Case 1
- First value (a)
- 4
- Second value (b)
- 9
6.000000
Open with these valuesGeometric Mean of Two Numbers
6.000000
Result: 6.000000For two values the geometric mean is the square root of their product: √(4 × 9) = 6. This calculator takes exactly two numbers, not a whole list. Use it where values multiply rather than add — growth factors, ratios, index numbers — and note it is never larger than the plain arithmetic mean shown beside it.
Worked examples
Case 2
- First value (a)
- 2
- Second value (b)
- 8
4.000000
Open with these valuesCase 3
- First value (a)
- 0.5
- Second value (b)
- 2
1.000000
Open with these valuesHow it's calculated
G = √(a × b)
- StepEnter two positive numbers; zero and negatives have no geometric mean.
- StepMultiply the two values together.
- StepTake the square root of that product.
- ResultCompare it with the arithmetic mean (a + b) ÷ 2 — it is never larger.
Reference table
| a, b | Arithmetic mean | Geometric mean |
|---|---|---|
| 1, 1 | 1 | 1 |
| 0.5, 2 | 1.25 | 1 |
| 2, 8 | 5 | 4 |
| 3, 12 | 7.5 | 6 |
| 4, 9 | 6.5 | 6 |
| 10, 40 | 25 | 20 |
Questions
How do I calculate the geometric mean of two numbers?
Multiply the two values and take the square root of the product: G = √(a × b). The geometric mean of 4 and 9 is √36 = 6. Both numbers must be positive for the result to exist.
What is the geometric mean?
It is an average found by multiplying the values and taking a root instead of adding and dividing. For two numbers that root is the square root of their product. It is the natural average for ratios, rates and growth factors, where values multiply rather than add.
How does it differ from the arithmetic mean?
The arithmetic mean adds and divides, (a + b) ÷ 2; the geometric mean multiplies and takes the root, √(a × b). For positive numbers the geometric mean is always less than or equal to the arithmetic one, and they are equal only when both values match.
When should I use the geometric mean?
Whenever you average things that compound: investment returns, growth rates, index numbers, percentage changes over time. Averaging a 4× gain and a 9× gain gives 6×, which reflects the compounded effect better than the arithmetic 6.5×.
Does it work for more than two numbers?
The geometric mean itself does — it is the nth root of the product of n values. This calculator is built for exactly two inputs, which is why it uses the square root.
Sources and last check
Information, not professional advice.