General

Standard Deviation Calculator

Paste numbers and instantly get mean, median, mode, range, sample SD, population SD and variance.

Numbers

Separate by commas, spaces, semicolons or new lines. Decimals OK.

Statistics

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Paste at least two numbers.

What this calculator does

Paste a list of numbers and get the full set of one-variable descriptive statistics: count, sum, mean, median, mode, min, max, range, both variances and both standard deviations. The calculator handles commas, spaces, semicolons and new lines as separators so you can paste straight from a spreadsheet column.

How to use it

Click the textarea and paste your data. Anything that is not a number is ignored, so you can paste a column with headers and the tool will skip the headers automatically. The result panel updates as you type.

The formulas

Mean: μ = Σx / n. Variance, sample: s² = Σ(x − μ)² / (n − 1). Variance, population: σ² = Σ(x − μ)² / n. Standard deviation: square root of the variance. Use sample SD when your numbers are a sample drawn from a larger group, and population SD when they are the whole group.

Sample vs population

Metric	Sample	Population
Variance (sample)	Σ(x − x̄)² ÷ (n − 1)	Σ(x − μ)² ÷ N
SD (sample)	√[ Σ(x − x̄)² ÷ (n − 1) ]	√[ Σ(x − μ)² ÷ N ]

Frequently asked questions

Sample or population?

Use sample SD when the data points are a subset drawn from a larger population (test scores from one class out of a school). Use population SD when you have every member of the population (every employee in a five-person team).

Why divide by n−1 for the sample?

Because the sample mean is itself estimated from the data, you have already used up one degree of freedom. Dividing by n−1 (Bessel's correction) gives an unbiased estimator of the true population variance.

How is the mode handled?

If a value appears more often than any other, it is the mode. Multimodal data lists every value tied for the highest frequency. If every value is unique, the mode is reported as "no mode".

Does it accept negative numbers and decimals?

Yes. Negative numbers, decimals and scientific notation (1.2e3) are all accepted. Thousand separators (1,234) are accepted as long as you also use a different separator between numbers, like spaces or new lines.

What about outliers?

Standard deviation is sensitive to outliers because it squares the distance from the mean. If your data has extreme values, look at the median and the inter-quartile range as well. Median is much more robust.

How many numbers can I paste?

There is no hard limit. Tens of thousands of values are fine in a modern browser. The calculation is single-pass O(n) so it stays fast.

Standard Deviation Calculator