finance calculator

CAGR Calculator

Calculate compound annual growth rate between two values.

Formula Verified by Dr. Elizabeth Vance, PhD

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Inputs

Starting value$

Ending value$

Period (years)

Results

CAGR

8.45%

Start value$10,000

End value$15,000

Period5 years

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Save this page to compare the annualized growth rates of stocks, mutual funds, real estate, or business revenues over varying timeframes.

Formula

CAGR formula

CAGR = (End / Start)^(1 / Years) - 1

CAGR smooths total growth into an annualized rate.

Step by step

How the calculation works

1Enter starting and ending values.
2Enter period in years.
3Calculator annualizes total growth into CAGR.

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How to understand and use this calculator

What is Compound Annual Growth Rate (CAGR)?

Compound Annual Growth Rate (CAGR) is the geometric average rate of return at which an investment grows annually, assuming profits are reinvested (compounded) at the end of each year.

CAGR is a highly useful financial metric because it smooths out the volatile, irregular annual returns of an investment, presenting a single annualized rate that represents the investment's overall growth velocity.

Unlike a simple average rate of return, CAGR accounts for compounding, making it the industry standard for comparing the performance of different assets or portfolios over identical historical periods.

The Mathematical CAGR Formula

To calculate the Compound Annual Growth Rate, apply the geometric growth formula:

$$\text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1$$

Where:

* $\text{Ending Value}$ is the final balance of the investment.

* $\text{Beginning Value}$ is the initial principal amount.

* $n$ is the number of years in the investment term (can be fractional).

This formula solves for the single constant annual growth rate that connects the beginning and ending values over the specified time horizon.

CAGR vs. Average Annual Return (AAR)

Average Annual Return (AAR) is a simple arithmetic average of annual gains and losses. AAR can be highly misleading because it ignores the mathematical effects of compounding and losses.

For example, if an investment of $10,000 gains 100% in year one (value becomes $20,000) and loses 50% in year two (value becomes $10,000), the AAR is $(100\% - 50\%) / 2 = 25\%$. However, you have made zero dollars. The CAGR is $(10,000 / 10,000)^{0.5} - 1 = 0\%$, which accurately reflects the real financial outcome.

Limitations of CAGR: The Smoothed Reality Trap

CAGR is a representational metric. It assumes a steady, constant growth rate over the entire investment term. In reality, assets experience volatility, down years, and rapid climbs. CAGR is best used to summarize long-term trends, but should be paired with standard deviation or maximum drawdown metrics to evaluate risk.

Related concepts

AAR

Average Annual Return: a simple arithmetic average of annual investment return rates.

IRR

Internal Rate of Return: the annualized return rate calculated for portfolios with complex ongoing cash flows.

Geometric Mean

The mathematical averaging method used by CAGR to accurately compound multi-period returns.

Frequently Asked Questions

What does CAGR stand for?+

CAGR stands for Compound Annual Growth Rate. It measures the annualized average growth rate of an investment over a multi-year period.

What is the formula for CAGR?+

CAGR = (Ending Value / Beginning Value) ^ (1 / Years) - 1. It calculates the smoothed constant annual rate of return.

How does CAGR differ from average annual return?+

Average annual return is a simple arithmetic average of annual returns. CAGR is a geometric average that accounts for compounding and the impact of losses, reflecting the real rate of return.

Can CAGR be negative?+

Yes. If the final value of the investment is lower than the initial investment, the CAGR will be negative, indicating an annualized average loss.

Does CAGR account for portfolio volatility?+

No. CAGR smooths out annual fluctuations, assuming a constant rate of growth. It does not measure or reflect the risk or volatility of the underlying asset.

Is CAGR useful for comparing different investments?+

Yes. CAGR annualized performance, allowing you to compare a 3-year investment directly against a 10-year investment on an equal annual basis.

Can I calculate CAGR for periods under one year?+

Yes, but it is less common. You can use fractional years (e.g., 6 months = 0.5 years) in the formula, but annualized short-term returns can distort long-term expectations.

