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How do you calculate the margin of error in a statistical sampling scheme?

Previously we have discussed how to calculate sample size for a survey. How do you calculate the margin of error given the sample size?
The Margin of Error (MOE) can be calculated using equation 1.

Equation 1. MOE = Z x √p x (1 - p) / √n

n: the sample size
Z: is the Z-score and is derived from the confidence limit. This has been explained previously.
p: is the sample proportion. In this equation it is represented as a decimal.
This equation requires the addition of a correction factor to allow for finite-size when working with small populations. Most student projects will have to work using this finite correction factor. The modified equation (equation 2) is shown below.

Equation 2. MOE= Z x √p x (1 - p) / √(N - 1) x n / (N - n)

Note the only new variable in equation 2 is N which is the size of sample population e.g. the number of employees at a cheese processing company.

The Z-score for commonly used confidence levels is given in Table 1.

Table1. The Z-score for commonly used confidence levels

Confidence Level (%)








The calculator below has been programmed to determine the MOE using a finite population e.g. your sub sample the number of people in a school, town, football club) of the much larger population of e.g. a country, province. Note the number of samples required has been rounded up to the next highest number.


Sampling- Margin of Error calculator

To use select confidence limit and add your values to the fields below.

Select confidence level
Sample proportion (%)
Sample size


Recommended further reading

Alreck, P.L. and  Settle, R.B. (2003).The Survey Research Handbook (paperback). 3rd edition. New York: McGraw-Hill  Professional.

Daniel WW (1999). Biostatistics: A Foundation for Analysis in the Health Sciences. 7th edition. New York: John Wiley & Sons.

How to cite this article

Mullan, W.M.A. (2021) [On-line] Available from: Accessed: