CAGR Growth Calculator: Formula and Worked Example

A CAGR growth calculator estimates the constant annual growth rate that would take a starting value to an ending value over a specified number of years. Enter the starting value, ending value, and elapsed years to get the compound annual growth rate as a percentage, along with the total percentage change.

Formula

The compound annual growth rate is the annualized rate that links a starting value to an ending value over a chosen period, assuming growth compounds at a steady rate:

CAGR = [(Ending value ÷ Starting value)^{1 ÷ Years} − 1] × 100

• Starting value is the amount or measure at the beginning of the period, in the unit that suits your subject.
• Ending value is the amount or measure at the end, in the same unit.
• Years is the elapsed time in years. It must be greater than zero for the formula to be meaningful.
• CAGR is expressed as a percentage per year. The calculator also reports total change as a percentage, calculated as [(ending value ÷ starting value) − 1] × 100.

The calculator accepts zero or positive starting and ending values. A zero starting value cannot be used in the ratio because division by zero is undefined. If the start is zero, or if the underlying measure can be negative, use a method designed for that data rather than interpreting this CAGR result.

Worked Example

Using the calculator’s default inputs—starting value 100, ending value 150, and 3 years:

1. Divide the ending value by the starting value: 150 ÷ 100 = 1.5.
2. Raise that ratio to the power of 1 ÷ 3: 1.5^1/3 ≈ 1.144714.
3. Subtract 1 and multiply by 100: (1.144714 − 1) × 100 ≈ 14.47% CAGR.
4. For total change, calculate (150 ÷ 100 − 1) × 100 = 50.00%.

The figures say the value increased by 50% overall, equivalent to a constant annual compound rate of about 14.47% across the three-year period. They do not say that the value actually rose by exactly 14.47% in each individual year.

What CAGR Means and When to Use It

CAGR compresses a start point, an end point, and elapsed time into one annualized rate. It is useful for comparing growth across periods of different lengths, or comparing measures that use the same units and are tracked consistently. Examples include the change in a company’s revenue, a website’s user count, a population estimate, or the size of a market over a defined period. The formula is arithmetic, not a forecast or an explanation of what caused the change.

It can also help summarize a series with uneven yearly results. Suppose a quantity rises in one year, falls in the next, and then rises again. CAGR answers: “What steady annual rate would connect the initial and final values over this period?” It does not reveal the intervening ups and downs, their timing, or how volatile the series was. For that, examine the individual observations as well.

How to Choose Inputs and Read the Result

• Use comparable endpoints. The starting and ending measurements should describe the same thing, follow the same definition, and use compatible units. Convert units first if necessary.
• Count the elapsed time correctly. Use the period between the observations, not automatically the number of data points. Annual values from year 1 through year 5 cover four elapsed years, not five.
• Use a consistent time basis. This calculator takes years. For a period measured in months, divide months by 12; for days, use an explicitly chosen year-length convention and apply it consistently.
• Interpret the sign. A positive CAGR means the ending value exceeds the starting value; a negative CAGR means it is lower. Equal positive endpoints produce 0%.
• Keep units attached to the underlying values. CAGR itself is a percentage per year, not dollars per year, people per year, or another absolute increase.

The calculator reports two different things: CAGR is an annualized rate, while total change is the net percentage difference over the entire period. They are not interchangeable. A 50% total rise over three years is not a 50% annual CAGR.

Common Mistakes and Limitations

A frequent mistake is treating CAGR as the actual year-by-year growth rate. It is a smoothed equivalent, and the real path may have been irregular or may have included declines. Another is using the number of calendar labels instead of elapsed intervals. If the measurements are taken at the starts of 2021 and 2024, the elapsed period is three years.

Make sure both endpoints are positive for this standard ratio formula. If either is zero, the calculation may be undefined or impossible to interpret; if values cross zero or represent signed quantities, a percentage growth rate may not be appropriate. Also avoid mixing nominal and inflation-adjusted values: the result describes whichever kind of data you enter. If you want growth in purchasing power, first use consistently inflation-adjusted endpoints.

Rounding the inputs or intermediate steps too early can shift the displayed result, especially for short periods or small changes. Keep full precision through the calculation and round only the final answer. The calculator displays CAGR and total change to two decimal places; unrounded results can differ slightly from those displayed.

CAGR Compared with Other Growth Measures

Total percentage change is the simplest endpoint comparison and ignores duration. CAGR adds a time dimension by converting the endpoint ratio into a constant annual compound rate. Arithmetic average growth, by contrast, averages the individual period rates. When rates vary, that arithmetic average generally does not equal the rate that compounds from the first value to the last. CAGR is the geometric annualized rate implied by the endpoints.

For example, if a value doubles and then halves, it finishes where it began. Its two-period CAGR is 0%, even though the arithmetic average of the two period changes, +100% and −50%, is +25%. The example shows why averaging yearly percentage changes can give a misleading summary of compounded growth. CAGR still cannot describe the path: pair it with annual data when the pattern matters.

Frequently Asked Questions

How do I calculate CAGR by hand?
Divide the ending value by the starting value, raise the result to 1 divided by the number of years, subtract 1, and multiply by 100 to express it as a percentage.

Can CAGR be negative?
Yes. With positive starting and ending values, a lower ending value produces a negative CAGR, indicating an annualized decline over the period.

Is CAGR the same as average annual growth?
Not necessarily. CAGR is the steady compounding rate implied by the endpoints. The arithmetic average of individual yearly rates can differ, particularly when those rates vary.

Can I calculate CAGR for less than one year?
The formula can be applied to a positive fractional number of years, but the period must be stated consistently. Very short periods can make an annualized rate look large and should not be mistaken for a prediction of future growth.

What if my starting value is zero?
The standard CAGR formula divides by the starting value, so a zero start makes it undefined. Report the absolute change or choose another measure appropriate to the data instead.

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in start | Starting value | - | 100 | 0
in end | Ending value | - | 150 | 0
in years | Years | years | 3 | 0
out cagr | CAGR | % | ((end / start) ^ (1 / years) - 1) * 100 | 2
out change | Total change | % | (end / start - 1) * 100 | 2