Geometric Mean Calculator
Geometric, harmonic and RMS means, and average growth rate.
About this tool
Paste a list of numbers to get all four means, or switch to percentage changes (such as yearly returns) to get the compound average growth rate, the simple average and the total change.
Choosing the right average
The geometric mean multiplies n numbers and takes the nth root: for 2 and 8 it's โ16 = 4, compared with an arithmetic mean of 5. It's the correct average for quantities that multiply together: investment returns, population growth, inflation, price indices and ratios. Gaining 10% and then losing 10% leaves you with 1.1 ร 0.9 = 0.99 of what you started with, a 1% loss, so the true average is โ0.5% per period, not the 0% that averaging the percentages suggests. The harmonic mean, n รท ฮฃ(1/x), is right for rates over equal amounts: driving 60 km at 30 km/h and 60 km at 60 km/h averages 40 km/h, not 45. The quadratic mean (root mean square) is used for AC voltages and measurement errors. For positive numbers they always obey harmonic โค geometric โค arithmetic โค quadratic, equal only when all values are the same. Honest limits: geometric and harmonic means need positive values; a loss of 100% or more makes the growth rate undefined. Not financial advice. The average calculator and the weighted average calculator are related.
Frequently asked questions
How do I calculate the geometric mean?
Multiply the n numbers together and take the nth root, or average their logarithms and exponentiate.
When should I use the geometric mean?
For growth rates, investment returns, ratios and anything that compounds or multiplies.
What is the average return of +10% and โ10%?
About โ0.5% per period: 1.1 ร 0.9 = 0.99, and โ0.99 โ 0.995.
What is the harmonic mean used for?
Averaging rates over equal amounts, such as speeds over equal distances.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.