Standard Deviation Calculator
Compute Population and Sample Standard Deviation from any dataset.
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Quick Tip
Paste your values, separated by commas, spaces or new lines. At least two are needed.
About This Tool
Why use Standard Deviation?
Standard deviation measures how far the values in a dataset sit from their mean. This calculator returns both versions — sample (s, dividing by n − 1) and population (σ, dividing by n) — along with the matching variances, the mean and the count.
Which one you need depends on your data. If your numbers are every member of the group you care about, use the population figure. If they are a sample drawn from a bigger group and you want to estimate that group's spread, use the sample figure: dividing by n − 1 (Bessel's correction) compensates for the fact that a sample tends to look slightly tighter than the population it came from.
Key Benefits
Sample and population in one view
Both s and σ are shown, so you do not have to remember which divisor the question expects.
Variance included
The squared measures s² and σ² are given alongside, ready for ANOVA, z-scores and other formulas.
Mean and count shown
Seeing the mean and how many values were read makes it easy to confirm the input was parsed as intended.
How to use Standard Deviation
- 1
Paste your values, separated by commas, spaces or new lines. At least two are needed.
- 2
Choose the figure that matches your data: sample (s) for a subset, population (σ) for the complete set.
- 3
Read the variance if a formula you are using needs the squared value.
- 4
Compare the standard deviation with the mean to judge whether the spread is large relative to typical values.
Best use cases
Answer statistics homework that asks for sample or population standard deviation.
Measure how consistent test scores, delivery times or measurements are.
Check the volatility of a series of returns.
Get the spread needed for a confidence interval or z-score.
Standard Deviation FAQs
What is the difference between sample and population standard deviation?
Population standard deviation divides the squared differences by n, and is used when your data covers the entire group. Sample standard deviation divides by n − 1, which makes it a better estimate of a larger population's spread. The sample figure is always slightly larger.
How is standard deviation calculated?
Find the mean, subtract it from each value and square the differences, average those squares (that is the variance), then take the square root. The square root brings the answer back to the original units.
What counts as a high standard deviation?
It depends on the scale. Compare it with the mean: a standard deviation of 5 is small next to a mean of 500 and very large next to a mean of 8. That ratio is the coefficient of variation.
Why is variance squared?
Differences from the mean are squared so that positive and negative gaps do not cancel out. The result is in squared units, which is why the square root is taken to get a standard deviation you can read in the original units.
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