CAGR Calculator
Find the steady yearly growth rate behind any change in value — the honest way to compare investments held for different periods.
What is Compound Annual Growth Rate (CAGR)?
Compound Annual Growth Rate (CAGR) is the single standardized annual growth rate that measures the smoothed year-over-year rate at which an investment would have grown from its initial value to its final value over a specified time horizon, assuming all profits were reinvested at the end of each compounding period.
In real-world financial markets, investment asset values do not climb in a smooth linear trajectory; they fluctuate erratically through bull runs, sharp market corrections, and periods of economic stagnation. CAGR cuts through this year-to-year volatility, providing institutional investors and retail savers with a clean geometric benchmark to compare fund performance across varying historical windows.
CAGR vs Average Annual Return (Geometric vs Arithmetic Mean)
A common pitfall in investment analysis is confusing CAGR with Simple Average Annual Return (Arithmetic Mean):
- The Arithmetic Mean Flaw: If you invest ₹1,00,000 and the portfolio gains 50% in Year 1 (rising to ₹1,50,000) and then loses 50% in Year 2 (dropping to ₹75,000), the simple arithmetic average return is (50% − 50%) ÷ 2 = 0%. However, you are actually ₹25,000 poorer!
- The Geometric CAGR Truth: The CAGR correctly computes: [ (75,000 ÷ 1,00,000)^(1/2) − 1 ] = −13.40% per annum. CAGR accurately accounts for portfolio compounding and drawdown recovery, reflecting true financial reality.
The CAGR Mathematical Formula
CAGR = [ (Final Value ÷ Initial Value)^(1 ÷ Years) − 1 ] × 100
- Initial Value: Starting investment capital or initial acquisition price (in ₹)
- Final Value: Ending valuation or terminal sale proceeds (in ₹)
- Years: Total duration of investment in years (fractions allowed for partial years: days ÷ 365)
- Total Growth %: [ (Final Value − Initial Value) ÷ Initial Value ] × 100
- Multiple: Final Value ÷ Initial Value (e.g., 2.5x indicates capital multiplied two and a half times)
Worked example: ₹1,00,000 Growing to ₹2,50,000 in 5 Years
Consider an equity portfolio or mutual fund investment of ₹1,00,000 that matures to ₹2,50,000 after 5 years:
- Initial Capital (P): ₹1,00,000
- Final Capital (A): ₹2,50,000
- Horizon (n): 5 years
- Capital Multiple: 2,50,000 ÷ 1,00,000 = 2.5x
- Total Absolute Growth: (1,50,000 ÷ 1,00,000) × 100 = 150%
- CAGR Calculation: [ (2.5)^(1 ÷ 5) − 1 ] × 100 = [ (2.5)^0.2 − 1 ] × 100 = 20.11% per annum
If the same investment had merely doubled to ₹2,00,000 over 5 years (2x), the CAGR would be 14.87% per annum, demonstrating how small improvements in annual compounding produce substantial gaps in end wealth.
Five-Year Wealth Outcomes and Their Corresponding CAGRs
| Ending Value of ₹1 Lakh | Capital Multiplier | Total Absolute Growth | Compound Annual Growth Rate (CAGR) |
|---|---|---|---|
| ₹1,50,000 | 1.5x | 50.0% | 8.45% per annum |
| ₹2,00,000 | 2.0x | 100.0% | 14.87% per annum |
| ₹2,50,000 | 2.5x | 150.0% | 20.11% per annum |
| ₹3,00,000 | 3.0x | 200.0% | 24.57% per annum |
| ₹3,33,333 | 3.33x | 233.3% | 27.23% per annum |
| ₹5,00,000 | 5.0x | 400.0% | 37.97% per annum |
The Rule of 72: Quick Mental Compounding
A famous mathematical shortcut in investment planning is the Rule of 72. To find out approximately how many years it will take for your money to double at a given CAGR, divide 72 by the annual return percentage:
- At 12% CAGR: 72 ÷ 12 ≈ 6 years to double.
- At 14.87% CAGR: 72 ÷ 14.87 ≈ 4.8 years (matches our 5-year 2x table row).
- At 8% CAGR: 72 ÷ 8 ≈ 9 years to double.
Limitations of CAGR: Volatility Blindness
While CAGR is an indispensable comparison tool, investors must recognize its structural blind spot: it ignores interim volatility and sequence of returns. Two mutual fund schemes can boast the exact same 12% CAGR over a 5-year cycle, yet Fund A grew steadily at 12% every single year, while Fund B experienced a devastating 40% crash followed by a 70% rebound.
Always evaluate a fund's CAGR alongside risk-adjusted metrics such as Standard Deviation and the Sharpe Ratio to measure return consistency.
Frequently Asked Questions on CAGR
Key insights into arithmetic vs geometric returns, SIP applicability, volatility, and tax implications.
Average annual return adds annual percentage changes and divides by the number of years (arithmetic mean), which severely distorts true performance when markets are volatile. CAGR is geometric: it calculates the constant compounding rate that actually converts starting capital into terminal wealth.
No. CAGR requires a single starting value and a single ending value. In a SIP, investments are staggered monthly across many dates, meaning each instalment compounds for a different duration. To calculate returns on SIPs, you must use the XIRR (Extended Internal Rate of Return) method.
No. Historical CAGR merely documents past performance over a specific calendar window. Market-linked equity returns fluctuate with macroeconomic cycles and corporate earnings. Past returns provide context but never guarantee future performance.
The Rule of 72 allows you to quickly estimate the doubling time of an investment: divide 72 by the CAGR. For instance, at a 15% CAGR, your investment doubles in approximately 72 ÷ 15 = 4.8 years.
No. Tax is not levied on theoretical annual compounding rates. In India, capital gains tax is triggered only when an investment is actually sold or redeemed (a realization event). Unrealized paper gains compounding year after year incur zero tax until liquidation.
While mathematically possible by using a fractional year (e.g., 6 months = 0.5 years), annualizing returns over periods shorter than 12 months is highly misleading because short-term market spikes can produce unrealistically inflated annual projections.
Absolute return measures total capital growth as a single percentage regardless of duration (e.g., ₹1 lakh growing to ₹2 lakh is 100% absolute return). CAGR incorporates the time horizon to reveal the equivalent annual compounding rate that produced that return.
Over multi-decade horizons (10 to 20 years), broad Indian market indices like Nifty 50 and Sensex have delivered long-term CAGRs ranging between 11% and 14%. Conservative financial planners typically assume a 12% CAGR for long-term equity planning.
Nominal CAGR reflects raw capital growth in rupees. To determine your "Real CAGR" (actual purchasing power expansion), adjust nominal CAGR for inflation using the Fisher equation: Real Rate ≈ Nominal CAGR − Inflation Rate. A 12% CAGR with 6% inflation delivers a Real CAGR of ~5.66%.
Yes. CAGR is asset-agnostic. Any asset with a documented purchase price, a terminal sale price, and a verified holding period (in years) can be evaluated using the CAGR formula.