How to calculate the geometric mean
✓ Verified in LibreOffice 25.8.7.3Average rates that compound — investment returns, growth factors, ratios — where a plain average overstates the true typical rate.
The formula
| App | Formula | Notes |
|---|---|---|
| Excel | =GEOMEAN(A2:A100) | Multiplies all values and takes the nth root. Every value must be POSITIVE — for percent growth, use growth factors (1.08 for +8%), not the raw percentages. |
| Google Sheets | =GEOMEAN(A2:A100) | Identical. |
| LibreOffice Calc | =GEOMEAN(A2:A100) | Identical. |
How it works
The geometric mean multiplies the values together and takes the nth root — for {1, 2, 4} that's the cube root of 8, which is 2. It's the correct 'average' whenever quantities compound or are ratios: average investment returns, population growth, or index changes. The arithmetic mean overstates these because it ignores compounding — average +50% one year and -50% the next and the arithmetic mean says 0%, but you're actually down 25%, which the geometric mean of the growth factors (1.5 and 0.5 → √0.75 ≈ 0.866, i.e. -13.4% per year) captures. Two rules: feed it GROWTH FACTORS not raw percentages (1.08 for +8%), and every input must be positive — a single zero makes the whole product zero and negatives are undefined. To turn a series of period returns into an average growth rate, take GEOMEAN of the factors and subtract 1.
Verified, not just documented
We ran =GEOMEAN(A2:A4) in LibreOffice 25.8.7.3 (headless, with forced recalculation) and it returned 2 — exactly the expected result. Every formula here is confirmed by actually executing it.
Functions used
GEOMEAN — see full Excel, Google Sheets & LibreOffice compatibility for each.