Geometric Mean (Average Growth Rate)

Excel Formulas › Statistics

All versionsGEOMEAN

For things that compound — growth rates, returns, ratios — the plain average overstates. The geometric mean multiplies the values and takes the n-th root, giving the true average rate that reproduces the total compounding.

Quick formula: for growth factors in B2:B6 (e.g. 1.10 for +10%):
=GEOMEAN(B2:B6)
Feed it the factors (1 + rate), not the percentages. Subtract 1 from the result to get the average growth rate.

Functions used (tap for the full reference guide):

GEOMEANPRODUCT

The example

Yearly growth factors; the geometric mean is the true average rate.

AB
1YearFactor
220231.20 (+20%)
320240.90 (−10%)
420251.15 (+15%)
5Geo mean1.073 (+7.3%)

The formula

The average compounding factor, then the rate:

=GEOMEAN(B2:B6) → 1.073 =GEOMEAN(B2:B6) - 1 → 7.3% average growth

How it works

The geometric mean respects compounding:

  1. It multiplies all the values together, then takes the n-th root (n = how many values).
  2. For growth, feed it the factors — 1.20 for +20%, 0.90 for −10% — not the raw percentages.
  3. The result is the single factor that, compounded each period, gives the same end result. Subtract 1 for the average rate.
  4. It’s always ≤ the arithmetic mean, and the gap grows with volatility — which is exactly why it’s the honest measure for returns.

Same as CAGR: the geometric mean of the yearly factors equals the compound annual growth rate. If you only have start and end values, =(end/start)^(1/years)-1 gives the same number without listing each factor.

Try it: interactive demo

Live demo

Enter yearly % changes, one per line.

Geo mean rate:   Arithmetic:

Variations

Average growth rate

Subtract 1 from the mean factor:

=GEOMEAN(B2:B6) - 1

From start & end (CAGR)

No per-year factors needed:

=(end/start)^(1/years) - 1

Manual n-th root

Same as GEOMEAN:

=PRODUCT(B2:B6)^(1/COUNT(B2:B6))

Pitfalls & errors

No zero or negative values. GEOMEAN needs all-positive inputs. Use growth factors (1 + rate), which stay positive even when a rate is negative.

Don’t feed it raw percentages. Averaging 20, −10, 15 directly is the arithmetic mean. Convert to factors (1.20, 0.90, 1.15) first.

Lower than the arithmetic mean. That’s correct, not a bug — volatility makes compounding underperform the simple average.

Practice workbook

📊
Download the free Geometric Mean (Average Growth Rate) practice workbook
A geometric-mean sheet with the growth-rate, CAGR, and manual n-th-root variants, plus 4 challenges with answers. No sign-up required.

Frequently asked questions

How do I calculate the geometric mean in Excel?
Use =GEOMEAN(range) on the growth factors (1 + rate). Subtract 1 from the result to get the average growth rate.
Why use geometric mean instead of average for growth rates?
The geometric mean accounts for compounding, so it reproduces the actual total growth. The arithmetic mean overstates returns whenever values vary.
Is the geometric mean the same as CAGR?
Yes — the geometric mean of the yearly factors equals the compound annual growth rate. With only start and end values, use =(end/start)^(1/years)-1.

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Related formulas: CAGR · Compound interest · Coefficient of variation

Function references: GEOMEAN · PRODUCT