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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 →
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.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerWhat Is a Percentile? The 90th Percentile ExplainedA percentile tells you where a value ranks within a group. Learn what the 90th percentile really means and why a percentile is not the same as a percentage.How-toHow to Calculate a Weighted AverageA weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.How-toHow to Calculate Percent Error: The Accuracy Formula for SciencePercent error tells you how close a measurement is to the true value. Learn the formula, work through an example, and see how scientists use it to judge accuracy.ExplainerPercentage Difference vs. Percentage Change vs. Percentage ErrorThree percentages that look alike but answer different questions. Learn the formula for each, when to use it, and why they give different numbers.