Harmonic Mean of N Numbers Calculator

✖Total Numbers is the total count of numbers in the set of numbers of which mean value is to be calculated.ⓘ Total Numbers [n]			+10% -10%
✖Harmonic Sum of Numbers is the sum of reciprocals of the numbers in the set of numbers of which harmonic mean value is to be calculated.ⓘ Harmonic Sum of Numbers [S_Harmonic]			+10% -10%

✖Harmonic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values.ⓘ Harmonic Mean of N Numbers [HM]

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Formula

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Harmonic Mean of N Numbers

Formula

`"HM" = "n"/"S"_{"Harmonic"}`

Example

`"125"="5"/"0.04"`

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Harmonic Mean of N Numbers Solution

STEP 0: Pre-Calculation Summary

Formula Used

Harmonic Mean = Total Numbers/Harmonic Sum of Numbers
HM = n/S_Harmonic
This formula uses 3 Variables

Variables Used

Harmonic Mean - Harmonic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values.
Total Numbers - Total Numbers is the total count of numbers in the set of numbers of which mean value is to be calculated.
Harmonic Sum of Numbers - Harmonic Sum of Numbers is the sum of reciprocals of the numbers in the set of numbers of which harmonic mean value is to be calculated.

STEP 1: Convert Input(s) to Base Unit

Total Numbers: 5 --> No Conversion Required
Harmonic Sum of Numbers: 0.04 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

HM = n/S_Harmonic --> 5/0.04

Evaluating ... ...

HM = 125

STEP 3: Convert Result to Output's Unit

125 --> No Conversion Required

FINAL ANSWER

125 <-- Harmonic Mean

(Calculation completed in 00.020 seconds)

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Credits

Created by Shivam Dixit

BSS Education Centre Kanpur (BSS College), Kanpur

Shivam Dixit has created this Calculator and 10+ more calculators!

Verified by CH V S M SRIRAM

GITAM SCHOOL OF SCIENCE (GITAM), HYDERABAD

CH V S M SRIRAM has verified this Calculator and 1 more calculators!

< 6 Harmonic Mean Calculators

Harmonic Mean of Four Numbers

Go Harmonic Mean = 4/(1/First Number+1/Second Number+1/Third Number+1/Fourth Number)

Harmonic Mean of Two Numbers

Go Harmonic Mean = (2*First Number*Second Number)/(First Number+Second Number)

Harmonic Mean of Three Numbers

Go Harmonic Mean = 3/(1/First Number+1/Second Number+1/Third Number)

Harmonic Mean of N Numbers

Go Harmonic Mean = Total Numbers/Harmonic Sum of Numbers

Harmonic Mean given Arithmetic and Geometric Means

Go Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean

Harmonic Mean of Reciprocal of First N Natural Numbers

Go Harmonic Mean = 2/(Total Numbers+1)

Harmonic Mean of N Numbers Formula

Harmonic Mean = Total Numbers/Harmonic Sum of Numbers
HM = n/S_Harmonic

What is Harmonic Mean?

Harmonic Mean is basically the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values. It is calculated by dividing the total count of numbers by the harmonic sum or the sum of reciprocals of the numbers. In many situations involving rates and ratios, the Harmonic Mean provides the correct average.

How to Calculate Harmonic Mean of N Numbers?

Harmonic Mean of N Numbers calculator uses Harmonic Mean = Total Numbers/Harmonic Sum of Numbers to calculate the Harmonic Mean, Harmonic Mean of N Numbers formula is defined as the average value or mean which signifies the central tendency of the set of n numbers by finding the reciprocal of their values and calculated using the harmonic sum of them. Harmonic Mean is denoted by HM symbol.

How to calculate Harmonic Mean of N Numbers using this online calculator? To use this online calculator for Harmonic Mean of N Numbers, enter Total Numbers (n) & Harmonic Sum of Numbers (S_Harmonic) and hit the calculate button. Here is how the Harmonic Mean of N Numbers calculation can be explained with given input values -> 50 = 5/0.04.

FAQ

What is Harmonic Mean of N Numbers?

Harmonic Mean of N Numbers formula is defined as the average value or mean which signifies the central tendency of the set of n numbers by finding the reciprocal of their values and calculated using the harmonic sum of them and is represented as HM = n/S_Harmonic or Harmonic Mean = Total Numbers/Harmonic Sum of Numbers. Total Numbers is the total count of numbers in the set of numbers of which mean value is to be calculated & Harmonic Sum of Numbers is the sum of reciprocals of the numbers in the set of numbers of which harmonic mean value is to be calculated.

How to calculate Harmonic Mean of N Numbers?

Harmonic Mean of N Numbers formula is defined as the average value or mean which signifies the central tendency of the set of n numbers by finding the reciprocal of their values and calculated using the harmonic sum of them is calculated using Harmonic Mean = Total Numbers/Harmonic Sum of Numbers. To calculate Harmonic Mean of N Numbers, you need Total Numbers (n) & Harmonic Sum of Numbers (S_Harmonic). With our tool, you need to enter the respective value for Total Numbers & Harmonic Sum of Numbers and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Harmonic Mean?

In this formula, Harmonic Mean uses Total Numbers & Harmonic Sum of Numbers. We can use 5 other way(s) to calculate the same, which is/are as follows -

Harmonic Mean = (2*First Number*Second Number)/(First Number+Second Number)
Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean
Harmonic Mean = 3/(1/First Number+1/Second Number+1/Third Number)
Harmonic Mean = 4/(1/First Number+1/Second Number+1/Third Number+1/Fourth Number)
Harmonic Mean = 2/(Total Numbers+1)

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