Geometric Mean Calculator
Enter two positive values to get the geometric mean — the square root of their product — alongside the arithmetic mean, so you can see why one average suits ratios and growth while the other suits plain totals.
Two averages at once
Enter both values and the calculator returns the geometric mean √(a · b) and the arithmetic mean (a + b) / 2 together, so you can compare them.
Positive values only
The geometric mean multiplies the inputs and takes a root, so both numbers must be greater than zero for the result to be a real number.
What is the geometric mean?
The average for things that multiply
The geometric mean calculator turns two positive numbers into the average you should reach for whenever values multiply rather than add. Instead of summing the inputs, the geometric mean multiplies them and takes the root — for two values that is simply the square root of their product. This makes it the natural average for ratios, rates, index numbers, and growth factors, where compounding matters. Average a 4× gain and a 9× gain arithmetically and you get 6.5×, but the geometric mean of 6× reflects the true combined effect of multiplying those factors together.
Enter two positive values to get the geometric mean and the arithmetic mean instantly, and see at a glance how the two averages differ.
The geometric mean of two values is the square root of their product, while the arithmetic mean is half their sum.
G = √(a × b)Worked example: take the values 4 and 9. Multiply them to get 4 × 9 = 36, then take the square root, √36 = 6 — that is the geometric mean. The arithmetic mean is (4 + 9) ÷ 2 = 6.5. The geometric mean comes out lower, which is always the case for two distinct positive numbers: the geometric mean is less than or equal to the arithmetic mean, with equality only when both values are identical.
The formula is exact, but a couple of practical points are worth keeping in mind.
Positive values and the right average
This calculator works with two strictly positive values: a zero collapses the product to zero, and a negative number makes the square root of the product undefined for real results. Reach for the geometric mean when your numbers are ratios, rates, or growth factors that multiply; for plain quantities that add up — such as test scores or weights — the arithmetic mean is the right choice.