CAGR Calculator
Find the compound annual growth rate (CAGR) between a start value and an end value, with a year-by-year path.
Results
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Year by year at this rate
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Quick Answer
CAGR = (end value ÷ start value) ^ (1 ÷ years) − 1. If $10,000 grows to $20,000 in 5 years, the CAGR is about 14.87% a year. That is the steady yearly rate that would double the money in 5 years.
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Table of Contents
- CAGR Calculator
- Quick Answer
- Related Calculators
- How This CAGR Calculator Works
- How to Use the CAGR Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- CAGR vs Average Annual Return
- Years to Double at Each CAGR
- CAGR, ROI and Average Return
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This CAGR Calculator Works
CAGR turns growth over several years into one steady yearly rate. It is used for investments, company revenue, prices and more. Enter a start value, an end value and the number of years.
Quick explanation: CAGR is the yearly rate that turns the start value into the end value, with compounding.
- Years: part years such as 2.5 are fine.
- Falling values: give a negative CAGR.
- Path: shows each year at the steady rate.
How to Use the CAGR Calculator
- Enter the start value, such as what an investment was worth at the beginning.
- Enter the end value.
- Enter the number of years between them. Part years are fine.
- Press Calculate.
- Read the CAGR and the year-by-year path at that steady rate.
Core Formulas
- CAGR: (end ÷ start) ^ (1 ÷ years) − 1
- Value after n years: start × (1 + CAGR) ^ n
- Total change: (end ÷ start − 1) × 100
Key Terms
- CAGR: compound annual growth rate, the steady yearly rate between two values.
- Compounding: growth that builds on earlier growth.
- Growth multiple: the end value divided by the start value.
- Rule of 72: a quick way to estimate doubling time: 72 ÷ yearly growth rate.
Worked Example
A company's revenue falls from $2.5 million to $1.8 million over 4 years.
- End ÷ start = 1.8 ÷ 2.5 = 0.72
- 0.72 ^ (1 ÷ 4) = 0.9212
- CAGR = -7.88% a year
Real-Life Examples
- A fund: $10,000 that grew to $18,000 in 6 years has a CAGR of 10.29% a year.
- A home's value: a house bought for $250,000 and worth $340,000 after 8 years grew at 3.92% a year.
- Business revenue: sales rising from $1.2 million to $2 million over 3 years is a CAGR of 18.56%.
- Up and down years: a stock that rises 50% and then falls 50% ends at 75% of its start. The CAGR over 2 years is -13.40%, even though the simple average return is 0%.
CAGR vs Average Annual Return
- Average return: adds up yearly returns and divides by the number of years. It ignores compounding.
- CAGR: the steady rate that links the start and end values, with compounding.
- Why it matters: when returns swing up and down, the average return can look much better than what you actually earned.
- Which to quote: use CAGR when you want to describe the real growth of money over several years.
Years to Double at Each CAGR
The rule of 72 is a quick estimate: 72 ÷ growth rate.
| CAGR | Exact years | Rule of 72 |
|---|---|---|
| 3% | 23.4 | 24.0 |
| 4% | 17.7 | 18.0 |
| 5% | 14.2 | 14.4 |
| 6% | 11.9 | 12.0 |
| 7% | 10.2 | 10.3 |
| 8% | 9.0 | 9.0 |
| 10% | 7.3 | 7.2 |
| 12% | 6.1 | 6.0 |
CAGR, ROI and Average Return
- ROI: total gain over the whole period, not per year.
- Average return: a simple average of yearly returns can overstate growth.
- CAGR: the compounded yearly rate, best for comparing over time.
- Deposits: CAGR ignores money added or taken out along the way.
Common Mistakes to Avoid
- Ignoring deposits and withdrawals. Added money inflates CAGR. Use start and end values without new money.
- Using the wrong number of years. Count the time between the two values, not the number of calendar years named.
- Reading it as a yearly guarantee. Real growth was rarely steady.
- Comparing different periods. A strong CAGR over a short, lucky period can mislead.
- Mixing up CAGR and total change. 100% total growth over 5 years is about 14.87% a year.
Frequently Asked Questions
Divide the end value by the start value, raise it to the power of 1 divided by the years, then subtract 1.
It depends on what you measure. Compare it with similar investments or companies over the same years.
Yes. If the end value is lower than the start value, the CAGR is negative.
ROI is the total return. CAGR is the steady yearly rate that gives the same result.
No. It only uses the start and end values.
About 10.2 years with compounding. The rule of 72 gives a quick estimate of 72 ÷ 7 ≈ 10.3 years.
It depends on the investment and its risk. Compare it with a broad market index or other options over the same years.
Multiply the start value by (1 + CAGR) raised to the number of years. $10,000 at 7% for 10 years grows to about $19,672.
Not quite. An interest rate is promised in advance. CAGR describes growth that already happened, smoothed into one yearly rate.
Yes. Enter the time in years, such as 0.5 for 6 months, and the result is still a yearly rate.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Investopedia, Compound Annual Growth Rate (CAGR) | CAGR definition and use. | https://www.investopedia.com/terms/c/cagr.asp |
| Wikipedia, Compound annual growth rate | The CAGR formula. | https://en.wikipedia.org/wiki/Compound_annual_growth_rate |