A Geometric Mean Calculator

The geometric mean is the average you use when values multiply rather than add. Multiply all the numbers together and take the root that matches how many there are.

First valueA positive number. For growth rates enter the factor, so 1.08 for 8 percent growth.Second valueThe second positive value, in the same units as the first.Third valueThe third positive value. Use 0.95 for a 5 percent decline.

Geometric mean

1.0474

Average growth rate: 4.74%
Arithmetic mean: 1.05
Product of the values: 1.1491
Geometric over arithmetic: 0.9975

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

Geometric mean = (x1 x x2 x ... x xn)^(1/n)

x1 ... xn: The values being averaged, all positive
n: How many values there are
product: The result of multiplying all the values

How to check the result by hand

1
Convert to growth factors
Add one to each rate. Returns of 8 percent, 12 percent and minus 5 percent become 1.08, 1.12 and 0.95, all positive so the root is defined.
2
Multiply the factors
1.08 times 1.12 is 1.2096, and 1.2096 times 0.95 is 1.14912. This is the total growth over the three periods.
3
Take the cube root
Raise 1.14912 to the power of one third. The cube root is 1.047422, the factor that repeated three times gives the same total.
4
Subtract one for the rate
1.047422 minus 1 is 0.047422, so the average growth rate is 4.7422 percent per period. The arithmetic mean would have been 5 percent.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Geometric Mean page.