GEOMEAN in Excel: Average Positive Multipliers and Growth Factors

• Introduced: first introduction version is not established by the official history reviewed; the current product list is not a launch record.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official GEOMEAN reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=GEOMEAN(number1, [number2], ...)

Microsoft documents 1–255 arguments, which can be values or ranges. Any participating value at or below zero gives #NUM!. Referenced text, logical values and empty cells are ignored; numeric zero is included and therefore violates the positive-data rule. Direct logical values and numeric text count.

The equal-weight mathematical result is the nth root of the product of n positive observations. The following controls use modest finite values, not a claim that explicitly multiplying huge or tiny inputs is a stable implementation.

Enter 2, 8, 32 in A2:A4:

=GEOMEAN(A2:A4)
=AVERAGE(A2:A4)

Expected values are 8 and 14. The product is 512 and its cube root is eight. The arithmetic mean instead divides the sum 42 by three.

Replacing the observations by three copies of their geometric mean preserves their combined product: 8×8×8=512. It does not preserve their sum. Choose the mean that matches the model rather than whichever result seems more convenient.

Suppose a fictional quantity rises by 20% in one period and falls by 20% in the next. Its multipliers are 1.2 and 0.8:

=GEOMEAN(1.2,0.8)
=GEOMEAN(1.2,0.8)-1

Expected results are approximately 0.979795897 and -0.020204103. Formatting the latter as a percentage gives approximately -2.020410289% per period in this equal-period model.

The total multiplier is 0.96. Starting from 100, the two periods end at 96, a total decline of 4%. Averaging +20% and −20% arithmetically gives zero and does not reproduce that multiplicative path.

Do not feed the signed changes 0.2 and -0.2 directly to GEOMEAN. They are not the positive factors required by this model or by the documented domain.

Suppose value two has weight one and value eight has weight three:

=GEOMEAN(2,8,8,8)

The independently expected result is approximately 5.656854249, the fourth root of 2×8×8×8=1024. By comparison, =GEOMEAN(2,8) gives four, because the two entries then have equal weight.

Repetition is practical only for small integer weights. A general weighted log model must define what the weights mean and verify their handling separately; GEOMEAN has no dedicated weight argument.

For numeric 1, 4, 16 in D2:D4, put =LN(D2) in E2 and fill down:

=EXP(AVERAGE(E2:E4))
=GEOMEAN(D2:D4)

Both expected results are 4. The logarithms are approximately 0, 1.386294361, 2.772588722, whose arithmetic mean is ln(4).

This demonstrates the positive-data identity using LN, EXP and AVERAGE. It does not promise identical final floating-point digits for all magnitudes or every Excel version.

Enter numeric 2, text 8 and logical TRUE in F2:F4:

=GEOMEAN(F2:F4)
=GEOMEAN(2,"8",TRUE)

Under the documented rules, the expected results are 2 and approximately 2.519842100. The direct call counts 2, 8 and 1, whose product is 16 and whose geometric mean is its cube root. The referenced call uses only the numeric two.

Numeric zero is not ignored. =GEOMEAN(2,0,8) and =GEOMEAN(2,-1,8) have vendor-documented expected error #NUM!. This does not establish a complete coercion matrix for every blank, error cell or imported string.

Confirm that growth inputs are positive factors, that all periods have the intended equal weight and that a percentage display has not been multiplied by 100 twice. Keep a missing observation distinct from a zero replacement. A zero factor is outside GEOMEAN’s documented domain and changes the modeling problem.

• Microsoft GEOMEAN reference.
• Editorial testing standards.

Inputs are fictional. Decimal answers are independent mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.