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Updated 2026 · By ToolFern

Standard Deviation Calculator

Paste any list of numbers to get the mean, variance and both the sample and population standard deviation at once. Everything updates as you type and is worked out

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Count
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Mean
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Sample standard deviation
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Population standard deviation
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Variance (sample)
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Sum

Distribution curve (68/95/99.7 rule)

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Z-score
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Percentile

The curve is drawn from the sample standard deviation shown above and needs at least two numbers. The shaded bands mark one, two and three standard deviations either side of the mean: the classic 68/95/99.7 rule for a normal distribution. The z-score and percentile use a standard error-function approximation of the normal distribution. Real data rarely follows it exactly.

How to use this standard deviation calculator

  1. Enter your numbers, separated by commas, spaces or new lines, in the box above.
  2. The tool ignores any non-numeric text, so you can paste straight from a spreadsheet or document.
  3. Read the count, mean, standard deviation and variance, they recalculate instantly with every keystroke.

Population vs sample standard deviation

Both figures start the same way. First you find the mean (the average) of your numbers. Then you take each value, subtract the mean, and square the result. The variance is the average of those squared differences from the mean, and the standard deviation is the square root of the variance, which puts the answer back into the same units as your original data.

The one difference is what you divide by. Population standard deviation divides the total of the squared differences by N, the full count of values. Sample standard deviation divides by N - 1 instead. That smaller divisor makes the sample figure slightly larger, correcting for the way a sample tends to underestimate the spread of the whole population it was drawn from.

In short: use the sample version when your numbers are a sample of a bigger group (the usual case), and the population version only when your data already covers the entire group you care about.

Note: this tool reports the sample variance (dividing by N - 1) alongside both standard deviations. With a single value the spread is zero, so the sample figures show "-" because N - 1 would be zero.

Frequently asked questions

What does a high standard deviation mean?

It means your values are spread far from the average. A low standard deviation means most values sit close to the mean, so the data is more consistent.

Which result should I report?

If your numbers are a sample taken from a larger group, report the sample standard deviation. If they cover the whole population, use the population figure.

Can I use negative numbers or decimals?

Yes. Decimals, negatives and scientific notation all work, and any text that is not a number is simply skipped.

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