How do I calculate average annual growth rate, or AAGR?

Add the observed annual percentage changes and divide by their count. For 20% and -10%, (20 - 10) / 2 is 5%. This arithmetic mean gives every observed year equal weight. It does not equal the compound annual equivalent, because compounding multiplies the growth factors rather than adding the percentages.

How does the geometric or compound mean differ from AAGR?

Convert each percentage r into the factor 1 + r/100, multiply the factors, take the root for the observed period count, subtract 1 and multiply by 100. For 20% then -10%, the factors 1.2 and 0.9 multiply to 1.08. The square root minus 1 gives about 3.923048% per year. The calculator displays this compound mean alongside the arithmetic mean rather than calling them interchangeable.

Can I average monthly growth rates and express the compound result annually?

Choose Months and enter one observed percentage per complete month. The headline is the arithmetic mean monthly change. The compound annual equivalent uses the product of the factors and the observed month count divided by 12. For two monthly changes of 1% and 1%, the arithmetic monthly mean is 1%, the total observed change is 2.01%, and the annual equivalent is about 12.682503%. Only two months were observed; the annual equivalent does not mean that change repeats.

What if I only have a starting value, ending value and number of years?

Use the dedicated CAGR workflow in ROI Calculator. It solves (ending / starting)^(1/years) - 1 from those known inputs, including elapsed months. Two endpoints determine a compound equivalent but do not reveal the individual annual percentages needed for an arithmetic AAGR. For 100 ending at 133.1 after three years, CAGR is 10%.

How do I calculate average annual growth rate in Excel?

For annual percentages stored as decimals in D2:D6, =AVERAGE(D2:D6) gives AAGR. In a helper column, use =1+D2 and copy down, then =GEOMEAN(E2:E6)-1 for the compound mean when every factor is positive. Format the results as percentages. This browser field reads 20% as numeric percentage 20 and performs the factor conversion itself. The page does not create a downloadable workbook.

Can growth be negative or reach -100%?

Yes. Losses down to -100% are accepted; -100% gives a zero growth factor and makes the product and compound equivalent zero and -100%, respectively. Changes below -100% give a negative factor and are refused. No deposits, withdrawals or new investment are inferred after a total loss; those cash flows require a different model.

Can I use irregular periods, missing years or a future expected return?

Every entered observation represents one equal-length complete year or month. Do not combine months with years, skip unknown periods or paste dated cash flows into this list. The calculator describes the supplied observed series; it does not look up investment history, select a good growth rate or estimate future returns. A supplied rate applied to a known starting amount belongs to the compound-interest workflow in APY Calculator.

Average Growth Rate Calculator

Enter the percentage change observed in each complete year or month. This page compares the arithmetic mean with the compound annual equivalent, so the two meanings of average growth stay visible. The annual example of 20% then -10% has an arithmetic mean of 5%; compounding takes 100 to 108 and gives an annual equivalent of about 3.923048%.

Arithmetic mean annual change · 2 observed years5%Compound annual equivalent: 3.92304845413% · observed 2 years

What to work out

Observed percentage changes: 20% -10%

Length of each observed period

Count: 2

Enter observed percentage changes for equal-length complete years or months. The arithmetic mean and compound equivalent answer different questions. No rate, missing period or cash flow is inferred.

Each entered number is a percentage for one complete year: 20% means a factor of 1.2, and -10% means 0.9. The arithmetic mean gives every observed period equal weight. Displayed figures use up to 12 significant digits; compound results are numerical approximations. The compound annual figure is a mathematical equivalent of the observed factors; it does not predict repetition or infer cash flows.

Compound change per observed periodgeometric mean of the growth factors minus 1
3.92304845413%
(product of observed growth factors)^(1/period count) minus 1 ≈ 3.92304845413%
Compound annual equivalentuses the observed duration in years
3.92304845413%
(product of observed growth factors)^(1/elapsed years) minus 1 ≈ 3.92304845413%
Total observed changeproduct of the growth factors minus 1
8%
product of observed growth factors minus 1 ≈ 8%

Common questions

How do I calculate average annual growth rate, or AAGR?: Add the observed annual percentage changes and divide by their count. For 20% and -10%, (20 - 10) / 2 is 5%. This arithmetic mean gives every observed year equal weight. It does not equal the compound annual equivalent, because compounding multiplies the growth factors rather than adding the percentages.
How does the geometric or compound mean differ from AAGR?: Convert each percentage r into the factor 1 + r/100, multiply the factors, take the root for the observed period count, subtract 1 and multiply by 100. For 20% then -10%, the factors 1.2 and 0.9 multiply to 1.08. The square root minus 1 gives about 3.923048% per year. The calculator displays this compound mean alongside the arithmetic mean rather than calling them interchangeable.
Can I average monthly growth rates and express the compound result annually?: Choose Months and enter one observed percentage per complete month. The headline is the arithmetic mean monthly change. The compound annual equivalent uses the product of the factors and the observed month count divided by 12. For two monthly changes of 1% and 1%, the arithmetic monthly mean is 1%, the total observed change is 2.01%, and the annual equivalent is about 12.682503%. Only two months were observed; the annual equivalent does not mean that change repeats.
What if I only have a starting value, ending value and number of years?: Use the dedicated CAGR workflow in ROI Calculator. It solves (ending / starting)^(1/years) - 1 from those known inputs, including elapsed months. Two endpoints determine a compound equivalent but do not reveal the individual annual percentages needed for an arithmetic AAGR. For 100 ending at 133.1 after three years, CAGR is 10%.
How do I calculate average annual growth rate in Excel?: For annual percentages stored as decimals in D2:D6, =AVERAGE(D2:D6) gives AAGR. In a helper column, use =1+D2 and copy down, then =GEOMEAN(E2:E6)-1 for the compound mean when every factor is positive. Format the results as percentages. This browser field reads 20% as numeric percentage 20 and performs the factor conversion itself. The page does not create a downloadable workbook.
Can growth be negative or reach -100%?: Yes. Losses down to -100% are accepted; -100% gives a zero growth factor and makes the product and compound equivalent zero and -100%, respectively. Changes below -100% give a negative factor and are refused. No deposits, withdrawals or new investment are inferred after a total loss; those cash flows require a different model.
Can I use irregular periods, missing years or a future expected return?: Every entered observation represents one equal-length complete year or month. Do not combine months with years, skip unknown periods or paste dated cash flows into this list. The calculator describes the supplied observed series; it does not look up investment history, select a good growth rate or estimate future returns. A supplied rate applied to a known starting amount belongs to the compound-interest workflow in APY Calculator.

Uses browser double precision with compensated sums and stable variance calculations. Median positions and mode frequencies are exact for the parsed numbers; arithmetic results can round. Unrepresentable inputs and intermediate results are explained.