CAGR Calculator
Calculate the Compound Annual Growth Rate (CAGR) for your investments or business metrics.
CAGR Calculation Inputs
Calculation Results
This formula calculates the average annual growth rate of an investment over a specified period, assuming profits were reinvested at the end of each year.
Investment Growth Over Time (CAGR Projection)
What is CAGR?
CAGR stands for Compound Annual Growth Rate. It's a financial metric used to measure the average annual rate at which an investment has grown over a specific period longer than one year. Unlike simple average growth, CAGR takes into account the effect of compounding, meaning that growth in one period contributes to growth in subsequent periods. It provides a smoothed-out rate of return, making it easier to compare the performance of different investments or to track the growth of a business over time.
Who should use it? CAGR is invaluable for investors looking to assess the historical performance of stocks, mutual funds, or other assets. Business owners and financial analysts use it to track revenue growth, profit margins, or customer acquisition rates. Essentially, anyone interested in understanding the consistent growth trajectory of a value over multiple years can benefit from calculating CAGR.
Common misconceptions: A frequent misunderstanding is that CAGR represents the actual year-to-year growth. In reality, CAGR is a hypothetical constant rate that would yield the same ending value from the same starting value over the same period. Actual returns can fluctuate significantly year by year. Another misconception is that CAGR is a predictor of future performance; it's a historical measure and doesn't guarantee future results.
CAGR Formula and Mathematical Explanation
The Compound Annual Growth Rate (CAGR) formula is designed to provide a single, representative annual growth figure over a multi-year period. It smooths out volatility and presents a clear picture of consistent growth.
The core formula is:
CAGR = [ (Ending Value / Starting Value) ^ (1 / Number of Years) ] – 1
Let's break down the components:
- Ending Value (EV): This is the value of the investment or metric at the end of the period.
- Starting Value (SV): This is the value of the investment or metric at the beginning of the period.
- Number of Years (n): This is the total duration of the investment period in years. It must be greater than zero.
Mathematical Derivation:
Imagine an investment grows from SV to EV over 'n' years. If it grew at a constant annual rate 'r' (which is CAGR), the value after each year would be:
- Year 1: SV * (1 + r)
- Year 2: [SV * (1 + r)] * (1 + r) = SV * (1 + r)^2
- …
- Year n: SV * (1 + r)^n
We know that the value after 'n' years is the Ending Value (EV). So, we have the equation:
EV = SV * (1 + r)^n
To solve for 'r' (CAGR), we rearrange the equation:
- Divide both sides by SV: EV / SV = (1 + r)^n
- Raise both sides to the power of (1/n) to isolate the (1 + r) term: (EV / SV)^(1/n) = 1 + r
- Subtract 1 from both sides to find 'r': r = (EV / SV)^(1/n) – 1
The result 'r' is the CAGR, typically expressed as a percentage by multiplying by 100.
CAGR Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| EV (Ending Value) | Final value of the investment or metric | Currency (e.g., $, €, £) or Unit (e.g., users, revenue) | Positive number, typically greater than SV for growth |
| SV (Starting Value) | Initial value of the investment or metric | Currency or Unit | Positive number |
| n (Number of Years) | Duration of the period in years | Years | Positive integer or decimal > 0 |
| CAGR | Compound Annual Growth Rate | Percentage (%) | Can be positive, negative, or zero |
Practical Examples (Real-World Use Cases)
Understanding how to calculate CAGR is best illustrated with practical scenarios:
Example 1: Investment Growth
An investor purchased shares for $10,000 five years ago. Today, those shares are worth $25,000. What is the CAGR of this investment?
- Starting Value (SV): $10,000
- Ending Value (EV): $25,000
- Number of Years (n): 5
Using the CAGR formula:
CAGR = [ ($25,000 / $10,000) ^ (1 / 5) ] – 1
CAGR = [ (2.5) ^ (0.2) ] – 1
CAGR = [ 1.2011 ] – 1
CAGR = 0.2011
Expressed as a percentage: 20.11%
Interpretation: This investment grew at an average annual rate of 20.11% over the five-year period, considering the effects of compounding.
Example 2: Business Revenue Growth
A small e-commerce business had $50,000 in revenue in 2019. By 2023, its revenue had grown to $120,000. What was the CAGR of its revenue?
