = [ (1.8)0.2 ] – 1
CAGR = [ 1.1247 ] – 1
CAGR = 0.1247
As a percentage: 0.1247 * 100 = 12.47%
This means your investment grew at an average annual rate of 12.47% over the five years.
Example 2: Business Revenue Growth
A small business had revenues of $500,000 in 2019 and $750,000 in 2023.
- Starting Value (SV): $500,000 (Revenue in 2019)
- Ending Value (EV): $750,000 (Revenue in 2023)
- Number of Years (n): 4 (2023 – 2019)
Using the CAGR formula:
CAGR = [ ($750,000 / $500,000)1/4 ] – 1
CAGR = [ (1.5)0.25 ] – 1
CAGR = [ 1.1067 ] – 1
CAGR = 0.1067
As a percentage: 0.1067 * 100 = 10.67%
The business's revenue experienced a compound annual growth rate of 10.67% between 2019 and 2023.
How to Use This CAGR Calculator
Our CAGR calculator simplifies the process of determining your investment's or metric's growth rate. Here's how to use it:
- Input Starting Value: Enter the initial amount or value of your investment or metric. This is your 'SV'.
- Input Ending Value: Enter the final amount or value at the end of the period. This is your 'EV'.
- Input Number of Years: Enter the total duration, in whole years, over which the growth occurred. This is your 'n'.
- Click Calculate: Press the "Calculate CAGR" button.
The calculator will instantly display:
- CAGR: The primary result, shown as a percentage.
- Growth Factor: The ratio of the ending value to the starting value.
- Arithmetic Average Annual Return: A simple average of annual returns (different from CAGR).
- Total Growth Percentage: The overall percentage increase from start to end.
You can also view a detailed breakdown in the table and a projected growth chart, and use the "Copy Results" button to save or share the output. The "Reset" button clears all fields for a new calculation.
Key Factors That Affect CAGR
While CAGR provides a smoothed-out view, several factors influence the actual growth path and the resulting CAGR:
- Initial Investment Amount (Starting Value): A larger starting value generally means a larger absolute gain for the same percentage CAGR, but the CAGR itself is less sensitive to the initial amount than the total return.
- Ending Value: This is a direct driver of CAGR. Higher ending values naturally lead to higher CAGRs, assuming the starting value and timeframe remain constant.
- Time Horizon (Number of Years): The longer the investment period, the more impact compounding has. A shorter period might show a higher CAGR, but it's less representative of long-term performance.
- Volatility: While CAGR smooths volatility, extreme ups and downs in value can still influence the final CAGR. A volatile investment might require a higher CAGR to achieve the same ending value as a stable one.
- Reinvested Dividends/Interest: For investments like stocks or bonds, the reinvestment of dividends or interest payments is crucial for maximizing compound growth. CAGR calculations assume reinvestment.
- Market Conditions and Economic Factors: Broader economic trends, interest rate changes, inflation, and industry-specific performance significantly impact asset values and thus CAGR.
- Fees and Taxes: Management fees, trading costs, and taxes reduce the net return. The CAGR calculated here is typically a pre-tax, pre-fee figure unless explicitly adjusted.
- Inflation: While CAGR shows nominal growth, real growth (adjusted for inflation) is often a more accurate measure of purchasing power increase.
Frequently Asked Questions (FAQ) about CAGR
Average annual return (arithmetic mean) simply sums up the annual returns and divides by the number of years. CAGR (geometric mean) accounts for the effect of compounding, providing a more accurate picture of the investment's growth over time, especially for volatile investments.
Yes, if the ending value is less than the starting value, the CAGR will be negative, indicating an overall loss in value over the period.
A CAGR of 0% means the investment's value remained the same from the beginning to the end of the period, with no net growth.
No, CAGR is a measure of historical growth rate and does not directly incorporate risk. Two investments with the same CAGR might have had very different risk profiles.
The standard CAGR formula requires the number of years ('n'). For periods not in whole years, you can use fractional years (e.g., 5.5 years). Our calculator expects a whole number but can be adapted for fractions.
CAGR is based on historical data and is not a reliable predictor of future performance. It describes past trends, not future outcomes.
The standard CAGR formula is best suited for lump-sum investments without interim cash flows. For investments with additions or withdrawals, metrics like the Internal Rate of Return (IRR) or time-weighted returns are more appropriate.
CAGR doesn't reflect volatility, risk, interim cash flows, fees, or taxes. It's a simplified metric for historical comparison.
Related Tools and Resources
Explore these related tools and articles to deepen your financial understanding:
- Simple Interest Calculator: Understand basic interest calculations.
- Compound Interest Calculator: Explore how interest accrues over time.
- Return on Investment (ROI) Calculator: Calculate the profitability of an investment.
- Inflation Calculator: See how inflation affects purchasing power.
- Understanding the Time Value of Money: Learn fundamental financial concepts.
- Key Investment Performance Metrics: A guide to evaluating investments.