Standard Error Calculator Formula

Understand the math behind the standard error calculator. Each variable explained with a worked example.

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Formulas Used

Standard Error

se = sigma / sqrt(n)

Variance of the Mean

variance_of_mean = pow(sigma, 2) / n

Relative SE (as % of SD)

relative_se = (1 / sqrt(n)) * 100

Variables

VariableDescriptionDefault
sigmaStandard Deviation15
nSample Size25

How It Works

How to Calculate the Standard Error

Formula

SE = sigma / sqrt(n)

The standard error of the mean measures the precision of the sample mean as an estimator of the population mean. It is the standard deviation of the sampling distribution of the mean. As sample size increases, SE decreases, making estimates more precise.

Worked Example

Population SD = 15, sample size = 25. What is the standard error?

sigma = 15n = 25
  1. 01SE = sigma / sqrt(n)
  2. 02SE = 15 / sqrt(25)
  3. 03SE = 15 / 5 = 3
  4. 04Variance of mean = 15^2 / 25 = 225 / 25 = 9

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