# Standard Deviation Calculator

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Standard deviation measures how much variation there is in a set of values.

A low standard deviation means that the values tend to be close to the mean value. A high standard deviation means that the values tend to be further from the mean.

Standard deviation is similar to variance. Standard deviation is the square root of the variance. The standard deviation is measured in the same unit as the data points, which is a convenient property.

This standard deviation calculator can be used to quickly calculate the standard deviation for a population or sample.

## What is the difference between the sample standard deviation and the population standard deviation

The population standard deviation measures the standard deviation of an entire population. The sample standard deviation measures the standard deviation of a sample of a population.

Let's say I wanted to know how satisfied people were with the standard deviation calculator. I run a survey of 100 people that have used the calculator and asked them to rate their experience between 1-10 (e.g. a net promoter score).

The 100 responses are a sample, where the population is "customers that used the standard deviation calculator". In this case, I should use the sample standard deviation.

If I managed to survey every person that has used the standard deviation calculator then I would use the population standard deviation.

If that seems confusing then there is good news. The sample and populations standard deviation formulas are very similar. They give similar outputs when N is above 30 or so, which makes calculating standard deviation simpler.

## Standard Deviation Formulas

You can use the standard deviation formulas if you want to calculate it directly, instead of using the standard deviation calculator.

## Population Standard Deviation Formula

Population standard deviation formula

## Sample Standard Deviation Formula

Sample standard deviation formula