CAGR Explained: Beginning Value, Ending Value and Years

CAGR annualizes the change between two values

Compound annual growth rate, or CAGR, is the constant annualized rate that connects a beginning value to an ending value over a specified duration. It smooths the full endpoint change into one yearly equivalent; it is not a record of the return achieved in each individual year.

CAGR can make endpoint growth over periods of different lengths easier to compare on an annualized basis. That comparison still needs context because CAGR does not reveal volatility, cash flows, costs, taxes or the path taken between the endpoints.

Beginning value, ending value and duration define the result

• Beginning value is the positive value at the start of the measured period.
• Ending value is the value at the end of that period and may be zero or positive.
• Duration is the number of whole years between the endpoints.

How the CAGR formula connects the endpoints

The calculator uses: CAGR = ((ending value / beginning value)^(1 / duration in years) - 1) × 100. Dividing the ending value by the beginning value gives the full-period growth factor. Taking its whole-period annual root converts that factor into a constant yearly equivalent, and subtracting one expresses the growth rate before conversion to a percentage.

This formula annualizes an endpoint relationship rather than teaching generic compounding mechanics. For that broader concept, see What Is Compound Interest?.

Worked example: value doubles over five years

A beginning value of ₹1,00,000 and ending value of ₹2,00,000 over five whole years produce the following engine-calculated result.

Positive, zero and negative CAGR describe endpoint direction

CAGR is positive when the ending value is above the beginning value and zero when the two values are equal. It is negative when the ending value is below the beginning value over the selected period; that description is mathematical, not investment advice.

The current engine returns -100% when the ending value is zero. It does not support a zero or negative beginning value, or a negative ending value.

Calculator boundaries and assumptions

• The beginning value must be greater than zero, while the ending value may be zero or positive.
• Negative values are unsupported.
• Duration must be a whole number from 1 to 100 years; fractional years are unsupported.
• The calculation uses only the two endpoints and duration.
• Periodic contributions, withdrawals, dividends and other interim cash flows are unsupported.

What CAGR does not show

CAGR does not show the sequence or volatility of values between the endpoints, and it does not prove that a constant return was actually realized each year. Two paths with identical endpoints and duration receive the same CAGR even when their interim movements differ.

CAGR is not a forecast, guarantee or complete assessment of investment quality. A higher CAGR alone does not establish that one investment is better, because risk, cash-flow timing, costs and other facts are outside this calculation.

Compare CAGR with absolute return, examine its year-to-year volatility limitation, or distinguish it from average annual return.