How do contributions affect CAGR calculations?+

CAGR assumes a single lump sum is invested at the beginning and grows to the end. It does not easily account for ongoing deposits or withdrawals, which require calculating Internal Rate of Return (IRR).

What is a good CAGR for a stock portfolio?+

Historically, a CAGR of 7% to 10% is considered strong for long-term equity portfolios, matching or exceeding historical index averages.

What is the difference between CAGR and IRR?+

CAGR measures growth from a single beginning value to an ending value. IRR (Internal Rate of Return) calculates returns for complex cash flows containing multiple recurring contributions or withdrawals.

How to understand and use this calculator

What is Compound Annual Growth Rate (CAGR)?

Compound Annual Growth Rate (CAGR) is the geometric average rate of return at which an investment grows annually, assuming profits are reinvested (compounded) at the end of each year.

The Mathematical CAGR Formula

To calculate the Compound Annual Growth Rate, apply the geometric growth formula:

$$\text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1$$

Where:

* $\text{Ending Value}$ is the final balance of the investment.

* $\text{Beginning Value}$ is the initial principal amount.

* $n$ is the number of years in the investment term (can be fractional).

This formula solves for the single constant annual growth rate that connects the beginning and ending values over the specified time horizon.

CAGR vs. Average Annual Return (AAR)

Average Annual Return (AAR) is a simple arithmetic average of annual gains and losses. AAR can be highly misleading because it ignores the mathematical effects of compounding and losses.

Limitations of CAGR: The Smoothed Reality Trap

Related concepts

AAR

Average Annual Return: a simple arithmetic average of annual investment return rates.

IRR

Internal Rate of Return: the annualized return rate calculated for portfolios with complex ongoing cash flows.

Geometric Mean

The mathematical averaging method used by CAGR to accurately compound multi-period returns.

Frequently Asked Questions

What does CAGR stand for?+

CAGR stands for Compound Annual Growth Rate. It measures the annualized average growth rate of an investment over a multi-year period.

What is the formula for CAGR?+

CAGR = (Ending Value / Beginning Value) ^ (1 / Years) - 1. It calculates the smoothed constant annual rate of return.

How does CAGR differ from average annual return?+

Average annual return is a simple arithmetic average of annual returns. CAGR is a geometric average that accounts for compounding and the impact of losses, reflecting the real rate of return.

Can CAGR be negative?+

Yes. If the final value of the investment is lower than the initial investment, the CAGR will be negative, indicating an annualized average loss.

Does CAGR account for portfolio volatility?+

No. CAGR smooths out annual fluctuations, assuming a constant rate of growth. It does not measure or reflect the risk or volatility of the underlying asset.

Is CAGR useful for comparing different investments?+

Yes. CAGR annualized performance, allowing you to compare a 3-year investment directly against a 10-year investment on an equal annual basis.

Can I calculate CAGR for periods under one year?+

Yes, but it is less common. You can use fractional years (e.g., 6 months = 0.5 years) in the formula, but annualized short-term returns can distort long-term expectations.

How do contributions affect CAGR calculations?+

What is a good CAGR for a stock portfolio?+

Historically, a CAGR of 7% to 10% is considered strong for long-term equity portfolios, matching or exceeding historical index averages.

What is the difference between CAGR and IRR?+

CAGR Calculator

Inputs

Results

Bookmark this CAGR Calculator

CAGR formula

How the calculation works

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

CAGR Calculator

Inputs

Results

Bookmark this CAGR Calculator

Key output metrics

Asset value growth comparison

Smoothed compound trajectory

How to understand and use this calculator

What is Compound Annual Growth Rate (CAGR)?

The Mathematical CAGR Formula

CAGR vs. Average Annual Return (AAR)

Limitations of CAGR: The Smoothed Reality Trap

Related concepts

Frequently Asked Questions

CAGR formula

How the calculation works

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Key output metrics

Asset value growth comparison

Smoothed compound trajectory

How to understand and use this calculator

What is Compound Annual Growth Rate (CAGR)?

The Mathematical CAGR Formula

CAGR vs. Average Annual Return (AAR)

Limitations of CAGR: The Smoothed Reality Trap

Related concepts

Frequently Asked Questions