Standard Deviation Calculator

Calculate standard deviation, variance, and statistical measures

About Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is from their average (mean). A low standard deviation means values cluster tightly around the mean; a high standard deviation means they're spread over a wider range. It's a core statistic used in finance, quality control, grading, and scientific research.

Formula

Population SD = √(Σ(x − mean)² / N); Sample SD = √(Σ(x − mean)² / (N − 1))

How It Works

Enter your list of numbers, separated by commas or line breaks
The calculator finds the mean (average) of all values
It then finds each value's squared difference from the mean
These squared differences are averaged (population) or divided by N−1 (sample) to get the variance
The square root of the variance gives the standard deviation

Tips

Use sample standard deviation (N−1) when your data is a sample of a larger population; use population standard deviation (N) only when you have every value in the population
Standard deviation is always in the same units as your original data, unlike variance
A standard deviation of 0 means all values are identical

Frequently Asked Questions

What's the difference between population and sample standard deviation?

Population SD divides by N and is used when your dataset IS the entire population; sample SD divides by N−1 (Bessel's correction) and is used when your data is a sample meant to estimate a larger population's spread — sample SD is slightly larger and is the more common choice in real-world statistics.

What does a high standard deviation mean?

It means values are spread widely from the mean; a low one means they're clustered close to it. Two classes with the same average test score can have very different standard deviations if one class has mostly similar scores and the other has a wide range of high and low scores.

How is standard deviation different from variance?

Variance is the average of squared differences from the mean; standard deviation is its square root, which puts the measure back into the original units, making it easier to interpret.

How do outliers affect standard deviation?

Because differences from the mean are squared, outliers have an outsized effect on standard deviation — a single extreme value can substantially increase it.

What is a 'normal' standard deviation?

There's no universal 'normal' value — it depends entirely on the scale and variability of your specific data. What matters is comparing standard deviations across similar datasets, not against an absolute benchmark.