What this calculator does
Sampling error is the natural difference that occurs between a value measured from a sample and the true value in the full population, simply because a sample is a subset rather than the whole. This calculator estimates the standard error and the margin of sampling error for a sample mean at a chosen confidence level.
How the calculation works
The standard error is calculated as the standard deviation divided by the square root of the sample size: SE = SD / sqrt(n). The margin of sampling error multiplies the standard error by a z-critical value that corresponds to your chosen confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%), giving the range within which the true population value is likely to fall.
Larger sample sizes shrink the standard error and therefore the margin of error, which is why bigger, well-designed samples generally produce more reliable estimates. This tool is for general statistics and survey-planning education.