Math

Standard Deviation Calculator

Enter a set of numbers to instantly compute mean, count, sample standard deviation, and population standard deviation.

Enter at least 2 numbers to calculate.

Enter values above to see the result.

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Standard Deviation Formula

Sample Std Dev (s)

s = √(Σ(xᵢ − x̄)² ÷ (n − 1))

Use when data is a subset of a larger group.

Population Std Dev (σ)

σ = √(Σ(xᵢ − μ)² ÷ n)

Use when data represents the entire population.

What is standard deviation?

Standard deviation quantifies how much the individual values in a dataset differ from the mean. It is one of the most widely used statistics in data analysis, quality control, finance, and science because it provides a single, interpretable number that summarises the variability in a distribution. A dataset where all values are identical has a standard deviation of zero; the more spread out the values, the higher the standard deviation.

The distinction between sample and population standard deviation is important when working with real-world data. Because a sample underestimates population variability, the sample formula uses n−1 in the denominator (Bessel's correction) to produce an unbiased estimate. For most practical analyses — surveys, A/B tests, quality sampling — the sample formula is the correct choice unless you have collected data from every member of the population.

Frequently asked questions

What is standard deviation?
Standard deviation is a measure of how spread out the values in a dataset are around the mean. A low standard deviation means data points are clustered closely around the average, while a high standard deviation means they are spread across a wider range.
What is the difference between sample and population standard deviation?
Population standard deviation (σ) is used when your dataset contains every member of the group you are analysing. Sample standard deviation (s) is used when your dataset is a subset of a larger population. Sample standard deviation divides by n−1 instead of n to correct for the bias introduced by working with a sample.
When should I use sample vs population standard deviation?
Use population standard deviation when you have data for every individual in the group, for example the exam scores of every student in a single class. Use sample standard deviation when your data is drawn from a larger group, for example survey responses from 200 people representing a city of millions.
How do I enter data into this calculator?
Type or paste your numbers separated by commas, spaces, or semicolons. For example: 10, 20, 30, 40, 50. The calculator accepts any mix of separators and will automatically extract the valid numbers from your input.
Why do I need at least two values?
Standard deviation measures variation between values, which requires at least two data points. With only one value there is no spread to measure, so the calculator requires a minimum of two valid numbers before computing results.
What does variance tell me compared to standard deviation?
Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance and is expressed in the same units as your original data, making it easier to interpret. Both measure spread, but standard deviation is more commonly used for practical data analysis and reporting.

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