📐 Margin of Error Calculator

What This Calculator Does

Margin of error tells you how much a survey or poll result could differ from the true value in the full population, at a given confidence level. It is commonly reported alongside poll results (for example, “52% ± 3%”).

The Formula

For a sample proportion, margin of error = z × √[p(1−p) / n], where p is the sample proportion (expressed as a decimal), n is the sample size, and z is the critical value for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%). If you provide a finite population size, a finite population correction factor is applied to slightly reduce the margin of error for a large sample relative to a small population.

Choosing Your Inputs

If you are not sure of your sample’s true proportion, 50% is the conservative default because it produces the largest (most cautious) margin of error. Larger sample sizes and lower confidence levels both reduce the margin of error.

Note: This tool is intended for general educational and planning purposes.