# Geometric Mean Calculator

To calculate the geometric mean enter values in the input box by using our Geometric mean calculator.

**Geometric Mean Formula**

**Geometric Mean = ((X _{1})(X_{2})(X_{3})........(X_{N}))^{1/N}**

## Geometric Mean Calculator

Geometric Mean is a type of mean or average that indicates the central tendency or typical value of a set of given numbers.

Geometric Mean is defined as the nth root of the product of the n units in a data set.

Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. Geometric mean is calculated for sets of positive real numbers. This is calculated by multiplying all the numbers (call the number of numbers n), and taking the nth root of the total.

Geometric Mean is used in the case when finding an average for set of numbers presented as percentages.

The geometric mean is an average that is useful for sets of positive numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean) e.g. rates of growth. The online Geometric Mean Calculator is useful in calculating the geometric mean for the given set of numbers.

__ Example__:

Calculate the geometric mean for the given set of numbers.

25,56,85,71,4,12,3,2,5

* Solution*:

**Apply Formula:**

Geometric Mean = ((X

_{1})(X

_{2})(X

_{3})........(X

_{N}))

^{1/N}

N = 9

1/N = 1/9

1/N = 0.111

Geometric mean = [(25)(56)(85)(71)(4)(12)(3)(2)(5)] 0.111

**Total Numbers: 9**

**Geometric Mean = 13.20001**

**Some examples of Geometric Mean in the following Table.**

Geometric Mean of 4/5 and 2 | 1.4 |

Geometric Mean of 14 and 56 | 35 |

Geometric Mean of 9 and 12 | 10.5 |

Geometric Mean of 7 and 12 | 9.5 |

Geometric Mean of 6 and 24 | 10 |

Geometric Mean of 6 and 16 | 11 |

Geometric Mean of 3 and 7 | 5 |

Geometric Mean of 4 and 7 | 5.5 |

Geometric Mean of 4 and 8 | 6 |

Geometric Mean of 25 and 35 | 30 |

Geometric Mean of 9 and 25 | 17 |

Geometric Mean of 2 and 32 | 17 |

Geometric Mean of 14 and 20 | 17 |

Geometric Mean of 6 and 13 | 9.5 |

Geometric Mean of 9 and 16 | 12.5 |

Geometric Mean of 7 and 11 | 9 |

Geometric Mean of 8 and 12 | 10 |

Geometric Mean of 3 and 12 | 7.5 |

Geometric Mean of 9 and 11 | 10 |

Geometric Mean for 4 and 25 | 14.5 |

Geometric Mean of 6 and 12 | 9 |

Geometric Mean of 25 and 35 | 30 |

Geometric Mean of 20 and 25 | 22.5 |

Geometric Mean of 2 and 8 | 5 |

**References: **

- What Is the Geometric Mean? by investopedia.com
- Geometric Mean -- from mathsisfun.
- Applications of the Geometric Mean. from math.toronto.edu