CAGR Calculator

What is CAGR?

CAGR, or Compound Annual Growth Rate, is a metric that describes the rate at which a value would have grown if it had increased at a constant rate every year. According to Wikipedia's CAGR article, it is not the actual average return (which would fluctuate year to year) but rather a hypothetical constant rate that produces the same final value from the same starting value over the same time period. Think of it as the "smoothed" annual growth rate that irons out volatility.

CAGR is used across finance, business, and economics. Investors use it to compare the performance of different investments. Business analysts use it to measure revenue or user growth. Economists use it to track GDP or population growth over decades. Any scenario where you have a starting value, an ending value, and a time period can be expressed as a CAGR.

The reason CAGR is preferred over simple averages is that it accounts for the compounding effect. If an investment grows 50% one year and then falls 50% the next, the arithmetic average is 0%, suggesting you broke even. But in reality, 100 growing 50% becomes 150, then falling 50% becomes 75. You actually lost 25%. The CAGR over these 2 years would correctly show -13.4%, reflecting the actual outcome.

The CAGR Formula

The formula for CAGR is straightforward:

CAGR = (End Value / Start Value) ^ (1 / n) - 1

Where:

• End Value = the final value of the investment or metric
• Start Value = the initial value
• n = the number of years between the start and end
• The ^ symbol means "raised to the power of"

The formula can be rearranged to solve for other variables. To find the future value given a known CAGR: End Value = Start Value x (1 + CAGR)^n. To find how many years are needed to reach a target: n = ln(End Value / Start Value) / ln(1 + CAGR), where ln is the natural logarithm. These rearrangements are what power the "Reverse CAGR" and "Target Value" modes in the calculator above.

A useful shortcut related to CAGR is the Rule of 72: divide 72 by the CAGR percentage to get an approximate number of years for the value to double. At 12% CAGR, money doubles in roughly 72/12 = 6 years. At 8% CAGR, it takes about 9 years. This rule is surprisingly accurate for rates between 5% and 20%.

Worked Example: Investment CAGR

Let us calculate the CAGR for a mutual fund investment. You invested 1,00,000 in January 2020 and by January 2025, the value had grown to 1,95,000. The period is 5 years.

CAGR = (1,95,000 / 1,00,000) ^ (1/5) - 1
CAGR = (1.95) ^ (0.2) - 1
CAGR = 1.1431 - 1
CAGR = 0.1431 or 14.31%

This tells you the investment grew at an equivalent of 14.31% per year, compounded annually. The actual year-to-year returns may have been very different (maybe 25% in one year, -5% in another), but the CAGR provides a single number for comparison. If another fund returned 12% CAGR over the same period, you know the first fund performed better on an annualized compound basis.

Using the Rule of 72: at 14.31% CAGR, the investment would double in approximately 72 / 14.31 = 5.03 years. Since the calculator shows the investment went from 1 lakh to 1.95 lakh in 5 years (nearly doubling), the Rule of 72 checks out.

CAGR vs Average Annual Return

This distinction trips up many investors, so it deserves careful explanation. The arithmetic mean (simple average) of annual returns is calculated by adding all the yearly returns and dividing by the number of years. The CAGR (geometric mean) accounts for the compounding effect where each year's return builds on the previous year's ending value.

Here is a stark example. Investment A returns: +40%, -20%, +30%, -10%, +25% over 5 years. The arithmetic average is (40-20+30-10+25)/5 = 13% per year. Starting with 1,00,000: Year 1: 1,40,000. Year 2: 1,12,000. Year 3: 1,45,600. Year 4: 1,31,040. Year 5: 1,63,800. The CAGR is (1,63,800/1,00,000)^(1/5) - 1 = 10.36%. The arithmetic average of 13% overstates the actual compounded growth by nearly 3 percentage points.

The gap between arithmetic and geometric mean widens as volatility increases. For very stable investments (like fixed deposits with consistent rates), the two are nearly identical. For volatile assets (small-cap stocks, crypto), the arithmetic mean can be dramatically higher than the actual CAGR. This is why fund advertisements often show trailing returns (which are CAGR-based) rather than average annual returns.

Real-world Applications of CAGR

Beyond investment returns, CAGR is used extensively in business and economics. Startup founders use revenue CAGR to pitch to investors. A SaaS company that grew revenue from $1 million to $8 million in 3 years has a CAGR of about 100%, which demonstrates explosive growth. Venture capitalists routinely compare portfolio company CAGR to benchmark against industry standards.

In market sizing, analysts use CAGR to project industry growth. When a research report says "the global AI market is expected to grow at a CAGR of 37.3% from 2023 to 2030," it means they expect the market size to compound at 37.3% annually. This projection helps investors and business leaders decide where to allocate resources.

Governments use CAGR to track economic indicators. India's GDP grew from approximately $2.1 trillion in 2014 to $3.7 trillion in 2024, representing a CAGR of about 5.8% in US dollar terms. Population CAGR, urbanization CAGR, and inflation CAGR are all standard metrics in economic analysis and policy planning.

Limitations of CAGR

Despite its usefulness, CAGR has meaningful blind spots. The most significant is that it only cares about the starting and ending points. An investment that grew steadily from 100 to 200 over 5 years and one that crashed to 30 in year 3 before recovering to 200 by year 5 have the same CAGR, even though the second investment put you through extreme stress and risk. CAGR tells you nothing about the journey, only the destination.

CAGR also cannot handle investments with multiple cash flows. If you invested 1 lakh initially, added 50,000 in year 2, and withdrew 30,000 in year 4, CAGR cannot account for those intermediate flows. You need XIRR (Extended Internal Rate of Return) for multi-cash-flow scenarios. Most SIP investors should measure performance using XIRR, not CAGR.

Finally, CAGR is backward-looking and says nothing about future performance. A stock that delivered 25% CAGR over the last 5 years may underperform in the next 5 years due to changed fundamentals, valuation expansion, or market conditions. Using historical CAGR to project future returns assumes that conditions will remain similar, which is rarely the case over long periods.

CAGR by Asset Class: Historical Reference

Understanding typical CAGR ranges by asset class helps set realistic expectations. Here are approximate 20-year historical figures:

• Indian Large-cap Equities (Nifty 50): 12-14% CAGR
• Indian Mid-cap Equities (Nifty Midcap 100): 15-18% CAGR
• US Large-cap Equities (S&P 500): 10-11% CAGR in USD
• Gold (in INR terms): 9-11% CAGR
• Indian Real Estate (metro cities): 8-12% CAGR depending on location
• Indian Fixed Deposits: 6-7% CAGR
• US Treasury Bonds: 3-5% CAGR in USD
• Inflation (India CPI): 5-6% CAGR

The key insight from this data is that equities have historically been the only asset class that consistently beats inflation by a significant margin over 20-year periods. But that outperformance comes with higher year-to-year volatility, which is why CAGR (not year-by-year returns) is the appropriate metric for long-term comparison.

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