Geometric Mean Calculator

This calculator finds the geometric mean of a set of positive numbers, the correct average to use for ratios, rates of change and anything that grows by multiplication. Most people reach for the ordinary, arithmetic mean by adding the values and dividing, but that gives the wrong answer for quantities that compound. The geometric mean instead multiplies all the values together and takes the root according to how many there are, which properly captures multiplicative growth. It is the right tool for averaging investment returns over several years, population or revenue growth rates, ratios and index numbers, and any situation where each value builds on the last. A classic example: if an investment grows 10 percent one year and falls 10 percent the next, the arithmetic mean suggests no change, but the geometric mean correctly shows a small loss, because the percentages compound rather than add. This tool makes it easy. You paste or type your numbers, which must be positive, and the calculator returns the geometric mean, along with the arithmetic mean for comparison and the count of values. The geometric mean is always less than or equal to the arithmetic mean, and the gap between them grows as the numbers become more spread out. The results update as you type. Use it to find an average growth rate, to average ratios correctly, or for statistics work where the geometric mean is required. When averaging growth, enter each period as a multiplier, so 5 percent growth is 1.05, and the geometric mean of those multipliers gives the average growth factor per period. The calculation uses logarithms internally to stay accurate for long lists.

Geometric mean = the nth root of the product of n values. All values must be positive. It is always less than or equal to the arithmetic mean.