- Starting Value (SV): $50,000 (Revenue in 2019)
- Ending Value (EV): $120,000 (Revenue in 2023)
- Number of Years (n): 4 (2023 – 2019 = 4 years)
Using the CAGR formula:
CAGR = [ ($120,000 / $50,000) ^ (1 / 4) ] – 1
CAGR = [ (2.4) ^ (0.25) ] – 1
CAGR = [ 1.2457 ] – 1
CAGR = 0.2457
Expressed as a percentage: 24.57%
Interpretation: The business's revenue grew at an average annual rate of 24.57% between 2019 and 2023.
How to Use This CAGR Calculator
Our CAGR calculator is designed for simplicity and accuracy. Follow these steps to get your CAGR results:
- Enter Starting Value: Input the initial value of your investment or metric in the "Starting Value" field. This could be the purchase price of a stock, the initial investment amount, or the revenue from the first year.
- Enter Ending Value: Input the final value of your investment or metric in the "Ending Value" field. This is the current market value or the revenue from the last year in your period.
- Enter Number of Years: Specify the total duration of the period in years in the "Number of Years" field. Ensure this value is greater than zero.
- Calculate: Click the "Calculate CAGR" button. The calculator will instantly compute the Compound Annual Growth Rate.
How to read results:
- CAGR (%): This is your primary result, displayed prominently. A positive percentage indicates growth, while a negative percentage indicates a decline.
- Intermediate Values: The calculator also displays your input values (Starting Value, Ending Value, Number of Years) for easy reference and confirmation.
- Chart and Table: The accompanying chart visually represents the projected growth based on the calculated CAGR, comparing it to a linear growth path. The table provides a structured view of the inputs and outputs.
Decision-making guidance: Use the calculated CAGR to compare the performance of different investments, assess the effectiveness of business strategies, or set realistic future growth targets. A higher CAGR generally indicates better performance.
Key Factors That Affect CAGR Results
While the CAGR formula is straightforward, several underlying factors influence the inputs and the interpretation of the results:
- Time Horizon (Number of Years): The longer the period, the more significant the impact of compounding. A short period might show misleadingly high or low CAGR due to temporary market fluctuations. A longer period provides a more stable and representative growth rate.
- Starting and Ending Values: The magnitude of these values directly impacts the CAGR. A small change in either the starting or ending value can significantly alter the calculated rate, especially over shorter time frames.
- Volatility of Returns: CAGR smooths out year-to-year fluctuations. An investment with a high CAGR might have experienced significant ups and downs, while another with a lower CAGR might have shown steady, consistent growth. Understanding this difference is crucial for risk assessment.
- Inflation: CAGR is a nominal rate. To understand the real growth in purchasing power, you need to adjust the CAGR for inflation. Subtracting the average inflation rate from the CAGR gives you the Compound Annual Growth Rate in real terms.
- Fees and Expenses: Investment fees (management fees, transaction costs) reduce the actual returns. The CAGR calculation typically uses gross values unless net values (after fees) are specifically used as inputs. Always consider the impact of fees on your net growth.
- Taxes: Capital gains taxes and income taxes on investment returns reduce the final amount received. CAGR doesn't account for tax implications. The effective post-tax return will be lower than the calculated CAGR.
- Cash Flows (Contributions/Withdrawals): The standard CAGR formula assumes a single initial investment and no further contributions or withdrawals. If you've added or removed money during the period, the IRR (Internal Rate of Return) is a more appropriate metric.
Frequently Asked Questions (FAQ)
A1: Simple average annual return calculates the arithmetic mean of yearly returns, ignoring compounding. CAGR accounts for compounding, providing a more accurate representation of growth over multiple periods.
A2: 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.
A3: A "good" CAGR depends on the asset class, market conditions, and risk tolerance. Historically, the stock market has averaged around 7-10% CAGR over long periods. For businesses, a CAGR of 15-20% or higher might be considered excellent, but context is key.
A4: No. CAGR is a historical measure. While it indicates past growth trends, it does not guarantee future results due to market volatility and changing economic conditions.
A5: The standard CAGR formula is not suitable for periods with multiple cash flows. You should use the Internal Rate of Return (IRR) calculation instead, which accounts for the timing and amount of each cash flow.
A6: CAGR requires a period longer than one year. The formula works for any period greater than zero years, but the results are more meaningful and stable over longer durations (e.g., 3-5 years or more).
A7: You can calculate CAGR for cryptocurrencies, but be aware that their extreme volatility means the CAGR might not reflect the actual investor experience due to significant price swings within the period. IRR might be more suitable if cash flows are involved.
A8: CAGR represents the annualized equivalent of the total return over the period. The total return is the overall percentage gain or loss, while CAGR breaks it down into an average annual rate.