Calculate the standard error of a sample mean with a finite population correction.
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.
Standard Error of Mean
SE = (s ÷ √n) × √((N − n) ÷ (N − 1))
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.
Sampling an entire population gives zero standard error, which the correction factor produces correctly and the uncorrected formula does not.
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.