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Standard Deviation Calculator

Work out the standard deviation, variance, mean, median, mode and range of any set of numbers.

  • Free
  • No sign-up
  • Runs in your browser

Separate values with commas, spaces or new lines. Decimals and negative numbers are fine.

Data set

Choose Sample when your numbers are a subset of a larger group (the usual case) and Population when they are the whole group.

–Standard deviation –Variance –Mean (average) –Count (n) –Sum of numbers –Median –Mode (most frequent) –Range (max − min) –Minimum –Maximum –Standard error of the mean –Coefficient of variation

Results update as you type

The sample standard deviation divides by n − 1 (Bessel's correction); the population standard deviation divides by N. Results are rounded to 4 decimal places. Everything is calculated in your browser.

Need percentages or percentage change? Use the Percentage Calculator.

How to use Standard Deviation Calculator

  1. Enter your numbersType or paste your data set, separated by commas, spaces or new lines. Decimals and negative numbers work too.
  2. Choose sample or populationPick Sample when the numbers are part of a bigger group (the default, divides by n − 1) or Population when they are the whole group (divides by N).
  3. Read the statisticsThe standard deviation, variance, mean, median, mode, range, count and sum update as you type, with the working shown. Copy the results to paste them into your homework or report.

Common uses

  • Check statistics homework and exam practice step by step
  • Measure how spread out test scores, sales or measurements are
  • Compare the variability of two data sets before a report

Frequently asked questions

How do I use Standard Deviation Calculator?

1. Enter your numbers: Type or paste your data set, separated by commas, spaces or new lines. Decimals and negative numbers work too. 2. Choose sample or population: Pick Sample when the numbers are part of a bigger group (the default, divides by n − 1) or Population when they are the whole group (divides by N). 3. Read the statistics: The standard deviation, variance, mean, median, mode, range, count and sum update as you type, with the working shown. Copy the results to paste them into your homework or report.

How do you calculate standard deviation?

Find the mean of the numbers, subtract the mean from each number and square the result, add up those squares, divide by n − 1 for a sample (or N for a population) to get the variance, and take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the population standard deviation is 2.

What is the difference between sample and population standard deviation?

The population formula divides by N and describes a complete group. The sample formula divides by n − 1 to correct for the fact that a sample tends to underestimate spread. If your numbers are a subset of a larger set, which is the usual case, use the sample option.

Does this work as a variance calculator?

Yes. The variance is shown next to the standard deviation, for both the sample and the population formula, together with the sum of squared differences used to get it.

Does it also give the mean, median and mode?

Yes. You get the mean (average), median, mode, range, minimum, maximum, count and sum of your data set, so it works as a mean, median and mode calculator too.

What does a high or low standard deviation mean?

A low standard deviation means the values sit close to the mean; a high one means they are spread out. Compare it with the mean, or use the coefficient of variation shown here, to judge whether the spread is large for your data.

Is my data sent anywhere?

No. Every calculation runs in your browser and your numbers are never sent to GigaTools.