Standard error calculator

Estimate uncertainty in a sample mean.

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Sample standard deviation

Sample size

Answer

…

Estimated standard error of the mean = sample standard deviation ÷ square root of sample size.

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Step-by-step calculation

Inputs are substituted below. Each line evaluates the next operation; intermediate values are displayed to 12 significant digits while the calculation uses full precision.

Saved scenario

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Formula and assumptions

Assumes independent observations and uses the sample standard deviation. Clustering, survey weights and finite-population adjustments are not included.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Standard error calculator

Estimated standard error of the mean = sample standard deviation ÷ square root of sample size.

Assumes independent observations and uses the sample standard deviation. Clustering, survey weights and finite-population adjustments are not included.

Next: Z score calculator

A worked example

With sample standard deviation = 12, sample size = 36, the standard error of the mean is 2.

Next: Expected value calculator

Before you use the result

Assumes independent observations and uses the sample standard deviation. Clustering, survey weights and finite-population adjustments are not included.

Example results for sample standard deviation

These examples use Sample size: 36. They are reference calculations, not recommended settings.

Sample standard deviation	Standard error of the mean
6	1
12	2
24	4

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ToolOctopus. “Standard error calculator.” Updated 2026-09-26. https://tooloctopus.com/standard-error-calculator.

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