What is Standard Error of the Mean (SEM)?

SEM measures how far the sample mean of the data is likely to be from the true population mean. It is always smaller than the Standard Deviation (SD).

SEM vs Standard Deviation?

SD measures the variability within a single sample (scatter of data). SEM measures the variability of the sample means if you repeated the experiment many times.

How does 'n' affect SEM?

SEM decreases as sample size (n) increases. A larger sample gives a more precise estimate of the population mean. SEM = SD / √n.

Standard Error Calculator

Calculate the Standard Error of the Mean (SEM) from standard deviation and sample size.

Standard Deviation (σ or s)

Sample Size (n)

Sample Mean (x̄) [Optional]

Used to display confidence intervals

Notice that as you increase the sample size (n), the Standard Error decreases. More data = precise mean estimate.

Standard Error (SEM)

0

Precision of the mean estimate

Estimated 95% Confidence Interval

0 — 0

Mean ± 1.96 × SEM

Standard Deviation

Sample Size

100

Documentation

Formulas

Standard Error

95% CI

Frequently Asked Questions

How to Use

About the Standard Error

What it calculates

This standard error solves mathematical and statistical problems using standard formulas. Calculate Standard Error of the Mean (SEM).

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Standard Error.

Explore More

Standard Error Calculator

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Estimated 95% Confidence Interval

Formulas

About the Standard Error

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