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Standard Deviation Calculator

Compute mean, variance, and standard deviation from a data set.

Separate numbers with commas, spaces, or new lines.
Sample uses n โˆ’ 1. Population uses n.
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Variance โ€”
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Use sample standard deviation when your data is a sample from a larger population.

How it works

Understand data spread

This Standard Deviation Calculator summarizes a numerical data set by calculating the mean, variance, standard deviation, minimum, maximum, range, count, and sum.

Paste your values into the data box using commas, spaces, tabs, or new lines. You can choose sample standard deviation for subset data or population standard deviation when the data includes every value in the group.

Enter your data set

Paste numbers from a spreadsheet, assignment, survey, experiment, or manual list. The calculator automatically separates values by commas, spaces, semicolons, or line breaks and ignores blank spacing.

Find the average

The mean is the central value of the data. Standard deviation is calculated by comparing each data point to this mean, so the average is the starting point for understanding spread.

Measure variation

Standard deviation shows how much values typically differ from the mean. A small standard deviation means values are clustered closely, while a large standard deviation means values are more spread out.

Sample vs population

Use population mode when your list includes every value you care about. Use sample mode when your list is only a sample from a larger group, such as survey responses or experimental observations.

Frequently asked questions

Standard deviation is a measure of how spread out numbers are around the mean. If most values are close to the mean, the standard deviation is small. If values are widely scattered, the standard deviation is larger.
Population standard deviation divides by n because the data set represents the whole group. Sample standard deviation divides by n โˆ’ 1 because it estimates variation in a larger population from a smaller sample.
Use sample standard deviation when your data is only part of a bigger group. Examples include survey responses, a sample of test scores, a small group of measurements, or experimental results that represent a wider population.
Variance is the average squared distance from the mean. It is useful mathematically, but because it is in squared units, standard deviation is often easier to interpret because it returns the spread to the original scale of the data.
Yes. Decimal values and negative values are supported. Make sure the input contains only valid numbers and separators. Extra labels, currency signs, or written units can prevent values from being read correctly.
Two data sets can share the same average while having very different spreads. For example, 9, 10, 11 and 1, 10, 19 both average to 10, but the second set is much more spread out, so it has a higher standard deviation.