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Standard deviation calculator

Compute the standard deviation, variance and mean of a list.

Related tools

All Statistics & probability tools →
Population standard deviation calculatorThe population standard deviation σ of a data set — how far the values spread from their mean when your data covers the whole group, dividing by N (not n−1). Enter the numbers and it returns σ, the variance σ², the mean and the count.Sample Standard Deviation CalculatorCompute the sample standard deviation (n−1), variance, mean and detect outliers.Mean absolute deviation (MAD) calculatorCompute the mean absolute deviation of a data set around its mean.Standard error calculatorCompute the standard error of the mean from a list of numbers.Median absolute deviation calculatorA robust measure of spread: the median of the absolute distances from the median. It shrugs off outliers where the standard deviation would blow up. Multiply by 1.4826 to estimate the standard deviation of clean data.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Quartile Deviation CalculatorCompute the semi-interquartile range and its coefficient, a spread measure that the extreme values cannot distort.Coefficient of variation calculatorCompute the coefficient of variation (CV) of a dataset — its relative variability.

The Standard deviation calculator turns Numbers into Std. deviation (σ), Variance, Mean, instantly and for free. For instance, with Numbers = 12, 18, 20, 25, 30 it returns Std. deviation (σ) = 6.132, Variance = 37.6 and Mean = 21.

How to use it

  1. Enter your values: Numbers.
  2. Read the result instantly: Std. deviation (σ), Variance, Mean.

Frequently asked questions

How does the Standard deviation calculator work?

It takes Numbers and derives Std. deviation (σ), Variance and Mean from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

A single value: Numbers. Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Numbers = 12, 18, 20, 25, 30, the calculator returns Std. deviation (σ) = 6.132, Variance = 37.6 and Mean = 21. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using Numbers = 12, 19, 22, 29, 36 instead, Std. deviation (σ) goes from 6.132 to 8.261 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Numbers = 12, 18, 20, Std. deviation (σ) comes out at 3.399. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

What is the difference between the Standard deviation calculator and the Population standard deviation calculator?

This one returns Std. deviation (σ) and Variance; the Population standard deviation calculator returns Population σ and Variance σ². That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Sample Standard Deviation Calculator is the closest one after this: Compute the sample standard deviation (n−1), variance, mean and detect outliers.

What else is worth having open alongside it?

Mean absolute deviation (MAD) calculator and Standard error calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.ExplainerThe Same Three Temperatures Give Three Different Coefficients of VariationFor 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.ExplainerForty Out and Sixty Back Averages Forty-EightThe harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.ExplainerIf the Variance Is Not the Mean, It Is Not PoissonWith an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.ExplainerTurn 30 Into 300 and the Interquartile Range Does Not MoveFor 2, 5, 7, 8, 10, 13, 18, 21, 25, 30 the range is 28, the standard deviation 9.24 and the IQR 13. Replace the last value with 300 and only the IQR survives unchanged.