Standard Error of the Mean

All versionsSTDEV

How precise is your sample average? The standard error — standard deviation divided by the square root of n — tells you how much the mean would wobble from sample to sample. Smaller is more reliable.

Quick formula: standard error of B2:B100:

=STDEV(B2:B100) / SQRT(COUNT(B2:B100))

It shrinks as the sample grows — quadrupling n halves the error.

Functions used (tap for the full reference guide):

STDEV SQRT

The example

Precision of a sample mean.

	A	B
1	Measure	Value
2	Std dev	10
3	n	25
4	Std error	2.0

The formula

The formula:

=STDEV(B2:B100) / SQRT(COUNT(B2:B100)) // = 10 / √25 = 2.0

How it works

How it works:

Compute the sample standard deviation with STDEV.
Divide by SQRT(COUNT(range)) — the square root of the sample size.
The result is the standard error of the mean: the typical distance between your sample mean and the true mean.
It drives confidence intervals: mean ± ~2×SE is roughly a 95% interval.

Standard deviation vs standard error: SD describes the spread of the data; SE describes the precision of the mean. Don’t mix them up — error bars on a chart should say which one they show.

Try it: interactive demo

Live demo

Values.

SD · SE

Variations

95% interval

Roughly:

=AVERAGE(rng) ± 1.96*SE

Margin of error

Built-in:

=CONFIDENCE.T(0.05, STDEV(rng), COUNT(rng))

SE of a proportion

Different formula:

=SQRT(p*(1-p)/n)

Pitfalls & errors

SE ≠ SD. Standard error is about the mean’s precision, not the data’s spread.

Use COUNT, not COUNTA. Divide by the count of numbers, or text inflates n.

Assumes a random sample. SE is only meaningful for representative data.

Practice workbook

📊

Download the free Standard Error of the Mean practice workbook

A standard-error sheet with the interval, margin, and proportion variants, plus 4 challenges with answers. No sign-up required.

Frequently asked questions

How do I calculate the standard error of the mean in Excel?

Use =STDEV(range) / SQRT(COUNT(range)). It estimates how much the sample mean would vary from sample to sample.

What's the difference between standard deviation and standard error?

Standard deviation measures the spread of the data; standard error measures the precision of the mean. SE shrinks as the sample grows.

How do I turn SE into a confidence interval?

Roughly, mean ± 1.96×SE is a 95% interval; or use CONFIDENCE.T for the exact margin.

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Function references: STDEV · SQRT