Geometric Mean Calculator
Enter positive numbers separated by commas, spaces, or new lines.
Tip: For investment returns, convert each period return to a growth factor first (e.g., +10% → 1.10, -5% → 0.95).
Result
What is the geometric mean?
The geometric mean is a way to find the “typical” value of a set of numbers when values multiply over time or across conditions. It is especially useful for compound growth, investment returns, ratios, and percentage changes. Unlike the arithmetic mean, which simply adds and divides, the geometric mean respects compounding.
GM = (x1 × x2 × ... × xn)1/nwhere all values must be greater than 0.
When to use a geometric mean calculator
- Calculating average growth rates over multiple periods
- Comparing investment performance with compounding
- Analyzing multiplicative processes (biology, economics, physics)
- Summarizing data with strong proportional changes
Common finance example
If a portfolio grows by +20% in year 1 and declines by -10% in year 2, the arithmetic average return is +5%, but that does not represent the true compound path. Use growth factors: 1.20 and 0.90. The geometric mean is sqrt(1.20 × 0.90) ≈ 1.0392, which corresponds to about 3.92% per year compounded.
How this calculator works
This tool parses your values and computes the geometric mean using logarithms:
GM = exp((ln x1 + ln x2 + ... + ln xn) / n)
Using logs avoids overflow/underflow issues that can happen when multiplying many values directly. That means the calculator stays stable even for large lists or extreme magnitudes.
Geometric mean vs arithmetic mean
Arithmetic mean
Best for additive situations: test scores, daily temperatures, or counts where values combine by summation.
Geometric mean
Best for multiplicative situations: returns, growth factors, index ratios, and scale-based changes. If your process compounds, geometric mean is usually the right average.
Input rules and limitations
- All numbers must be positive (> 0)
- Zero values make geometric mean zero mathematically, but log-based formulas cannot use zero, so this calculator requires strictly positive input
- Negative numbers are invalid in standard real-valued geometric mean calculations
Practical tips for accurate results
- Use consistent units (all factors, all ratios, or all raw values)
- For returns, convert percentages to factors before entering
- Use enough decimal places for precision in scientific or financial work
- Double-check outliers, because very small values can pull the geometric mean down sharply
FAQ
Is geometric mean the same as CAGR?
They are closely related. CAGR is effectively the geometric mean growth rate over periods, usually expressed as a percentage.
Can I use negative values?
Not in this calculator. Standard geometric mean in real numbers requires strictly positive values.
Why does geometric mean often look lower than arithmetic mean?
Because variability penalizes compounded growth. In volatile data, the geometric mean better reflects the true “compounded” average experience.
Can I paste data from spreadsheets?
Yes. You can paste values separated by spaces, commas, or line breaks directly into the input box.