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Standard Error of Mean Calculator

Calculate the standard error of a sample mean with a finite population correction.

About Standard Error of Mean Calculator

When a sample covers a substantial fraction of a finite population, the standard error is smaller than the infinite-population formula suggests. The correction becomes material above about a 5 per cent sampling fraction. Sampling an entire population gives zero standard error, which the correction factor produces correctly and the uncorrected formula does not.

Formula

Standard Error of Mean

SE = (s ÷ √n) × √((N − n) ÷ (N − 1))

finite population correction
Reduces standard error when the sample is a large share of the population

Worked example

With the default values below, Standard Error of Mean Calculator returns Standard Error of the Mean of 1.608473. Change any input above and every figure here is recalculated in your browser.

Inputs used

Standard deviationminimum 0
20
Sample sizeminimum 1
150
Population sizeminimum 1
5,000

Results

Standard Error of the Mean
1.608473
Standard Error Without the Correction
1.632993
Finite Population Correction Factor
0.984984
Sampling Fraction
3.000%
Width of a 95 Per Cent Interval
6.30510

Step by step

  1. 1Values used
  2. 2Standard Error of Mean
  3. 3Standard Error of the Mean= 1.608473
  4. 4Standard Error Without the Correction= 1.632993
  5. 5Finite Population Correction Factor= 0.984984
  6. 6Sampling Fraction= 3.000
  7. 7Width of a 95 Per Cent Interval= 6.30510

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Standard Error of Mean calculated?

SE = (s ÷ √n) × √((N − n) ÷ (N − 1)) When a sample covers a substantial fraction of a finite population, the standard error is smaller than the infinite-population formula suggests. The correction becomes material above about a 5 per cent sampling fraction.

Why does Standard Error of Mean matter?

Sampling an entire population gives zero standard error, which the correction factor produces correctly and the uncorrected formula does not.

What values do I need to enter?

This calculator takes 3 inputs: Standard deviation, Sample size, Population size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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