CAGR Calculator — Compound Annual Growth Rate

What CAGR is and what the calculator works out

CAGR answers one specific question: if the investment had grown by the same percentage every year, what would that percentage have to be to get from the starting value to the ending value over the period observed? The result is a smoothed, averaged path rather than a description of what actually happened. That is exactly why it is useful for comparison — it reduces a messy history of good and bad years to a single number.

Use CAGR when comparing the performance of two instruments held for different lengths of time, when assessing the growth rate of a company\'s revenue or customer base, when checking whether a fund has delivered what it promised, or when converting a total return over a period into an annual equivalent. It applies to a lump-sum investment with no interim contributions or withdrawals. If money went in or out during the period, CAGR will mislead you — the correct measure is then XIRR.

The formula explained in words

CAGR = (Vf / V₀)^(1/t) − 1

• V₀ — starting value at the beginning of the period.
• Vf — ending value at the end of the period.
• t — number of years between the two values. Count intervals, not observations: end of 2019 to end of 2026 is 7 years, not 8.

The logic runs as follows. The ratio Vf / V₀ gives the multiple by which the value grew over the whole period. Raising it to the power 1/t takes the t-th root, spreading that total growth evenly across the years — multiplicatively rather than additively. Subtracting one converts the growth factor into a percentage.

This multiplicative logic is what separates CAGR from an arithmetic average return, and why the two almost never coincide. The arithmetic mean of annual returns is always greater than or equal to CAGR, and the gap widens with volatility. Take three years returning +40%, −25% and +30%: the arithmetic mean is 15% a year, while the actual outcome is growth from 100 to 136.50, a CAGR of 10.93%. The number that describes the wealth actually accumulated is the second one.

A worked example

You invested €40,000 in equities through an exchange-traded fund. Seven years later the position is worth €72,000. You made no further contributions or withdrawals.

1. Take the ratio: 72,000 ÷ 40,000 = 1.80. The value grew 1.8 times, or by 80% over the whole period.
2. Take the seventh root: 1.80^(1/7) = 1.087596.
3. Subtract one: 0.087596, so CAGR = 8.76% a year.

Check: 40,000 × 1.087596^7 = €72,000. The smoothed path looks like this:

Note which answer is not correct. Dividing the total return by the number of years — 80% ÷ 7 = 11.43% — ignores compounding and overstates the rate by more than 2.5 percentage points. This is the single most common error in annualising a return.

The same formula works for corporate metrics. A company with revenue of €1,500,000 four years ago and €2,400,000 today has grown at (2,400,000 ÷ 1,500,000)^(1/4) − 1 = 12.47% a year.

Practical guidance and the Bulgarian context

The first rule when working with CAGR is to scrutinise the choice of start and end points. The measure rests entirely on two numbers and is acutely sensitive to them: a period beginning at a market bottom will show an impressive rate, while the same investment measured from the preceding peak looks mediocre. When you are reviewing someone else\'s figures, always ask why those particular dates were chosen.

The second rule is to set CAGR against inflation over the same period. A nominal 8.76% against average annual inflation of 3% means a real rate of (1.0876 ÷ 1.03) − 1 = 5.59%. Real return is the figure that matters for purchasing power.

For individuals in Bulgaria, capital gains on shares and units traded on a regulated market in the EU or EEA are exempt from tax, which means that for such instruments the gross CAGR is close to the net figure. Taxable income is subject to the flat 10% rate on the gain realised; for other categories, check the rules currently in force under the Personal Income Taxes Act. Tax treatment can reverse the ranking of two instruments with otherwise similar gross CAGRs.

If you are comparing funds, check whether the published return is based on net asset value after fees and whether the share class is accumulating or distributing. For a distributing class without dividend reinvestment, the CAGR of the price understates the total return.

Limitations of the calculation

CAGR says nothing about risk. Two investments with an identical 8.76% CAGR can have entirely different histories — one rising steadily, the other falling 40% midway through. Assessing risk requires additional measures such as standard deviation and maximum drawdown.

It does not handle interim contributions or withdrawals, since it assumes the starting amount sits untouched. For a portfolio with regular purchases use XIRR, which accounts for the exact date of every movement. CAGR is also unusable when the starting or ending value is negative or zero — with negative equity or a loss, the formula returns a meaningless result.

Finally, CAGR describes the past and is not a forecast. That an investment grew 8.76% a year over the last seven years is no basis for expecting the same over the next seven. Use the measure to understand what happened, not to assume what will.