Standard Deviation Calculator

Find sample and population standard deviation, variance, mean, range, and count from a list of numbers with this free standard deviation calculator.

Calculate Standard Deviation

Standard deviation = √(variance)
Your result will appear here.

How standard deviation is calculated

Mean:
Sum of values ÷ number of values

Population variance:
Σ(x − μ)² ÷ n

Sample variance:
Σ(x − x̄)² ÷ (n − 1)

Standard deviation:
√variance

Why standard deviation matters

Standard deviation measures how far values typically spread out from the mean. It helps show consistency, variability, and risk in a dataset.

It is commonly used in statistics, finance, business, science, and quality control.

What your result means

Your result shows how tightly grouped or spread out the data is around the mean. A smaller standard deviation means the values stay closer to the average.

A larger standard deviation means the values are more widely spread, which can signal more variability or less consistency.

Standard deviation calculator tips

Frequently asked questions

What is standard deviation?

Standard deviation is a measure of how spread out numbers are from their mean.

What is the difference between variance and standard deviation?

Variance is the average squared distance from the mean, while standard deviation is the square root of variance.

When should I use sample standard deviation?

Use sample standard deviation when the data is a sample from a larger population.

Can I use decimals and negative numbers?

Yes. This calculator works with whole numbers, decimals, and negative values.