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Standard error calculator

Compute the standard error of the mean from a list of numbers.

Related tools

All Statistics & probability tools →
Standard deviation calculatorCompute the standard deviation, variance and mean of a list.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.Percentage error calculatorCompute the percentage error between a measured and a true value.Coefficient of variation calculatorCompute the coefficient of variation (CV) of a dataset — its relative variability.Confidence interval calculatorCompute a confidence interval for a mean from its standard deviation and sample size.Correlation coefficient calculatorCompute Pearson's correlation coefficient between two lists of numbers.Expected value calculatorCompute the expected value from a list of outcomes and their probabilities.

The Standard error calculator turns Numbers (comma-separated) into Standard error, Standard deviation, instantly and for free. For instance, with Numbers (comma-separated) = 10, 12, 15, 11, 13, 14 it returns Standard error = 0.764 and Standard deviation = 1.871.

How to use it

  1. Enter your values: Numbers (comma-separated).
  2. Read the result instantly: Standard error, Standard deviation.

Frequently asked questions

What does the Standard error calculator actually compute?

It takes Numbers (comma-separated) and derives Standard error and Standard deviation from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

A single value: Numbers (comma-separated). Nothing else is required — no account, no file upload.

Can you show a worked example?

With Numbers (comma-separated) = 10, 12, 15, 11, 13, 14, the calculator returns Standard error = 0.764 and Standard deviation = 1.871. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Numbers (comma-separated) = 10, 13, 17, 13, 16, 18 instead, Standard error goes from 0.764 to 1.232 — 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 (comma-separated) = 10, 12, 15, Standard error comes out at 1.453. 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 error calculator and the Standard deviation calculator?

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

Is there a tool for the next step?

Population standard deviation calculator is the closest one after this: The 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.

What else is worth having open alongside it?

Sample Standard Deviation Calculator and Percentage error calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
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.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.ExplainerAn r of 0.85 That Proves NothingFive points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.ExplainerQuadruple the Sample to Halve the IntervalA mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.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.ExplainerA Country of 68 Million Needs Fifteen More People Than a Town of 10,000The population barely enters the sample size formula. What does enter it is the margin of error, and halving that margin quadruples the survey — from 385 people to 1,537.