Geometric mean

Type two numbers. The calculator computes the square root of the product, √(a·b). 4 and 9 give 6. 2 and 8 give 4. 1 and 1 give 1.

Only two numbers. √(a Γ— b). A negative product yields a blank value and a blank. Zero with a positive gives 0.

Input data

Results

Enter data and click Calculate.

How it works

The geometric mean of two numbers is the square root of their product. 4 and 9 give √36 = 6. 2 and 8 give √16 = 4. 1 and 1 give 1. The calculator takes the square root of a times b and for an integer result shows a string with no six zeros.

This is not the arithmetic mean. 4 and 9 have arithmetic mean 6.5, and the geometric mean is 6. The geometric mean is not larger than the arithmetic mean when both numbers are positive.

The fields are a and b. Order does not change the product. A negative product, for example βˆ’4 and 9, has no real square root. The engine then leaves a blank, not a zero.

The arithmetic mean of a list is on the neighbouring page. Weighted average on the neighbouring card does not average two weights, it only returns the first field. Here you really get a square root.

The header units switch does not multiply anything. 4 and 9 stay 6 whatever the label says. A fraction would get six decimal places.

4 and 9 give 6. 2 and 8 give 4. 1 and 1 give 1. A negative product leaves a blank.

Formula

√(a Γ— b)

How to use

  1. Type two numbers, for example 4 and 9.
  2. Click Calculate. The geometric mean comes out 6.
  3. 2 and 8 give 4. 1 and 1 give 1.
  4. A negative product leaves a blank, because the root is not real.
  5. A sum over n lives on the arithmetic mean calculator.

4 and 9 give 6

The geometric mean is the square root of the product. 4 and 9 give 6. 2 and 8 give 4. A negative product leaves a blank.

geometric
The square root of the product of two numbers. 4 and 9 give 6.
product
a times b before the root. 1 and 1 give product 1 and result 1.
root
√(a·b). 2 and 8 give 4. A negative product has no real square root.

Examples

Example 1

  • 4
  • 9

6

What is the geometric mean of 4 and 9? 6. Square root of 36.

Example 2

  • 2
  • 8

4

What is the geometric mean of 2 and 8? 4. Square root of 16.

Example 3

  • 1
  • 1

1

What is the geometric mean of 1 and 1? 1. Square root of 1.

Related calculators

Arithmetic mean calculator

Arithmetic mean calculator: a list of numbers in one field, with spaces or commas.

Use calculator β†’

Weighted average

Weighted average: a value and a weight.

Use calculator β†’

All mathematics calculators

Common questions

What is the geometric mean of 4 and 9?

6. Square root of 36. Not the arithmetic 6.5.

What do 2 and 8 give?

4. Square root of 16.

What do 1 and 1 give?

1. Product 1, root 1.

What if the product is negative?

The square root of a negative product leaves a blank value. The result field stays blank, not zero.

Do 0 and 9 give 0?

Yes. Product 0, square root 0.

Does the order of a and b change the result?

No. 4 and 9 and 9 and 4 both give 6.

How is this different from the arithmetic mean?

Arithmetic divides the sum by 2. 4 and 9 give 6.5, here 6.

Does a fraction get six decimals?

Yes, when the root is not an integer. 6 stays the string 6.

Does a comma in 4.5 work?

Yes. 4.5 and 4,5 are the same number.

Where is the mean of a list?

On the arithmetic mean calculator. Here only two numbers and a square root.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.